This paper addresses the problem of controlling the single-phase grid connected to the photovoltaic system through a full bridge inverter with LCL-filter. The control aims are threefold: (i) imposing the voltage in the output of PV panel to track a reference provided by the MPPT block; (ii) regulating the DC-link voltage to guarantee the power exchange between the source and AC grid; (iii) ensuring a satisfactory power factor correction (PFC). The problem is dealt with using a cascade nonlinear adaptive controller that is developed making use of sliding-mode technique and observers in order to estimate the state variables and grid parameters, by measuring only the grid current, PV voltage, and the DC bus voltage. The control problem addressed by this work involves several difficulties, including the uncertainty of some parameters of the system and the numerous state variables are inaccessible to measurements. The results are confirmed by simulation under MATLAB∖Simulink∖SimPowerSystems, which show that the proposed regulator is robust with respect to climate changes.
The global concern about climate change and the growing energy demand of industrialized countries have necessarily led to exploring other new sources like the renewable energy. The main advantages of this type of renewable energies reside in the reduction of pollution caused by the production of greenhouse gases. Among different types of these energies, the photovoltaic energy has obtained a great attention.
The photovoltaic energy systems are classified according to their use. The two principal classifications are grid-connected systems and stand-alone systems. The first one is connected to the grid through a three-phase or single-phase inverter; this category is used to deliver the power directly to utility grid and must be properly controlled according to power electrical legislations. The second one is used with a battery bank for electrifying remote rural areas.
The power factor correction, the DC output voltage regulation, and the maximization of the power provided by the PV modules are the main control objectives for allowing high power quality to the grid. To meet these requirements, various control methods have been proposed in [
In the literature, a few papers dealt with state-feedback control [
In this work, we seek a control strategy that meets the following three control objectives simultaneously: Perfect power factor correction (PFC): the grid phase currents and its corresponding voltages must be in phase. DC output voltage regulation: this voltage must be tightly regulated to a constant reference value to ensure the power exchange between AC grid and the DC bus. Maximization of the power provided by the PV models.
To achieve the above objectives, a cascaded nonlinear adaptive controller is designed. The latter is constituted by a PV voltage loop and grid current loop. The first one is designed to extract the maximum power from the PV array by regulating the voltage provided by the PV generator. The second one includes the inner loop and aims to regulate the grid current to meet the PFC, and the outer loop is intended to enhance the power exchange, between the source and the grid, by regulating the DC-link voltage. These loops are designed based on sliding-mode technique combined with a Luenberger and extended Kalman filter type. Compared to previous works, the contribution of the present study enjoys several interesting features including the following: Several control objectives are simultaneously considered (MPPT, DC Regulation, and PFC) while only some of these objectives have been tackled in previous works [ The nonlinearity of the controlled system was preserved [ The grid voltage is not accessible to measurement and the internal impedance is assumed to be unknown, unlike previous works which assumed that voltage is available and the grid impedance is null or known [ The present nonlinear adaptive control system does not necessitate many sensors for the measurement of some needed variables unlike previous works [
The paper is structured as follows: in Section
This section describes the modelling of photovoltaic system connected to the grid. The power plant under study is shown in Figure
Photovoltaic system tied to the single-phase grid.
By analyzing the circuit and applying the well-known Kirchhoff laws, the equations describing the dynamics of the system of Figure
The above instantaneous model (
The supply net voltage
State variables and unknown parameters.
Variables and parameters | Definition | Observation |
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Nonaccessible to measurements |
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Nonaccessible to measurements |
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Unknown parameter |
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Unknown parameter |
In this section, an output-feedback nonlinear controller will be synthetized. As represented by the averaging model (
Schematic diagram of nonlinear adaptive controller.
In addition, the observers are designed to estimate the values of unmeasurable states. The first task is dedicated to the design of the observers and the second task is devoted to development of an output-feedback nonlinear controllers.
