# Nonlinear Robust Control for Low Voltage Direct-Current Residential Microgrids with Constant Power Loads

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## Abstract

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## 1. Introduction

- Robust stability against arbitrary (bounded) changes in source voltage, output power, inductance and capacitance on the desired operating-point.
- Flexibility for use with the basic converters and even in a reconfigurable scheme.
- Low implementation time and cost.
- Easy tuning for a certain desired response.

## 2. Modeling

#### 2.1. Voltage-Mode Modeling

- S1, S2 closed, S3, M2 open and PWM switching on M1, buck.
- M1, S2 closed, S1, S3 open and PWM switching on M2, boost.
- M2, S3 closed, S1, S2 open and PWM switching on M1, buck-boost.

- a buck PEC if $0\le u\le 1$
- a boost PEC if $u>1$
- a buck-boost PEC if $u<0$

- buck duty-cycle for $0\le u\le 1$ is $u=\stackrel{\u02c7}{u}$
- boost duty-cycle for $u>1$ is $u=\frac{1}{1-\widehat{u}}$
- buck-boost duty-cycle for $u<0$ is $u=\frac{\tilde{u}}{\tilde{u}-1}$

#### 2.2. Current-Mode Modeling

## 3. Controller Design and Stability

#### 3.1. Feedback Linearization for Voltage-Mode Controller

**Proposition**

**1.**

#### 3.2. Taylor Series Linearization for Voltage-Mode Controller

#### 3.3. Taylor Series Linearization for Current-Mode Controller

## 4. Experimental Behavior

#### 4.1. Equipment

#### 4.2. Procedure

#### 4.3. Discussion of the Results

#### 4.4. Brief Comparison with Other Proposals

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**Illustrative block diagram of a microgrid. RPEC, reconfigurable power electronic converter.

**Figure 7.**Output voltage (purple, bottom) and current responses (yellow, middle) for e (blue, top) abrupt changes.

**Figure 8.**Output voltage (purple, bottom) and current responses (yellow, middle) for constant e (blue, top) and P abrupt changes.

**Figure 9.**Output voltage (purple, bottom) and current responses (yellow, middle) for constant e (blue, top) and a capacitor change from 1 to $4.9$ $\mathsf{\mu}\mathrm{F}$ alternating every 5 s.

**Figure 10.**Output voltage (purple, bottom) and current responses (yellow, middle) for constant e (blue, top) and an inductor change from $1.15$ to $2.3$ mH alternating every 5 s.

**Figure 11.**Output voltage (purple, bottom) and current responses (yellow, middle) for constant e (blue, top) and a large P change (out of the design bound $P\left(t\right)=110\notin [45,100]$ W).

Type of Controller | Theory Difficulty | Implementation Complexity | Dynamic Response | Remarks |
---|---|---|---|---|

Active stabilizer [8] | High | High | Good | Good performance and a digital platform is used, in this case, a dSPACE. |

Active damping [9] | Medium | Medium | Good | Good performance and a digital platform is used, in this case a pair of DSPs. |

Linear [10] | High | High | Good | Good performance and only numerical results are reported. |

Sum of squares [11] | High | High | Medium | Medium performance and only numerical results are reported. |

Algebraic [12] | Medium | Medium | Medium | Medium performance and only numerical results are reported. |

Sliding mode [13] | Medium | High | Good | Good performance and only numerical results are reported. |

Linear damping [14] | Medium | High | Good | Good performance and a digital platform is used, in this case a DSP. |

Robust stability [15] | High | High | Medium | Medium performance and only numerical results are reported. |

Drop control [16] | High | High | Good | Good performance and only numerical results are reported. |

Fractional order controller [17] | High | High | Medium | Medium performance and only numerical results are reported. |

Robust stability [19] | High | High | Medium | Medium performance and only numerical results are reported. |

Proposed approach | Medium | Low | High | Good performance and a low cost digital platform is used, in this case, a microcontroller. |

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## Share and Cite

**MDPI and ACS Style**

Rodríguez-Licea, M.-A.; Pérez-Pinal, F.-J.; Nuñez-Perez, J.-C.; Herrera-Ramirez, C.-A. Nonlinear Robust Control for Low Voltage Direct-Current Residential Microgrids with Constant Power Loads. *Energies* **2018**, *11*, 1130.
https://doi.org/10.3390/en11051130

**AMA Style**

Rodríguez-Licea M-A, Pérez-Pinal F-J, Nuñez-Perez J-C, Herrera-Ramirez C-A. Nonlinear Robust Control for Low Voltage Direct-Current Residential Microgrids with Constant Power Loads. *Energies*. 2018; 11(5):1130.
https://doi.org/10.3390/en11051130

**Chicago/Turabian Style**

Rodríguez-Licea, Martín-Antonio, Francisco-Javier Pérez-Pinal, Jose-Cruz Nuñez-Perez, and Carlos-Alonso Herrera-Ramirez. 2018. "Nonlinear Robust Control for Low Voltage Direct-Current Residential Microgrids with Constant Power Loads" *Energies* 11, no. 5: 1130.
https://doi.org/10.3390/en11051130