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This paper deals with the modeling and control of a new twostage photovoltaic conversion cascade composed of a ThreeLevel Boost (3LB) converter and a threephase NPC fivelevel inverter (5LI). The main objective is to ensure the continuity of energy transfer from a renewable continuous source to the electrical grid while regulating the voltages of the DC bus capacitors with a new proposed configuration. The 3LB is controlled in MPPT based on fuzzy logic. A PI regulator is introduced into the 3LB regulation loop in order to maintain the equality of the two output voltages. The overall voltage of the DC bus being regulated by the control of the multilevel inverter interconnected to the grid, using synchronous reference frame control. Therefore, in our case there is the problem of voltages imbalance caused by the 5LI. We propose in this work to introduce two Clamping Bridges (CBs) each one is composed by a transistor in series with a resistor. These CBs are introduced in parallel with two capacitors of the DC bus. This solution avoids us to use the control algorithm by redundant configurations in the regulation loop of the 5LI. The results obtained show the effectiveness of the proposed control in stabilizing and maintaining the four DC bus voltages at equal values. With four balanced capacitor voltages, we get symmetrical inverter output voltage waveforms, which directly affects the quality of the current injected to the grid.
ThreeLevel Boost, fivelevel inverter, clamping bridges, SVPWM, DC bus control
To cope with the decrease in fossil resources and climate change, renewable energies are a particularly suitable response to the energy needs of the world. They therefore play an important role in the fight against climate change and therefore in the protection of human health. Migration to this type of energy allows longterm control of energy prices since it concerns energies produced from inexhaustible and free resources. Today, photovoltaic (PV) systems, wind generators and hydroelectric systems are the most widely used in the production of clean electrical energy. Currently, investment in the development and integration of these clean sources is becoming essential in order to meet the energy needs of countries.
In the early 1960s, multilevel converters made their appearance. These converters have several advantages: On the one hand, they allow distribution of the voltage stress on the power switches, which offers much higher performance than that of conventional structures. On the other hand, the waveform of the output voltage is of better spectral quality compared to that of a twolevel voltage inverter. Indeed, the fact of increasing the number of switching cells per leg makes it possible to reduce the level of harmonic distortion of the output voltages. Today, these converters are increasingly used in production systems from renewable energies.
The history of multilevel converters began in the 1960s. The first structure described is an Hbridge series connection. Then, in the late 1970s, the Neutral Point Clamped (NPC) converter appeared [1]. This topology is considered the first multilevel converter intended for medium power applications. Since then, many studies have been proposed to study its properties and the possible evolutions of this structure.
Nowadays, new configurations of multilevel converter (DC/DCDC/AC) topologies have appeared such as the fivelevel ITtype NPC inverter [2] or the singleinput dualoutput threelevel DCDC converter [3].
A multilevel NPC inverter uses intermediate capacitors which define the different voltage levels at its output. The major problem for the control of this type of converter is the balancing of the voltages of its capacitors in order to ensure the safety of the semiconductors. Indeed, the floating voltages evolve according to the command and the direction of circulation of the load current.
Several solutions are proposed by researchers for balancing capacitor voltages such as the use of balancing bridge [47] or redundant vectors [810].
Multilevel inverter structures are applied in singlestage or twostage photovoltaic conversion cascades [1117]. In this work, we are interested in the second configuration.
Belabbas et al. [7] in their work used a single DC/DC boost converter to fed the four capacitors of the 5LI (Figure 1). In this case, the authors use four balancing bridges to regulate the voltage values of the DC bus capacitors.
Figure 1. PV generator DC/DC Boost converter  5LI
Sarthi et al. [18], Laib et al. [19] use four DC/DC Boost converters, each powered by its own photovoltaic generator (Figure 2). The redundant vectors of the vector diagram are applied for balancing the input voltages of 5LI.
Figure 2. Four PV generator Four DC/DC Boost converters 5LI
Abdullah et al. [20] in their work used a threelevel boost connected with only two 5LI capacitors (Figure 3). In this case, the authors use two circuits composed of an inductance, a transistor and a diode to control the voltage of the upper and lower capacitors.
Figure 3. PV generator Threelevel boost converter  5LI
de Britto Florencio et al. [21] uses series interleaved threelevel boost to fed the four capacitors of the 5LI (Figure 4). In this case, the two DC/DC converters regulate the capacitor voltages.