The purpose of the present subsection is to design the observers, which provide accurate estimates of states variables and use them later to develop an output-feedback controller such that the estimation errors converge to zero. For that, an adaptive observer and Luenberger observer [
The model described by (
Obviously
The design strategy consists in synthesizing separately an observer for each one of subsystems (
The form of system
From (
The gain vector
Introduce the following Lyapunov function candidate:
The system
To study the convergence of the proposed observer (
To analyze the error system (
Under condition (
The PV output voltage
The control objective is to enforce the voltage provided by the PV panel to track the desired signal in order to achieve maximum power point. This regulator consists of two loops: a loop for seeking of the nominal power point, in which we used the IncCond algorithm, and a loop for regulating the voltage
To design a controller for subsystem (
In order to stabilize subsystem (
The dynamics of the surface are given by
The equivalent command
Consider the closed-loop control system, consisting of system (
To guarantee high performance transmission of the power and good functioning of the system, the current and voltage grid should be in phase. Hence, there is a necessity for regulator that enforces the estimate current
Then, (
The convergence properties of the adaptive observer are analyzed based on the following error system dynamics:
The stability results are summarized in the proof which can be found in [
To elaborate the discontinuous control, consider the following Lyapunov function candidate:
Figure
Errors between
In this section, the controller that has been designed in the above section using output nonlinear feedback technique will be tested. The simulation results have been obtained under normal conditions (
PV system and single-phase grid characteristics.
Parameters | Symbol | Value |
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Network |
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Boost |
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LCL-filter |
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2mH, 5mΩ, 5 |
PWM switching frequency |
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14Khz |
DC capacitance |
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4mF |
Controller parameters.
Parameters | Value | |
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Luenberger observer |
|
6399 |
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6166 | |
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1776 | |
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Current regulator (PFC) |
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4500, 40 |
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||
Voltage regulator |
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44.16, 19.6 |
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||
DC Link regulator |
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|
|
|
Figures
(a) Grid current and its estimate. (b) Capacitor filter voltage and its estimate. (c) Inverter output current and its estimate. (d) PV voltage and its estimate. (e) Current of inductance boost and its estimate.
FFT analysis of grid current.
Unknown parameter
Unknown parameter
Grid voltage
Grid current
PV voltage and its reference.
Injected current and its reference.
DC bus voltage.
PFC checking.
PV power.
Active grid power.
Reactive grid power.
Figure
Figure
Different powers of the system are given by Figures
The robustness of the nonlinear adaptive controller is checked under a time variation climate conditions. The purpose of this simulation is to test the closed-loop system under a change in the PV output that occurred by a sudden change in climate change. In the following simulations, the DC-link capacitor voltage is kept constant equal to 650 V.
The levels of the irradiance are illustrated in Figure
Irradiance variations.
In the following simulations, the output-feedback controller performances are illustrated by Figure
Tracking performances of controllers. (a) PV voltage. (b) Grid current. (c) DC-link capacitor voltage. (d) Voltage and grid current.
The aim of this test is to check the grid current controller performance in the presence of variations in the network impedance. The elements of the impedances (
Grid impedance variation.
The following figures present the simulation results in the case of variations undergone by the network impedance. Figures
The parameter
The parameter
Grid current and its estimate.
PFC checking.
This test aims at evaluating the performance of the system against the change of the amplitude and the frequency of the grid. The amplitude and the reference of the grid are modified according to the protocol presented in Figure
Grid amplitude
Grid frequency
Figures
Reference tracking.
PFC checking under grid faults.
Note that, for all simulations, it is clear that the proposed controller reacts in a quick manner to reach the reference and to remove the steady-state error quickly to keep the stability of the system.
An output-feedback nonlinear control strategy for a single-phase grid-connected PV system is proposed in this paper. The system is described by 6th order nonlinear averaged model. The controller design is made based on a combination of robust sliding-mode control strategy and nonlinear observers. The simulations under MATLAB/Simulink prove that the controller meets the performance for which it was designed. Specifically, it is shown that all control objectives are achieved, including PFC requirement, extracting a maximum power from the PV array and DC-link voltage regulation without requiring a lot of current and voltage sensors.
The authors declare that there are no conflicts of interest regarding the publication of this paper.