# Digital Twins of the Water Cooling System in a Power Plant Based on Fuzzy Logic

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## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. Cooling System Description

#### 3.1. Power Plant Specifications

#### 3.2. Water Cooling System

## 4. Digital Twins of the Cooling System

#### 4.1. Data Acquisition Systems

#### 4.2. Data Preprocessing

#### 4.3. Reduction of Variables

#### 4.4. Automatic Extraction of Rules Using Fuzzy Logic

#### 4.5. Dynamically Updating the Knowledge Base

#### 4.6. Cooling System Fan Optimization Module

## 5. Experimental Results

#### 5.1. Operation of the Model during Steady-State

#### 5.2. Operation of the Model during the Plant Stop and Start Ramps

#### 5.3. Model Operation during Period with Transients

#### 5.4. Optimization of the Number of Fans Using Digital Twins

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

DG | Diesel Genset |

SCADA | Supervisory Control and Data acquisition |

PID | Proportional–Integral–Derivative controller |

GAs | Genetic Algorithms |

LT | Low Temperature |

HT | High Temperature |

NumFanOn | Number of Fans connected |

${T}_{in}\_HT$ | Reference Temperature at the radiator’s HT inlet |

${T}_{out}\_HT$ | Reference Temperature at the radiator’s HT Outlet |

ANN | Artificial Neural Network |

SVM | Support Vector Machine |

VIA | Validity Internal Analysis |

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**Figure 15.**Process inputs: (

**a**) powers of DGs; (

**b**) ${T}_{in}\_HT$ and environmental temp, and (

**c**) reduced inputs and $NumFanOn$.

**Figure 17.**Process inputs: (

**a**) powers of DGs; (

**b**) ${T}_{in}\_HT$ and environmental temp, and (

**c**) reduced inputs and $NumFanOn$.

**Figure 19.**Result of model’s self-validation versus actual ${T}_{out\_HT}$ value and instantaneous percentage error.

**Figure 20.**Process inputs: (

**a**) powers of DG’s; (

**b**) ${T}_{in}\_HT$ and environmental temp, and (

**c**) reduced inputs and $NumFanOn$.

E\ΔE | NB | NM | NS | Z | PS | PM | PB |
---|---|---|---|---|---|---|---|

NB | NVB | NB | NB | NM | NM | NS | Z |

NM | NB | NB | NM | NM | NB | Z | PS |

NS | NB | NM | NM | NS | Z | PS | PM |

Z | NM | NM | NS | Z | PS | PM | PM |

PS | NM | NS | Z | PS | PM | PM | PB |

PM | NS | Z | PS | PM | PM | PB | PB |

PB | Z | PS | PM | PM | PB | PB | PVB |

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**MDPI and ACS Style**

Alves de Araujo Junior, C.A.; Mauricio Villanueva, J.M.; Almeida, R.J.S.d.; Azevedo de Medeiros, I.E.
Digital Twins of the Water Cooling System in a Power Plant Based on Fuzzy Logic. *Sensors* **2021**, *21*, 6737.
https://doi.org/10.3390/s21206737

**AMA Style**

Alves de Araujo Junior CA, Mauricio Villanueva JM, Almeida RJSd, Azevedo de Medeiros IE.
Digital Twins of the Water Cooling System in a Power Plant Based on Fuzzy Logic. *Sensors*. 2021; 21(20):6737.
https://doi.org/10.3390/s21206737

**Chicago/Turabian Style**

Alves de Araujo Junior, Carlos Antonio, Juan Moises Mauricio Villanueva, Rodrigo José Silva de Almeida, and Isaac Emmanuel Azevedo de Medeiros.
2021. "Digital Twins of the Water Cooling System in a Power Plant Based on Fuzzy Logic" *Sensors* 21, no. 20: 6737.
https://doi.org/10.3390/s21206737