Control Methods on Three-phase Power Converters in Photovoltaic Systems

Received Sep 2, 2018 Revised Sep 11, 2018 Accepted Sep 25, 2018 In this paper, a three-phase load connected to a NPC three-level inverter is presented. To generate gate signals for the multilevel inverter, two commands are developed and compared: the phase disposition pulse width modulation (PDPWM) and the space vector pulse width modulation (SVPWM). DC supply is provided by photovoltaic cells. Boost converter controls the power transfer from photovoltaic generator. Due to nonlinear I-V characteristics of photovoltaic cells, a maximum power point tracking algorithm is adopted to maximize the output power, the nonlinear controller (sliding mode) is developed and simulated. To verify the effectivnesse of the introdueced controller, it is compared with the fuzzy logic controller. Matlabsimulink is used for simulation, analysis and interpretation the results of these controllers Keyword:


INTRODUCTION
Solar energy is a valuable alternative to the energy from fossil fuels. The PV energy is developing very rapidly, it is durable and without polluting the environment. For controlling, the delivered electric power it is anticipated an action on electronic power interface connecting the PV generator with its load. The PV system generates a power that is dependent on the changing climate conditions: the solar irradiation, the temperatures of the panels and the load change [1]. Thus, a method of searching the maximum point power (MPP) for controlling the duty cycle of DC/DC converter is necessary to ensure optimal operation for PV system under different operating conditions [2]. Several techniques are developed for tracking the maximum point power (MPPT) satisfying the non-linearity of the characteristic of PV modules and the conditions described above, each has their own advantage and disadvantages [3]- [5].
This paper focuses on the comparison of static and dynamique regime of Sliding Mode Controller (SMC) and Fuzzy Logic Controller (FLC) for the tracking of the maximum power point under irradiance change. The efficiency and precision of solar power system are influenced by to the nonlinear variations, thus SMC is designed and compared with FLC for effective operation under non-linear parameters variations [6]- [10].
The controlled developed helps to avoid the drawback of the FLC, in this method the system state is confined on the sliding surface and is driven to the origin: the sliding surface is selected to ensure that the system state will hit the surface and produce maximum power output persistently, to avoid saturation of proposed control the scaling constant k is used, its value must not be large and it can be determined by .

PV SYSTEM
A photovoltaic cell is made of semi-conductor materials and converts light energy directly into electrical energy. It is based on physical phenomenon called photovoltaic effect. To produce more power, the solar cell is assembled to form a module. The serial connections of several cells increase the voltage, while the implementation in parallel increase the current.
Several models of cells exist, the model used in this paper is shown in Figure 1. Because of its simplicity, this empirical model is currently the more commonly used. It is made of a constant current source modelling the magnetic flux where is photocurrent create by radiation from sun and of diode, which represents a − junction of the cell, the losses are modelled by two resistors: a shunt resistance and a series resistance [14], [15].

MPPT CONTROL
The operating power of generators is calculated from the voltage current product. However, the determination of the reference power is more delicate because it is a function of meteorological parameters (temperature, irradiance). The operating at maximum power point is difficult to achieve because this reference is variable and characterized by a nonlinear function. Several techniques are developed to provide the optimal aerating [16], [17]. Figure 2 shows the PV array characteristic curve with the maximum point power variation under different irradiation (400 600 800 1000 W/m 2 ).

DC/DC Converter (Boost Converter)
This DC/DC converter also called boost converter is a static electronic power converter device thereby increasing the initial continuous voltage, it makes to impose the current determined by MPPT algorithm. The system including the boost converter consist of two operating sequence, the first sequence shown in Figure 3 is characterized by a closed switch (S=1) and the diode is open. In this case, the equations describing the system are: An open switch characterizes the second sequence and the diode is closed. This sequence is shown in Figure 4.
From two systems of equations (6,7), the model mathematic of the boost converter is given by [18]: Where is the state of the switch . Equations 3 can be described by:

