A random PWM control strategy for a three-level inverter used in a grid connected photovoltaic system

Received Jan 22, 2020 Revised Apr 4, 2020 Accepted Apr 26, 2020 The work presented in this paper is devoted to the control of a photovoltaic system connected to grid by a three-level diode clamed inverter. A control structure based on three parts: dc link voltage control, power injected control and current control is proposed. In this work, the random PWM strategy is used to generate control signals for the multilevel inverter used us an interface to connect photovoltaic generators to the grid. Numerical simulations are performed using MATLAB/Simulink software, the simulation results for the proposed system indicate the performances of the proposed control structure, minimization of harmonics by the random PWM strategy applied and injection to the grid more active power by the multilevel inverter structure.


INTRODUCTION
Currently, renewable energies are considered as the alternative to fossil combustible in order to reduce pollution. The grid connected PV systems generally use a two-level inverter to send to grid the generated PV power, or it used to feed linear and nonlinear loads connected at the ac side [1][2][3][4][5][6]. Nevertheless, the conventional inverter is very limited in its output voltage levels. It only gives three levels of phase to phase output voltage and poor spectral quality [7][8]. To deal with this problem, researchers have proposed other structures called multilevel inverters to perform these grids connected photovoltaic systems such as: flying capacitors structure, the cascaded H-Bridge structure, the diode clamped inverters structure and the full bridge with cascaded transformers inverters. Theses multilevel inverters allow obtaining high output voltages with better spectral quality moreover; they offer several possibilities for the connection of photovoltaic generators or batteries to their continuous bus [9][10][11][12][13][14].
In literature, many works have used three level inverters in grid connected photovoltaic systems and proposed several control strategies for it. In [15], authors present the control of a three-level Neutral Point Clamped (NPC) voltage source inverter for grid connected photovoltaic (PV) systems; the control method used is the Extended Direct Power Control (EDPC), which is a generic approach for Direct Power Control (DPC) of multilevel inverters based on geometrical considerations. Also, in [16], authors used to control the three-level inverter, a modified version of voltage-oriented control (VOC) method and the space vector pulse width modulation (SVPWM) technique. To reduce the harmonic content of grid-connected current and to

MODELING OF THE PROPOSED SYSTEM
The proposed system is shown in Figure 1. It consists of two photovoltaic generators connected to the three levels Diode Clamped Inverter through a DC bus; the multilevel inverter is connected to grid by a filter.

Photovoltaic generator modeling
Solar cells are usually associated in series and in parallel, and then encapsulated under glass to obtain a photovoltaic module. PV modules are usually connected in series-parallel to increase the voltage and current at the photovoltaic generator output. The interconnected modules are mounted on metallic supports and inclined according to the desired angle depending on the location. Study and modeling of a photovoltaic generator and the I-V characteristic is based on a cell elementary modeled by the well-known equivalent circuit of Figure 2.
This circuit introduces a current source and a diode in parallel, as well as series resistance Rs and parallel resistance Rsh to take into account the dissipative phenomena [18].
Where: I ph : The photo-current, I s : The saturation current of diode, m: ideality factor, and ℎ : series and parallel resistance, T: junction temperature, K: Boltzmann constant, q: electron charge.

Model of DC/DC converter
The DC / DC converter used in this work is the most frequently used as boost converter (Boost) as shown in Figure 3. This converter is modeled by the following equations: Where α, Vo and Io respectively denote the duty cycle, the voltage of output and the output current of the Boost converter. The cyclic ratio α, is the MPPT control system output (P & O).

Model of three level diode clamped inverter
A three-phase three-level diode-clamped inverter is shown in Figure 4 [19]. It is composed by three arms and two DC voltages. Each arm has four switches in series and two median diodes. Each switch consists of a transistor and an antipallel diode. The midpoint of each arm is connected to a DC source voltage (Uc). With a capacitive voltage divider formed by the filter capacitors C 1 and C 2 of same capacity C, we obtain two secondary DC sources each delivering a half voltage (Uc / 2). Being connected to each other at a neutral point noted O.
For each leg of the inverter, we define three connection functions, each one is associated to one of the three states of the leg: As indicated in Table 1, each leg of the inverter can have three possible switching states P, O, N. The output voltages of a three-level diode clamped inverter are expressed as follows: . Three level diodes clamped inverter (DCI).