Figure 4. PV generators series interleaved threelevel boost converters  5LI
Figure 5 presents the proposed configuration. Rosmadi et al. in their cascade introduced their 3LB to feed the two capacitors C_{2} and C_{3} [20]. Therefore, the voltages across them are constant. The voltages of the other capacitors C_{1} and C_{4} are regulated using an external circuit. In the configuration that we propose, the 3LB is introduced to regulate the sum of the voltages of the capacitors C_{1} and C_{2} as well as the sum of the voltages of the capacitors C_{3} and C_{4}. Therefore, in our case there is the problem of voltages imbalance caused by the 5LI. We use in our case to solve this problem, two clamping bridges, each composed of a transistor and a resistor.
Figure 5. Proposed DC bus configuration
The threelevel boost uses two switches and two diodes but only one inductor (Figure 6). The advantage of this structure is initially to halve the voltage constraints of the switches. The two switches are controlled with the same duty cycle but their controls are shifted from each other by half a period [22]. The averaged model of 3LB is:
$\left\{\begin{array}{l}L \frac{d i}{d t}=V_e\left(1\alpha_1\right) V_{d c 1}\left(1\alpha_2\right) V_{d c 2} \\ V_{d c 1}+V_{d c 2}=V_s\end{array}\right.$ (1)
Figure 6. Threelevel boost
For the duty cycle α=α_{1} less than 0.5 and greater than 0.5, we have the waveforms of the current in the inductance of Figure 7.
Figure 7. Current waveform (α<0.5 left, α>0.5 right)
In the case where α<0.5, we have:
$\left(V_e\frac{V_s}{2}\right) \alpha=\left(V_eV_s\right)(0,5\alpha)$ (2)
Similarly, in the case where α>0.5, we have:
$V_e(\alpha0,5)=\left(V_e\frac{V_s}{2}\right)(1\alpha)$ (3)
We deduce from the two previous relations, the voltage gains of the converter:
$\frac{V_s}{V_e}=\frac{1}{1\alpha}$ (4)
The current ripple and the output voltage ripple are written:
$\left\{\begin{array}{l}\Delta i=\frac{V_e}{2 L f} \frac{\alpha(12 \alpha)}{1\alpha} \\ \Delta V_s=\frac{2 I_s(0,5\alpha)}{C f}=\frac{V_e(12 \alpha)}{(1\alpha) R C f}\end{array} \quad\right.$ for $\alpha<0.5$ (5)
$\left\{\begin{array}{l}\Delta i=\frac{V_e}{2 L f}(2 \alpha1) \\ \Delta V_s=\frac{2 I_s(\alpha0,5)}{C f}=\frac{V_e(2 \alpha1)}{(1\alpha) R C f}\end{array} \quad\right.$ for $\alpha>0.5$ (6)
where, C=C1=C2.
The voltages at switches terminals and the diodes have the value:
$V_{k, \max }=\leftV_{d, \max }\right=V_{c, \max }=\frac{V_e}{1\alpha}+\frac{\Delta V_c}{2}$ (7)
with
$\Delta V_c=\frac{V_e}{R C f}$ for $\alpha<0.5$ (8)
and
$\Delta V_c=\frac{\alpha V_e}{(1\alpha) R C f}$ for $\alpha>0.5$ (9)
Similarly, the maximum currents crossing the switches and the diodes are:
$i_{k, \max }=i_{d, \max }=i_{\max }=I+\frac{\Delta i}{2}$ (10)
There are several methods for finding the maximum power point (MPP) of a field of photovoltaic modules, which the efficiency and speed vary. Among these methods, the control of the MPPT based on fuzzy logic. Fuzzy logic controllers have been widely used in industrial processes in recent years due to their heuristic nature coupled with simplicity, efficiency and consideration of its multirule variable for parameter variation linear and nonlinear system.
We apply in our work to the input of our regulator the variations of the power and voltage of the photovoltaic generator. We obtain at the output the variation of the duty cycle to which we add the duty cycle to obtain the control order D_{1} of the first transistor of the 3LB (Figure 8).