Sliding Mode Control
The sliding mode control is a nonlinear control, it is characterized by the discontinuity of the control in passage by switching surface called: sliding surface [19], [20].
Choice of sliding surface: the condition of maximum power point PPM is given by In this condition, it is guaranteed that the system state will hit the surface and produce maximum power output persistently.
Calculation of the equivalent control, it is determined from the flowing condition: (8) Knowing that the surface S depends on L i then we can write: Then, the expression of equivalent control can be derived from the condition x1=0 eq 0 Finally, the real control signal is given by: Where k is positive scaling constant, the equivalent control is comprised with eq u and kS ,where eq u is the required effort for and kS can be considered as the effort to track the MPP. The surface sliding and duty cycle versus operation region are shown in Figure 5.   (15) Substituting (14) and (15) into (7), the sliding surface can be written: The time derivative of S can be written as: 1. Case S (x) > 0: In this case, the voltage must be decreased to reach the PPM, it means that 0 pv dV dt  , by replacing equation (17), we get S > 0, which means S (x) S (x) < 0. It is concluded that the sliding mode is provided.

Case S (x) > 0:
In this case, the voltage must be decreased to reach the PPM, it means that by replacing equation (17), we get 0 It is concluded that the sliding mode is provided.

Fuzzy Logic Controller
The fuzzy logic controller is advantageously a robust control, which does not require the exact knowledge of the mathematical model of the system. This command is better adapted to the nonlinear systems [21], [23]. Figure 6 shows the proposed structure of fuzzy logic controller; it consists of two input (E, CE) and one output (Duty cycle), the relation between the input an output is given by following equations.

DC/AC STATIC CONVERTER
The voltage extracted from the PV generator is the DC voltage, to connect a three-phase load it is necessary to use the DC/AC converter. To meet the above requirement, the Neutral Point Clamped (NPC) three level inverter is used in this work. Figure 8 shows the neutral point clamped (NPC) three-level inverter. To generate the command impulses of converter an N voltage levels, N-1 triangular carriers are necessary. These carriers have the same frequency and the same amplitude the carriers can be shifted horizontally, the phase difference between two consecutive signals is given by , the carriers have the same shifted vertical. They are then compared with a reference signal of amplitude and frequency .
The Amplitude modulation index is given by: The frequency modulation index f m is given by: In this case all carriers are identical in amplitude A C , in phase and in frequency F C .

SVPWM (Space Vector PWM):
This is an advanced PWM method because of its superior performance characteristics, it has been finding widespread applications in recent years [23], [24].  The amplitude and angle of the reference vector are given by: The vector diagram of a three-level inverter is shown in Figure 9, it can be subdivided into six sectors (I to VI).  Figure 8, the region may be determined, according to the following conditions: The reference vector in sector I and region 2 is shown in Figure 10.
Where : Knowing that: The switching time in the sector I and region 2 can be written: The switching sequences in the sector I and region 2 is defined by:

SIMULATION RESULT
To evaluate the performance and robustness of the system were developed a comparative study based on simulation in Matlab/Simulink between sliding mode and perturb&observe controllers. The proposed system including the three-phase three-level inverter shown in Figure 11, the proposed MPPT nonlinear controller is evaluated by varying the irradiance. The output power and voltage of the boost converter obtained by using FLC and sliding mode are shown in Figure 12 and Figure 13. It is observed that both SMC and FLC can track the MPP, we can also confirm that the SMC provides better reponse time, omproved transient behavior. About DC/AC conversion, the output three level inverter is shown in Figure 14 and Figure 15. We note that the three-level voltage remains stable and has a desired value in sliding mode controller. The harmonic analysis of output three level voltage is shown in table 2 and table 3, the SPWM generates less Total Harmonic Distortion (THD) and higher output quality. Based on obtained results, the SVPWM technique remains the more reliable solution.

CONCLUSION
In this paper, fuzzy logic controller and sliding mode controller have been designed and simulated for the proposed PV system, comparison for simulation results have been presented for the same environmental conditions. The maximum power point (MPP) to be achieved through the too controller, sliding mode has proved a satisfactory behavior: the stability is easily achieved, and guaranteed during irradiance change, the SMC shows a better performance in transitional and permanent regime.
The NPC three level is used for the DC/AC conversion, two commands have been developed and tested for different modulation indices ranging from 0.8-1.