THE PROPOSED CONTROL STRATEGY
The objective of control structure is to regulate the DC-link voltage and to set a unit power factor. Figure 5 shows the whole bloc diagram of the control structure.

DC/DC converters control (MPPT control)
The principle of this command is to generate disturbances by decreasing or increasing the cyclic ratio α and to observe the effect on the power delivered by the photovoltaic generator [20][21]. Its algorithm is illustrating in Figure 6.  Figure 6. Flowchart of P&O algorithm.

DC bus control
The DC voltage corrector is used to regulate the DC bus and sets the active power .
Where: = : is the maximal power of the photovoltaic generator The voltage must be carefully chosen to ensure the controllability of the current at all operating points.

Power control
The active and reactive power ( , ) can be both expressed by using Park components of supply voltage ( , ) and line current ( , ) as follows: Reference currents ( , ) which allows setting the desired reference active and reactive powers( , ), as follows: The unity power factor is obtained simply by setting the reactive power reference null. We can also generate or absorbe ( < 0 > 0).

Current control
The vector current control in Park reference frame is carried out by using the synchronized reference with the grid voltage. Bloc diagram as shown in Figure 8. The electric equations of the filter ( , ) connected to the grid are given bellow:

Random PWM control strategy for the three levels DCI
The PWM based on the comparison between the carrier wave which is in the most time triangular and the reference wave which is even provide directly by the programmer or by the far control technique like  . so, we find that the highest harmonics are the ± 2 than ± 4 etc…, the same with 2 and 3 and all the "m" multiple what we called harmonics families.
The method is based on a random selection of the carrier frequency for each carrier period [22][23][24][25]. In this technique the randomization of frequency of carrier wave is by taking some times the carrier wave and the other times the inverse of carrier wave. So, for do this we work with PRBS (the random bits generator, Figure 9 which it generates random bites even 0 or 1.

Figure 9. PRBS 9 bits scheme
In our scheme, PRBS signal is generated using a linear feedback shift register (LFSR), shown in Figure 9. It has 9 data storing units (delay line in optics), each unit is capable of storing one bit of binary data temporarily during one clock period. The whole system is synchronized with a clock. At each period, the 5 and 9 bit goes through a XOR process. The XOR logic is used in the PRBS to drive the input bit with the XOR of some bits of the overall shift register value, also A XOR gate can give very short pulse duration (< 1 ps). Then, we take the result of PRBS and multiple with the carrier wave and the inverse of PRBS multiple with the inverse of carrier wave and add the both results like it's been shown in Figure 10 and Figure 11. By using the PRBS scheme and the carrier wave and the reference scheme we can build the bloc of PRWM with pseudorandom carrier. Figure 10. Carrier wave generation Figure 11. Carrier wave form

SIMULATION RESULTS
In this section, the proposed photovoltaic grid connection system is simulated using MATLAB/Simulink. We have connected two PV generators (each generator is composed of 13 panels of 150 W put in series) to the continuous bus as shown in Table 2. The reactive power is controlled by controlling in park frame the injected currents in the grid, we impose a grid reactive power equal to zero ( = 0), and the reference active power is calculated by the DC bus control bloc.    1555 Figure 17. Voltages U c1 and U c2 Figure 18. Grid voltage and current Figures 14,15 and 16 respectively show the total produced photovoltaic power, the active power and the reactive power transmitted to the electrical network. These results show that all the PV power produced is injected to grid with a unit power factor because we have imposed a reference reactive power equal to 0. Figure 17 shows the voltages of the two capacitances of the DC bus. The two capacitance are equal (C 1 = C 2 = 0.2 mF). the grid voltage and the grid current of phase 1are illustrated in Figure 18.

CONCLUSION
This paper presents the advantages of three level diodes clamped inverter for grid connected photovoltaic systems. The proposed system produces less dv/dt stresses imposed on the switching devices and generates fewer harmonic in voltage and current by using Random PWM control strategy. The using of three levels DCI, allows connecting two PV generators to the grid. Also, it possible to transmit more power to grid by increasing the DC bus voltage, and a reduction of the filter elements. The circuit provides good decoupling of the voltage loops V d and V q since the V q remains constant under variations which shows high dynamic performances of the controllers. Thus, the active and reactive power follows quietly the reference signals. The grid voltage and current are in phases there by the power factor at the grid connection is almost unity.