# Data-Driven Decentralized Algorithm for Wind Farm Control with Population-Games Assistance

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## Abstract

**:**

## 1. Introduction

- the algorithm proposed in this paper uses historical information of the system evolution to compute multiple directions of the gradient estimations in a decentralized fashion and for every single wind turbine, i.e., it is not necessary to share information among turbines, and
- the proposed approach produces global solutions due to the availability of the total generated power amount.

#### Notation

## 2. Problem Statement

## 3. Preliminary Concepts

#### 3.1. Gradient Estimation

**Remark**

**1.**

- 1.
- to be able to capture measurements of the unknown function f, and
- 2.
- to know the correspondence of the measurement with the element in the domain of f, i.e., for a measurement $f\left(\mathit{d}\right)$ the element $\mathit{d}$ in the domain of f is known.

#### 3.2. Population-Game Role

**Definition**

**1.**

**Definition**

**2.**

## 4. Algorithms According to Information Availability

#### 4.1. Using Multiple Measurements at Each Iteration

**Remark**

**2.**

#### 4.2. Using a Single Measurement at Each Iteration

## 5. Data-Driven Decentralized Control of Wind Farms

## 6. Case Study and Simulation Results

- Scenario 1: the free-stream wind speed was below the rated value and all wind turbines are working in maximization of the energy capture.
- Scenario 2: the free-stream wind speed was above the rated value and some turbines are working in power limitation (at 2 MW).

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Example gradient estimation with four strategies $\mathcal{S}\left(k\right)\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}\{{\mathit{s}}_{k}^{1},{\mathit{s}}_{k}^{2},{\mathit{s}}_{k}^{3},{\mathit{s}}_{k}^{4}\}$, i.e., $n=4$, and $f:{\mathbb{R}}^{2}\mapsto \mathbb{R}$, i.e., $m=2$. Vectors illustrate the direction for the strategies update and the superposition of influences over strategy with index 1. (

**a**) Various available measurements every iteration, (

**b**) one available measurement every iteration.

**Figure 4.**General scheme for the gradient-estimation-based algorithm with population-games assistance.

**Figure 5.**Typical decentralized control scheme. Each wind turbine has information about the total generated power and its own axial induction factor.

**Figure 7.**(

**a**) Total powers for scenario 1 (free-stream wind speed of 10 m/s) for four wind speed directions. (

**b**) Power generated by wind turbines 1–10 and with wind direction of ${45}^{\xb0}$. (

**c**) Axial coefficients for wind turbines 1–10 and with wind direction of ${45}^{\xb0}$.

**Figure 8.**(

**a**) Total powers for scenario 2 (free-stream wind speed of 12 m/s) for four wind speed directions. (

**b**) Power generated by wind turbines 1–10 and with wind direction of ${45}^{\xb0}$. (

**c**) Axial coefficients for wind turbines 1–10 and with wind direction of ${45}^{\xb0}$.

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## Share and Cite

**MDPI and ACS Style**

Barreiro-Gomez, J.; Ocampo-Martinez, C.; Bianchi, F.D.; Quijano, N.
Data-Driven Decentralized Algorithm for Wind Farm Control with Population-Games Assistance. *Energies* **2019**, *12*, 1164.
https://doi.org/10.3390/en12061164

**AMA Style**

Barreiro-Gomez J, Ocampo-Martinez C, Bianchi FD, Quijano N.
Data-Driven Decentralized Algorithm for Wind Farm Control with Population-Games Assistance. *Energies*. 2019; 12(6):1164.
https://doi.org/10.3390/en12061164

**Chicago/Turabian Style**

Barreiro-Gomez, Julian, Carlos Ocampo-Martinez, Fernando D. Bianchi, and Nicanor Quijano.
2019. "Data-Driven Decentralized Algorithm for Wind Farm Control with Population-Games Assistance" *Energies* 12, no. 6: 1164.
https://doi.org/10.3390/en12061164