# A Novel Two Stage Controller for a DC-DC Boost Converter to Harvest Maximum Energy from the PV Power Generation

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## Abstract

**:**

## 1. Introduction

## 2. Photovoltaic System Model

#### 2.1. Photovoltaic Cell Modeling

#### 2.2. The Boost Converter Model

## 3. Control Design of The Proposed Two-Stage MPPT Algorithm

#### 3.1. MPP Searching Algorithm

- Case 1: $\Delta {P}_{pv}={P}_{pv}\left(k\right)-{P}_{pv}(k-1)>0\phantom{\rule{0.277778em}{0ex}},\Delta {V}_{pv}={V}_{pv}\left(k\right)-{V}_{pv}(k-1)>0$$\Delta {P}_{pv}$ is the difference of the present power ${P}_{pv}\left(k\right)$ minus the previous ${P}_{pv}(k-1)$ and $\Delta {V}_{pv}$ is also the gap among the actual PV voltage ${V}_{pv}\left(k\right)$ and the previous one ${V}_{pv}(k-1)$. In Case 1, both $\Delta {P}_{pv}$ and $\Delta {V}_{pv}$ are positive. Therefore, the algorithm decreases the duty cycle $\alpha $ so that ${V}_{pv}$ continues to rise to reach MPP.
- Case 2: $\Delta {P}_{pv}={P}_{pv}\left(k\right)-{P}_{pv}(k-1)>0\phantom{\rule{0.277778em}{0ex}},\Delta {V}_{pv}={V}_{pv}\left(k\right)-{V}_{pv}(k-1)<0$Here, $\Delta {P}_{pv}$ is positive while $\Delta {V}_{pv}$ is negative; referring to Figure 5, the PV module is working in the right of MPP. The algorithm’s action is to decrease the PV voltage by increasing the duty cycle $\alpha $ until MPP is reached.
- Case 3: $\Delta {P}_{pv}={P}_{pv}\left(k\right)-{P}_{pv}(k-1)<0\phantom{\rule{0.277778em}{0ex}},\Delta {V}_{pv}={V}_{pv}\left(k\right)-{V}_{pv}(k-1)<0$In this case, both $\Delta {P}_{pv}$ and $\Delta {V}_{pv}$ are negative. The control decision is to reduce the duty cycle $\alpha $ to raise the PV voltage until reaching MPP.
- Case 4: $\Delta {P}_{pv}={P}_{pv}\left(k\right)-{P}_{pv}(k-1)<0\phantom{\rule{0.277778em}{0ex}},\Delta {V}_{pv}={V}_{pv}\left(k\right)-{V}_{pv}(k-1)>0$In the last case, $\Delta {P}_{pv}$ is negative while $\Delta {V}_{pv}$ is positive. The decision assumed is to increase the duty ratio to lead the decreasing of the PV voltage ${V}_{pv}$.

#### 3.2. Sliding Mode Controller

**When $\mathbf{s}>\mathbf{0}$:**This denotes that the voltage reference ${V}_{ref}$ provided by the MPP searching algorithm based on P&O is bigger than the PV voltage of the PV module, i.e., ${V}_{ref}>{V}_{pv}$. Afterwards, this leads s to zero $(s=0)$, meaning $({V}_{pv}={V}_{ref}={V}_{MPP})$. As shown in Figure 5, ${V}_{pv}$ should increase and ${I}_{pv}$ should decrease; therefore, as a result, ${R}_{pv}$ must increase through decreasing the duty cycle $\alpha $, which is deduced from Equation (9).As a conclusion, the system is stable when ${V}_{pv}$ is increased, which implies that $\dot{s}=-{\dot{V}}_{pv}<0$, then $s\dot{s}<0$, and our system moves toward the maximum power point.**When $\mathbf{s}<\mathbf{0}$:**Based on Equation (10), $({V}_{pv}>{V}_{ref})$; thus, to stabilize our system $(s=0)$ and according to Figure 5, ${V}_{pv}$ must decrease and ${I}_{pv}$ should increase. Therefore, ${R}_{pv}$ has to drop, which occurs through raising the duty ratio $\alpha $, denoting that $\dot{s}=-{\dot{V}}_{pv}>0$ and $s\dot{s}<0$.Finally, based on Lyapunov stability theory, we deduce that the control law is stabilizing.

