# Assessment of Resource and Forecast Modeling of Wind Speed through An Evolutionary Programming Approach for the North of Tehuantepec Isthmus (Cuauhtemotzin, Mexico)

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## Abstract

**:**

## 1. Introduction

## 2. Study Location and Measured Data

#### 2.1. Specific Site Location

#### 2.2. Experimental System and Instrumentation

## 3. Wind Assessment

#### 3.1. Hellman Power Law

#### 3.2. Wind Distribution Function

#### 3.3. Assessment Results

#### 3.3.1. Wind Profile

#### 3.3.2. Data Analysis

^{−3}°C

^{−1}for the warm humid tropical climate conditions of the region. Additionally, presences of $RH$ in the air reduces significantly ${\rho}_{air}$. The statistical results indicate that, for Cuauhtemotzin zone, $RH$ presents a variation of 20% per year with a Std. Dev. $\pm 8.8614$, being the element with the greatest impact on annual ${\rho}_{air}$ fluctuations. Based on the previous description, annual reports of ${\rho}_{air}$ are lower than the standard value assumed in the literature for the evaluation of the wind potential ($\rho $ = 1.225 kg/m${}^{3}$). Therefore, the use of the standardized $\rho $ for the location of Cuauhtemotzin underestimates the wind potential for up to 6.3%.

## 4. Artificial Intelligence Forecasting Modeling

#### 4.1. Multi-Gene Genetic Programming Approach

#### 4.2. Computational Methodology

#### 4.3. Sensitivity Analysis

#### 4.4. Forecast Model Results

#### 4.4.1. Multi-Gene Genetic Programming Model

#### 4.4.2. Sensitivity Analysis Evaluation

#### 4.4.3. MGGP Forecast Model Validation

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Wind power density at 80 m.a.g.l. for the territory of Mexico [6].

**Figure 2.**Location map: (

**a**) the location for Tabasco State; (

**b**) zoom of masts in Cuauhtemotzin (I and II) in municipality of Cardenas; and (

**c**) location and isotach of Cuauhtemotzin site inside orography trajectory to La Venta, Oaxaca showing proximity in latitude and longitude.

**Figure 3.**Sample of wind speeds recorded in Cuauhtemotzin zone for the study heights (26, 33, and 54 m).

**Figure 5.**Bimodal distribution for the wind speeds obtained in the measurement campaign: (

**a**) 26 m (Cuauhtemotzin II); (

**b**) 33 m (Cuauhtemotzin I); and (

**c**) 54 m (Cuauhtemotzin I).

**Figure 6.**Wind direction from the annual measuring campaign in 2016: (

**a**) wind measurements from Cuauhtemotzin I; and (

**b**) wind measurements from Cuauhtemotzin II.

**Figure 8.**Autocorrelation function of the forecast errors for the MGGP with significant limits of 95%.

**Figure 9.**Sensitivity analysis results for the forecasting multi-gene genetic programming developed model.

**Figure 10.**Comparison between experimental WS and simulated values for the first semester of the year (

**a**) January; (

**b**) February; (

**c**) March; (

**d**) April; (

**e**) May; and (

**f**) June.

**Figure 11.**Comparison between experimental WS and simulated values for the second semester of the year: (

**a**) July; (

**b**) August; (

**c**) September; (

**d**) October; (

**e**) November; and (

**f**) December.

Landscape | $\mathit{\alpha}$ |
---|---|

Flat land with ice or grass | 0.08–0.12 |

Sea and coasts | 0.14 |

Little hilly areas | 0.13–0.16 |

Rural zones | 0.20 |

Rugged terrains and forests | 0.20–0.26 |

Very rugged terrains and cities | 0.25–0.40 |

**Table 2.**Comparison and evaluation of the wind profile for Cuauhtemotzin considering implementation cases at different heights.

Parameters | Measured | $\mathit{\alpha}=0.140$ | $\mathit{\alpha}=0.143$ | $\mathit{\alpha}=0.200$ | $\mathit{\alpha}=0.260$ | $\mathit{\alpha}=0.400$ | $\mathit{\alpha}=0.598$ |
---|---|---|---|---|---|---|---|

WS [m/s] | 4.12 | 2.8458 | 2.8520 | 2.9734 | 3.1067 | 3.4414 | 3.9796 |

Error [-] | - | 0.3093 | 0.3078 | 0.2783 | 0.2460 | 0.1647 | 0.0341 |

WTM | h [m] | ${\mathit{WS}}_{\mathit{c}}$ [m/s] | ${\mathit{WS}}_{\mathit{r}}$ [m/s] | ${\mathit{WS}}_{\mathit{\alpha}=\mathbf{0.598}}$ [m/s] | |||