Figure 8. Fuzzy logic controller
The fivelevel threephase inverter used consists of three legs and four DC voltage sources. Each leg has eight switches and two middle diodes (Figure 9) [23].
Figure 9. Circuit diagram of 5LI
The following Table 1 summarizes the states of the inverter switches, which make it possible to obtain the five output voltages.
Table 1. States of the inverter switches
Switching States 
Output Voltage 

S_{i1} 
S_{i2} 
S_{i3} 
S_{i4} 
S_{i5} 
S_{i6} 
S_{i7} 
S_{i8} 

ON 
ON 
ON 
OFF 
OFF 
OFF 
OFF 
OFF 
P_{2}=E1+E_{2} 
ON 
ON 
OFF 
OFF 
OFF 
ON 
ON 
OFF 
P_{1}=E_{1} 
ON 
OFF 
OFF 
ON 
OFF 
ON 
OFF 
OFF 
0 
OFF 
OFF 
ON 
ON 
ON 
OFF 
OFF 
ON 
N_{1}=E_{3} 
OFF 
OFF 
OFF 
ON 
ON 
ON 
OFF 
OFF 
N_{2}=E_{3}E_{4} 
From the desired output voltages, we define the output voltage vector:
$v_s=V_A e^{j 0}+V_B e^{j 2 \pi / 3}+V_C e^{j 2 \pi / 3}=v_d+j v_q$ (11)
Depending on the states of the inverter switches, this vector can take several positions in the d−q plane. These positions are shown on the vector diagram in Figure 10. There are 60 discrete positions, distributed over four hexagons, in addition to a position in the center of the hexagon. Some positions are created by several redundant states. From the external hexagon towards the internal hexagon, the positions of the vector V_{s} are created respectively by one, two, three or four redundant states. The position of the center of the hexagon, which corresponds to a zero output voltage, is created by five redundant states. There are thus 24 positions with a single redundancy (hexagon 1), 18 positions with two redundancies (hexagon 2), 12 positions with three redundancies (hexagon 3) and 6 positions with four redundancies (hexagon 4) (Figure 11).
Figure 10. Fivelevel inverter vector diagram
Figure 11. Hexagons of 5LI space vector diagram
The voltages of capacitors V_{dc1} and V_{dc2} (Figure 5) are balanced by the control of the 3LB, but the voltages of capacitors U_{c1}, U_{c2}, U_{c3}, U_{c4} and U_{c4} are not equal. We use two balancing bridges to make them at equal value.
$V_{d c 1}=U_{c 1}+U_{c 2}$ (12)
$V_{d c 2}=U_{c 3}+U_{c 4}$ (13)
7.1 Capacitor voltage balancing of threelevel boost
Various works have been carried out in order to maintain the equality of the voltage values of the two capacitors of the 3LB. To achieve this goal, Krishna et al. [16] in his twostage conversion cascade composed by a 3LB and a threelevel inverter uses two PI regulators. Another work presented in the ref. [24] introduces a PI and fuzzy logic regulators. In this work, we use only a single PI regulator for the regulation of the voltages of the two capacitors (Figure 12). D_{2} is the control order of the second transistor of the 3LB.
Figure 12. 3LB regulation loop
7.2 Clamping bridge
The clamping bridge consists of a transistor and a resistor connected in parallel with the capacitor whose voltage is unbalanced, as shown in Figure 13. In our case, we introduce two clamping bridges in parallel with capacitors U_{c1} and U_{c4} (Figure 5). Its mathematical model is:
$C_i \frac{d U_{c i}}{d t}=I_{\text {redi }}+i_{r(i+1)}+i_{c(i+1)}i_{d i}i_{r i}$ (14)
$i_{r i}=T_i \frac{U_{c i}}{R_{p i}}$ (15)
Figure 13. Clamping bridge cell structure
The balancing bridge through its algorithm removes energy from the capacitor with the highest voltage and then transfers that energy to the capacitor with the lowest voltage until the voltage is equalized across all capacitors. The control algorithm used is as follows.
