# Sliding Mode Based Control of Dual Boost Inverter for Grid Connection

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## Abstract

**:**

## 1. Introduction

## 2. Topology Description

## 3. Control Strategy

#### 3.1. Inner Current Control Loop

#### 3.1.1. Sliding Surface Selection

#### 3.1.2. Equivalent Control

#### 3.1.3. Existence Condition

#### 3.2. Outer Current Loop

#### 3.2.1. Linearization

#### 3.2.2. Outer Control Design

## 4. Experimental Results

_{dc}, while the grid has been emulated using an AC source (Chroma 61704) operating at 110 V

_{ac,rms}/60 Hz . The experimental results are shown in Figure 8.

_{ac,rms}, which is higher than the grid voltage (110 V

_{ac,rms}) .

_{ac,rms}. This generates an increase of the AC component in the voltage of both output capacitors (${\upsilon}_{\mathrm{c}1}$ and ${\upsilon}_{\mathrm{c}2}$), while the grid current (${i}_{\mathrm{s}}$) remains controlled without reflecting any change caused by this perturbation, highlighting the robustness of the proposed control method. However, since the inductor current ${i}_{\mathrm{L}1}$ (and ${i}_{\mathrm{L}2}$) depends on the difference between the input voltage ${v}_{\mathrm{in}}$ and the voltage in each output capacitor, a small variation is experienced by ${i}_{\mathrm{L}1}$ and ${i}_{\mathrm{L}2}$. Please note that during this test the output (grid) current reference was kept constant.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**The cascaded control scheme of the grid-connected DBI, with external PR controller and internal sliding mode controller.

**Figure 5.**Bode diagrams: (

**a**) plant and phase compensator, (

**b**) closed-loop without and with the phase compensator.

**Figure 7.**Analog circuit for control stage, where R = 20 kΩ, R

_{1}= 10 kΩ, ${V}_{\mathrm{C}\mathrm{C}1}$ = 2.5 V, ${V}_{\mathrm{C}\mathrm{C}2}$ = 5 V, and ${C}_{1}$ = 0.1 µF.

**Figure 8.**Experimental results with grid connection and input voltage of 70 V: (

**a**) reference and measurement of grid current, difference of the inductor currents and output of outer control loop (${k}_{2}$), (

**b**) voltage of the capacitors (${\upsilon}_{\mathrm{c}1}$, ${\upsilon}_{\mathrm{c}2}$) and current through the inductors (${i}_{\mathrm{L}1}$, ${i}_{\mathrm{L}2}$), (

**c**) voltage of the capacitors (${\upsilon}_{\mathrm{c}1}$, ${\upsilon}_{\mathrm{c}2}$), voltage of the line filter, output voltage (${\upsilon}_{\mathrm{o}}$) and (

**d**) ${\upsilon}_{\mathrm{c}1}$, ${i}_{\mathrm{L}1}$, grid voltage and current.

**Figure 10.**Experimental results under variations in the output current reference (voltage of the capacitor ${C}_{1}$ (${\upsilon}_{\mathrm{c}1}$), current through the inductor ${L}_{1}$ (${i}_{\mathrm{L}1}$), reference (${i}_{\mathrm{s}}^{*}$) and measurement (${i}_{\mathrm{s}}$) of grid current): (

**a**) Step-down in the output current reference, and (

**b**) Step-up in the output current reference.

**Figure 11.**Experimental dynamic performance under grid perturbation (from 20% voltage dip to nominal voltage): voltage of the capacitor ${C}_{1}$ (${\upsilon}_{\mathrm{c}1}$), current through the inductor ${L}_{1}$ (${i}_{\mathrm{L}1}$), measurement of grid current (${i}_{\mathrm{s}}$), and grid voltage (${\upsilon}_{\mathrm{s}}$).

Symbol | Parameter | Experimental Value |
---|---|---|

Grid Parameters | ||

${\upsilon}_{\mathrm{s}}$ | Grid voltage | 110 [${V}_{\mathrm{rms}}$] |

${f}_{\mathrm{s}}$ | Grid frequency | 60 [Hz] |

${L}_{\mathrm{s}}$ | Grid filter inductance | 10 [mH] |

Converter Parameters | ||

${V}_{\mathrm{in}}$ | Input voltage | 70 [V] |

${L}_{1}$, ${L}_{2}$ | Inverter inductors | 55 [µH] |

${C}_{1}$, ${C}_{2}$ | Inverter capacitors | 5 [µF] |

Control Parameters | ||

k | Gain of ${C}_{\varphi}$ | 1 |

${k}_{\mathrm{p}}$ | Proportional gain of PR | 50 |

${k}_{\mathrm{i}}$ | Resonant gain of PR | 700 |

${\omega}_{\mathrm{c}}$ | Cut-off frequency of PR | 5 [rad/s] |

a | Zero of phase compensator | 2000 |

b | Pole of phase compensator | 35,000 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lopez-Caiza, D.; Flores-Bahamonde, F.; Kouro, S.; Santana, V.; Müller, N.; Chub, A. Sliding Mode Based Control of Dual Boost Inverter for Grid Connection. *Energies* **2019**, *12*, 4241.
https://doi.org/10.3390/en12224241

**AMA Style**

Lopez-Caiza D, Flores-Bahamonde F, Kouro S, Santana V, Müller N, Chub A. Sliding Mode Based Control of Dual Boost Inverter for Grid Connection. *Energies*. 2019; 12(22):4241.
https://doi.org/10.3390/en12224241

**Chicago/Turabian Style**

Lopez-Caiza, Diana, Freddy Flores-Bahamonde, Samir Kouro, Victor Santana, Nicolás Müller, and Andrii Chub. 2019. "Sliding Mode Based Control of Dual Boost Inverter for Grid Connection" *Energies* 12, no. 22: 4241.
https://doi.org/10.3390/en12224241