Gamesa G58-850 | 54 | 3.0 | 12.0 | 3.9796 | |||

Unison U54-750 | 60 | 3.0 | 12.0 | 4.2387 | |||

Dewind D4/48-600 | 70 | 3.0 | 12.0 | 4.6486 |

**Table 3.**Statistical parameters results of climatic annual variations for for Cuauhtemotzin, Mexico.

Variable | Units | min. | max. | mean | Std Dev | WS Cross Corr % | |
---|---|---|---|---|---|---|---|

Air temperature | (${T}_{a}$) | [${}^{\circ}$C] | 12.896 | 39.420 | 26.158 | 2.9626 | 11.13% |

Atmospheric Pressure | (${P}_{atm}$) | [mbar] | 998.45 | 1027.55 | 1011.35 | 4.05087 | 21.91% |

Relative Humidity | ($RH$) | [%] | 37.8 | 100 | 86.3940 | 8.8614 | 30.53% |

Wind Direction | ($WD$) | [${}^{\circ}$Deg] | 0 | 355.2 | 125.0309 | 112.5971 | 5.6566% |

Air Density | (${\rho}_{air}$) | [kgm${}^{-3}$] | 1.12274 | 1.24206 | 1.17845 | 0.01488 | 1.6011% |

Solar Radiation | ($SR$) | [Wm${}^{-2}$] | 0.6 | 1276.90 | 198.3771 | 295.9758 | 18.9817% |

Rain | ($Rn$) | [mm] | 0 | 22.61 | 0.044 | 0.46154 | 8.641% |

**Table 4.**PDF models fit comparison for the estimation of wind resource probability in Cuauhtemotzin.

Weibull PDF | ||||||||||

h [m] | c | k | R^{2} | KS | WS [m/s] | WPD [W/m${}^{\mathbf{2}}$] | ||||

26 | 6.1606 | 1.1935 | 0.4107 | 0.9564 | 2.83 | 53.26 | ||||

33 | 6.9670 | 1.2075 | 0.3426 | 0.9521 | 3.43 | 94.83 | ||||

54 | 7.5346 | 1.3035 | 0.2247 | 0.9242 | 4.12 | 144.17 | ||||

Bimodal PDF | ||||||||||

h [m] | A${}_{\mathbf{1}}$ | A${}_{\mathbf{2}}$ | ${\mathit{\sigma}}_{\mathbf{1}}$ | ${\mathit{\sigma}}_{\mathbf{2}}$ | ${\mathit{\mu}}_{\mathbf{1}}$ | ${\mathit{\mu}}_{\mathbf{2}}$ | R${}^{\mathbf{2}}$ | KS | WS [m/s] | WPD [W/m${}^{\mathbf{2}}$] |

26 | 0.0167 | 0.5176 | 0.9201 | 1.6791 | 7.3874 | 2.5156 | 0.9443 | 0.0115 | 2.83 | 51.64 |

33 | 0.0365 | 0.4949 | 1.8319 | 1.8302 | 9.5346 | 2.8232 | 0.9918 | 0.0117 | 3.43 | 114.71 |

54 | 0.4829 | 0.4661 | 2.5970 | 1.8458 | 10.1692 | 3.4685 | 0.9963 | 0.0045 | 4.12 | 181.73 |

Directions [${}^{\circ}$] | Average Wind Velocity [ms${}^{-1}$] | Maximum Wind Velocity [ms${}^{-1}$] | Frequency [Times] | Mean Differences [ms${}^{-1}$] |
---|---|---|---|---|