$\left\{\begin{array}{l}U_{c i}U_{c r e f}=\varepsilon_i \\ \text { if } \varepsilon_i \geq 0 \text { we have } T_i=1 \Rightarrow i_{r i}=T_i \frac{U_{c i}}{R_{p i}} \\ \text { if } \varepsilon_i \leq 0 \text { we have } T_i=0 \Rightarrow i_{r i}=0\end{array}\right.$ (16)
The photovoltaic conversion cascade is shown in Figure 14. We use Matlab simulink software to simulate our system. The solar radiation applied to the photovoltaic generator is fixed at Ray=1000 W/m^{2}. The reference DC bus voltage is V_{dcref}=650V.
Figure 14. PV generatorThreelevel boost converter5LIGrid
The P(V) characteristic of the photovoltaic generator composed of 20 solar modules of 270W (four in series and five in parallel) each one with V_{mpp}=35V and I_{mpp}=7.7A is shown in Figure 15. We note that the maximum power that the photovoltaic generator can deliver is 5400 W.
Figure 15. P(V) Characteristic of the photovoltaic generator
Figure 16 presents the voltage V_{pv}, the current I_{pv} and the power P_{pv} of the photovoltaic generator. We notice that the voltage at the point of maximum power is 140V and the power is 5400 W. So the fuzzy logicbased MPPT algorithm works correctly.
Figure 17 shows the voltage of the three legs of the fivelevel inverter. The waveform obtained clearly presents the five voltage levels, which proves the effectiveness of the applied space vector modulation algorithm.
Figure 18.a presents the sum of the voltages V_{dc1} and V_{dc2}. This value of the global bus voltage is regulated by the control of the inverter where the value obtained is equal to the value of the reference voltage imposed in the control loop of 5LI.
Figure 16. Voltage V_{pv}(V), Current I_{pv}(A), Power P_{pv}(W) of the photovoltaic generator
Figure 17. Three legs voltages of 5LI
After imposing the global bus voltage by the control of the inverter, the 3LB will also ensure by its control, in addition to extracting the maximum power from the photovoltaic generator, the maintaining equality of the voltages V_{dc1} and V_{dc2}. Figure 18.b shows that the output voltages of the 3LB are of equal values.
The four voltages of the capacitors U_{c1}, U_{c2}, U_{c3}, and U_{c4} are presented in Figure 19. The control of the 3LB ensures that the value of the sum of the voltages U_{c1}+U_{c2} and U_{c3}+U_{c4} is maintained, but the NPC structure of the inverter used does not make it possible to maintain the equality of the voltages U_{c1} and U_{c2} as well as U_{c3} and U_{c4}. In this case, the two balancing bridges introduced into the DC bus intervene to balance and maintain the equality between the voltages U_{c1} and U_{c2} as well as U_{c3} and U_{c4}.
The result obtained shows the efficiency of the proposed solution to maintain equal the four bus voltages of this cascade.
Figure 18. (a) Voltage V_{dc1} + V_{dc2}, (b) Voltages V_{dc1} and V_{dc2} of 3LB
Figure 19. Capacitor voltages U_{c1}(V), U_{c2}(V), U_{c3}(V), U_{c4}(V)
Figure 20. Voltage and current of grid
With four balanced capacitor voltages, we get symmetrical inverter output voltage waveforms, which directly affects the current output waveform. Figure 20 shows the voltage and current of the first phase of the grid. We note from the result that the control of the 5LI allowed injecting into the grid a current in phase with the grid voltage.
This article presents a new configuration of a twostage photovoltaic conversion cascade interconnected to the grid based on 3LB and 5LI, with a DC Bus voltage balancing solution adapted to this configuration.
The proposed solution is able to regulate and maintain stable the four DC bus capacitor voltages. The regulation of the global bus voltage is ensured by the control of the multilevel inverter by the method of synchronous reference frame control. This overall voltage is divided into two equal voltages by the 3LB control, which at the same time ensures, via a fuzzy regulator, the extraction of the maximum power from the photovoltaic generator. Therefore, in our case there is the problem of voltages imbalance caused by the 5LI.
We have proposed to solve this problem, the introduction of two CBs, each one composed of a transistor in series with a resistor.
These CBs were introduced in parallel with two DC bus capacitors. The results obtained by simulation present:
With four balanced capacitor voltages, we obtained symmetrical inverter output voltage waveforms and a good quality of the current injected to the grid.
This project was financially supported by the Directorate General for Scientific Research and Technological Development  Algerian Ministry of Higher Education and Scientific Research.
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