## 4. Instrumentation Used in Real Time Experiments

#### 4.1. Atersa PV Panel

#### 4.2. Boost Converter

#### 4.3. DSP1104

**Matlab/Simulink and Control Desk**:The software packages used in the experimental test are Matlab-Simulink and Control Desk 5.1. Indeed, the way we made our control strategies is the same as making any Simulink project, by using basics blocs or toolboxes via installing the library RTI 1104 in Simulink-Matlab. Thereafter, we compiled the Simulink model and generated a (.sdf) file, which is a specific code in real time.Control Desk 5.1 is wasused for creating an interface with the GUI (graphical user interface). Figure 6 illustrates how the real-time code is obtained from (.sdf) file generated from Simulink, which allows us to access and modify the variable control system in real time.**I/O ribbon cable**:It is used to connect the DS1104 R&D controller card to the I/O box.**CP 1104 I/O box**:It is an input/output interface board between the DS1104 R&D controller board and the system.It contains eight analog input digital converters (ADCs), eight analog output digital converters, and two digital input incremental encoders.**DS1104 R&D controlled board**:This board is installed in the computer and connected to the CP 1104 I/O through a master I/O ribbon cable. The DS1104 runs with Power PC 603e core at 250 MHz with 32 MB of SDRAM and 8 MB of flash memory.

## 5. Simulation Results

#### 5.1. Effects of Parasitic Components

#### 5.2. Simulation under Steady Temperature

^{2}for $1\phantom{\rule{0.277778em}{0ex}}\mathrm{s}$ and it decreases quickly to 400 W/m

^{2}over $1\phantom{\rule{0.277778em}{0ex}}\mathrm{s}$.

#### 5.3. Simulation at Steady Irradiation

^{2}while the temperature started at 45 °C within $1\phantom{\rule{0.277778em}{0ex}}\mathrm{s}$ and then decreased to 20 °C for $1\phantom{\rule{0.277778em}{0ex}}\mathrm{s}$.

## 6. Experimental Results and Discussion

- DS1104_Mux_ADC DS1104: This block is for reading the four A/D converter channels. The two algorithms only need the irradiation (G) and the temperature (T) at every sample time.
- DS1104_ADC_CX: It is devoted to reading the data of the four signals from (ADC_C5 to ADC_C8). ADC_C5 is dedicated to reading the photovoltaic voltage (${V}_{Solar}$=${V}_{pv}$), ADC_C6 to reading the photovoltaic current (${I}_{Solar}$=${I}_{pv}$), ADC_C7 to ${V}_{O}$, and ADC_C8 to ${I}_{O}$.
- DS1104SL_DSP_PWM3: It allows generating standard PWM pulses.
- Low pass filters: They are used to remove the undesirable high-frequency noise.

#### 6.1. Perturbation and Observation Algorithm

^{2}.

#### 6.2. Two-Stage MPPT Control

^{2}and T = 23 $\xb0$C. The real test was carried out under a variable resistance load. It started from a value of ${R}_{o}=30\phantom{\rule{3.33333pt}{0ex}}\Omega $, increased to 50 $\Omega $, and then decreased again to 40 $\Omega $.

## 7. Conclusions and Perspectives

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MPPT | Maximum power point tracking |

PV | Photovoltaic |

MPP | Maximum power point |

P&O | Perturbation and observation |

DSP | Digital signal processor |

MPV | Maximum power voltage |

FLC | Fuzzy logic control |

SMC | Sliding mode control |

ADC | Analog to Digital Converter |

DAC | Digital to Analog Converter |

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**Figure 14.**Real behaviors of ${P}_{pv}$, ${P}_{Load}$, ${V}_{Load}$, and ${V}_{pv}$ using two-stage MPPT control.