N | 3.3588 | 11.84 | 6588 | 0.78989 |

NNE | 3.1223 | 11.08 | 7470 | 0.5533 |

NE | 2.9911 | 10.07 | 8462 | 0.42205 |

ENE | 2.8269 | 8.56 | 8091 | 0.25788 |

E | 1.9709 | 8.81 | 3272 | −0.5981 |

ESE | 1.4297 | 8.81 | 1830 | −1.1393 |

SE | 1.1499 | 8.81 | 1884 | −1.4191 |

SSE | 1.2714 | 8.31 | 1894 | −1.2976 |

S | 1.3896 | 14.35 | 1916 | −1.1794 |

SSW | 1.6059 | 11.84 | 1678 | −1.9631 |

SW | 1.3656 | 11.58 | 1353 | −1.2034 |

WSW | 1.0818 | 7.05 | 1023 | −1.4872 |

W | 1.0568 | 6.8 | 1116 | −1.4074 |

WNW | 1.1616 | 6.3 | 1000 | −1.4074 |

NW | 2.0518 | 10.07 | 1140 | −0.5172 |

NNW | 3.9586 | 11.33 | 3518 | 1.3895 |

Parameter | Minimum | Maximum | Units |
---|---|---|---|

Input variables: | |||

Temperature (${T}_{air}$) | 12.896 | 39.420 | [${}^{\circ}$C] |

Relative Humidity ($RH$) | 37.8 | 100 | [%] |

Atmospheric Pressure (${P}_{atm}$) | 998.45 | 1027.55 | [mbar] |

Global Solar Radiation (G) | 0.6 | 1276.90 | [Wm${}^{-2}$] |

1st Past WS ($W{S}_{-1}$) | 0 | 14.35 | [ms${}^{-1}$] |

2nd Past WS ($W{S}_{-2}$) | 0 | 14.35 | [ms${}^{-1}$] |

3rd Past WS ($W{S}_{-3}$) | 0 | 14.35 | [ms${}^{-1}$] |

4th Past WS ($W{S}_{-4}$) | 0 | 14.35 | [ms${}^{-1}$] |

Output variables: | |||

Wind Speed ($WS$) | 0 | 14.35 | [ms${}^{-1}$] |

Parameter | Value |
---|---|

Tournament Size | 10 |

Function Set | $+,\text{}-,\text{}x,\text{}/,\text{}\sqrt{},\text{}sin,\text{}cos,\text{}tan,\text{}sinh,\text{}cosh,\text{}tanh,\text{}ln,\text{}exp,\text{}lo{g}_{10}$ |

Population Size | 100 |

Mutation Probabilities | $0.4$ |

Maximum Tree Depth | 13 |

Maximum Total Nodes | ∞ |

Maximum Genes | 30 |

Maximum Generations | 30 |

Input Variables | 8 |

Elite Fractions | $0.05$ |

ERC Probability | $0.1$ |

Crossover Probability | $0.55$ |

Statistic Parameter | ARIMA | MGGP | |
---|---|---|---|

Train | Test | ||

RMSE | 0.5922 | 0.51799 | 0.52877 |

MAE | 0.4348 | 0.38342 | 0.38831 |

MPE | −8.4893 | −8.5578 | −13.5836 |

R | 0.9498 | 0.95855 | 0.95668 |

Input Variables | Units | ${\mathit{\sigma}}_{\mathit{i}}$ |
---|---|---|

Environmental Temperature | ${T}_{a}$ | $0.014$ |

Relative Humidity | $RH$ | $0.002$ |

Atmospheric Pressure | ${P}_{atm}$ | $0.001$ |

Global Solar Radiation | G | $0.946$ |

1st Past WS | $W{S}_{-1}$ | $1.453$ |

2nd Past WS | $W{S}_{-2}$ | $1.230$ |

3rd Past WS | $W{S}_{-3}$ | $0.782$ |

4th Past WS | $W{S}_{-4}$ | $0.001$ |

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## Share and Cite

**MDPI and ACS Style**

López-Manrique, L.M.; Macias-Melo, E.V.; May Tzuc, O.; Bassam, A.; Aguilar-Castro, K.M.; Hernández-Pérez, I. Assessment of Resource and Forecast Modeling of Wind Speed through An Evolutionary Programming Approach for the North of Tehuantepec Isthmus (Cuauhtemotzin, Mexico). *Energies* **2018**, *11*, 3197.
https://doi.org/10.3390/en11113197

**AMA Style**

López-Manrique LM, Macias-Melo EV, May Tzuc O, Bassam A, Aguilar-Castro KM, Hernández-Pérez I. Assessment of Resource and Forecast Modeling of Wind Speed through An Evolutionary Programming Approach for the North of Tehuantepec Isthmus (Cuauhtemotzin, Mexico). *Energies*. 2018; 11(11):3197.
https://doi.org/10.3390/en11113197

**Chicago/Turabian Style**

López-Manrique, Luis M., E. V. Macias-Melo, O. May Tzuc, A. Bassam, K. M. Aguilar-Castro, and I. Hernández-Pérez. 2018. "Assessment of Resource and Forecast Modeling of Wind Speed through An Evolutionary Programming Approach for the North of Tehuantepec Isthmus (Cuauhtemotzin, Mexico)" *Energies* 11, no. 11: 3197.
https://doi.org/10.3390/en11113197