# Multi-Objective Predictive Control Optimization with Varying Term Objectives: A Wind Farm Case Study

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Multi Objective Optimization with Priorities

#### 2.2. Area-Wise Wind Speed Estimation

#### 2.3. Windmill Park Simulator

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

MPC | Model Predictive Control |

dMPC | distributed Model Predicitve Control |

MOOP | Multi Objective Optimization Procedure |

UAV | Unmanned Aerial Vehicle |

## References

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**Figure 2.**Windmill park conceptualisation as area-wise controlled sub-systems with limited interaction from wind direction and speed. The interaction intensity fades (with colour) as it travels through the system; the direction is limited to the arrow indicators, hence the interaction matrix is not fully coupled, which further motivates the use of distributed control.

**Figure 3.**Schematic summary of the over-simplified model used for each sub-system in the windmill park.

**Figure 4.**Flowchart of the sequential prioritized optimization scheme. Model based predictive control (MPC).

**Figure 5.**Illustration of the multiple objectives as a function of time and operation range percentage.

**Figure 7.**Example of testing the safety limits of operation of the park. Contour plot, blue colour denotes lowest values. The maximum value (red) corresponds to a 90–100% power extraction, while the lowest value (blue) corresponds to 0–10% power extraction.

**Figure 8.**Contour plot of power output for variable wind speed conditions.

**Left**: MOOP optimization.

**Right**: global optimization. The maximum value (red) corresponds to a 90–100% power extraction, while the lowest value (blue) corresponds to 0–10% power extraction.

**Figure 9.**Contour plot of power output for constant wind speed conditions. Left: MOOP optimization. Right: Global optimization. The maximum value (red) corresponds to a 90–100% power extraction, while the lowest value (blue) corresponds to 0–10% power extraction.

**Table 1.**Normalized units in percent for variable wind speed conditions. Distributed MPC (dMPC), Global and Multi-objective optimization priority (MOOP) methods.

Method | Performance | Total Power Output | Cost |
---|---|---|---|

Global dMPC | 88 | 85 | 91 |

MOOP dMPC | 63 | 71 | 68 |

Method | Performance | Total Power Output | Cost |
---|---|---|---|

Global dMPC | 90 | 95 | 91 |

MOOP dMPC | 87 | 91 | 88 |

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**MDPI and ACS Style**

Ionescu, C.M.; Caruntu, C.F.; Cajo, R.; Ghita, M.; Crevecoeur, G.; Copot, C.
Multi-Objective Predictive Control Optimization with Varying Term Objectives: A Wind Farm Case Study. *Processes* **2019**, *7*, 778.
https://doi.org/10.3390/pr7110778

**AMA Style**

Ionescu CM, Caruntu CF, Cajo R, Ghita M, Crevecoeur G, Copot C.
Multi-Objective Predictive Control Optimization with Varying Term Objectives: A Wind Farm Case Study. *Processes*. 2019; 7(11):778.
https://doi.org/10.3390/pr7110778

**Chicago/Turabian Style**

Ionescu, Clara M., Constantin F. Caruntu, Ricardo Cajo, Mihaela Ghita, Guillaume Crevecoeur, and Cosmin Copot.
2019. "Multi-Objective Predictive Control Optimization with Varying Term Objectives: A Wind Farm Case Study" *Processes* 7, no. 11: 778.
https://doi.org/10.3390/pr7110778