Symbol | Definition |
---|---|

${I}_{ph}$ | Photo current [A] |

${I}_{d}$ | Reverse saturation current [A] |

A | Ideality factor |

${I}_{scr}$ | Short circuit current [A] |

${v}_{oc}$ | Open circuit voltage [V] |

${K}_{i}$ | Temperature coefficient of short circuit current [A/K] |

${T}_{ak}$ | Cell temperature [K] |

${T}_{rk}$ | Cell reference temperature [K] |

S | Solar irradiation [W/m^{2}] |

K | Boltzmann constant, $K=1.38\times {10}^{-23}$ [J/K] |

${E}_{g}$ | Band gap energy [eV] |

q | Electron charge, $q=1.6\times {10}^{-19}$ [C] |

Measurements | Voltage ${\mathit{V}}_{\mathit{pv}}$ | Duty Cycle ($\mathit{\alpha}$) |
---|---|---|

$\Delta {P}_{pv}>0,\Delta {V}_{pv}>0$ | Rise | Drop |

$\Delta {P}_{pv}>0,\Delta {V}_{pv}<0$ | Drop | Rise |

$\Delta {P}_{pv}<0,\Delta {V}_{pv}<0$ | Rise | Drop |

$\Delta {P}_{pv}<0,\Delta {V}_{pv}>0$ | Drop | Rise |

Parameter | Value |
---|---|

Power (W in test $\pm 10\%$) | 55 W |

${N}_{s}$ | 36 |

${I}_{mp}$ | $3.4$ A |

${V}_{mp}$ | $16.2$ V |

${I}_{sc}$ | $3.7$ A |

${V}_{oc}$ | $20.5$ V |

Temperature coefficient of ${I}_{sc}$ | $1.66$ mA/ C |

Temperature coefficient of ${V}_{oc}$ | $-84.08$ mV/ C |

Parameter | Type | Value |
---|---|---|

L | 6xPCV-2-564-08 | 560 $\mathsf{\mu}$H, 7 A, 42 m$\Omega $ |

C | 2xTK Series | 1500 $\mathsf{\mu}$F, 250 V |

${C}_{1}$ | 1xTK | 1000 $\mathsf{\mu}$F, 250 V |

Schottky diode | 2xMURF1560GT | 600 V, 15 A, $0.4$ V |

IGBT | 1xHGT40N60B3 | 600 V, 40 A, $1.5$ V |

${F}_{s}$ | 20 KHz | |

${V}_{imax}$ | 60 V | |

${I}_{imax}$ | 20 A | |

${V}_{Omax}$ | 250 V | |

${I}_{Omax}$ | 20 A | |

${\alpha}_{min}$ | $0.1$ | |

${\alpha}_{max}$ | $0.9$ |

Settling Time 2% | Overshoot | Ripple | Efficiency | Error | ||||||
---|---|---|---|---|---|---|---|---|---|---|

P&O | Two-Stage MPPT | P&O | Two-Stage MPPT | P&O | Two-Stage MPPT | P&O | Two-Stage MPPT | P&O | Two-Stage MPPT | |

Fast irradiance variation (W/m^{2}):from (1):S = 700 to (2): S = 400 | ||||||||||

(1) | 241 ms | 61 ms | 0.17 W | 0.12 W | 0.313 | 0.098 | 99.87 | 99.97 | 0.12 | 0.02 |

(2) | 472 ms | 0 ms | 0.55 W | 0.02 W | 0.011 | no ripple | 90.26 | 99.92 | 9.73 | 0.08 |

Fast temperature variation (°C)from (1):T = 45 to (2): T = 20 | ||||||||||

(1) | 240 ms | 54 ms | 0.01 W | 0.04 W | 0.283 | 0.096 | 99.89 | 99.89 | 0.106 | 0.106 |

(2) | 216 ms | 8 ms | 2.15 W | 0 W | 0.037 | 0.015 | 97.72 | 99.80 | 2.273 | 0.191 |

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**MDPI and ACS Style**

Charaabi, A.; Barambones, O.; Zaidi, A.; Zanzouri, N. A Novel Two Stage Controller for a DC-DC Boost Converter to Harvest Maximum Energy from the PV Power Generation. *Actuators* **2020**, *9*, 29.
https://doi.org/10.3390/act9020029

**AMA Style**

Charaabi A, Barambones O, Zaidi A, Zanzouri N. A Novel Two Stage Controller for a DC-DC Boost Converter to Harvest Maximum Energy from the PV Power Generation. *Actuators*. 2020; 9(2):29.
https://doi.org/10.3390/act9020029

**Chicago/Turabian Style**

Charaabi, Asma, Oscar Barambones, Abdelaziz Zaidi, and Nadia Zanzouri. 2020. "A Novel Two Stage Controller for a DC-DC Boost Converter to Harvest Maximum Energy from the PV Power Generation" *Actuators* 9, no. 2: 29.
https://doi.org/10.3390/act9020029