# Wind Speed Forecast for Sudan Using the Two-Parameter Weibull Distribution: The Case of Khartoum City

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{p}of grid-connected wind power plants is planned to be constructed in high-potential regions [5]. In 2021, the country witnessed the arrival of the first wind turbine, which will have its electricity generation fed into the national network serving 14,000 people, and has already been installed in Dongola, a rich in wind energy northern city [6].

## 2. Experimental Setup

## 3. Analysis Methodology

#### 3.1. Data Filtering

#### 3.2. Missing Data Imputation

#### 3.3. Weibull Distribution

#### 3.4. Parameter Estimation

#### 3.4.1. Analytical Methods

#### Energy Pattern Factor Method

#### Graphical Method

#### Method of Moments

#### Least Square Method

#### 3.4.2. Stochastic Method

#### Firefly Algorithm

#### Objective Function

#### 3.5. Goodness-of-Fit

^{2}), represented by Equation (20) [19,50,55], the mean absolute error (MAE) in Equation (21) [50,55,57], and the Kolmogorov–Smirnov test (K-S) presented in Equation (22) [45,56]. If we used the cumulative density function to evaluate these metrics, the latter variants are associated with the P-P plot. On the other hand, the variants evaluated using the probability density function are associated with the Q-Q plot. However, the P-P goodness-of-fit criteria are favored because the cumulative density function generates an unbiased estimate of the Weibull parameters [60].

## 4. Results and Discussion

^{2}

_{PP}and R

^{2}

_{QQ}. If we rely on visual comparison and inspection to determine the quality of the methods used in estimating the parameters of the Weibull distribution, then Figure 12, Figure 13, Figure 14 and Figure 15 explicitly show the superiority of the artificial intelligence technique. Additionally, these figures prove that the Weibull distribution perfectly describes the wind data at the NERC site. We can understand the dominance of the FA over the rest of the prediction methods due to the apparent nonlinearity in the wind speed data by looking at the regression analysis results in Table 5, which favors the stochastic metaheuristic methods in such cases. Moreover, the average wind speeds were evaluated by employing $\widehat{k}$ and $\widehat{c}$ to Equation (3), and are given in Table 4. The average speed corresponding to the FA method equals $3.73\mathrm{m}/\mathrm{s}$.

_{p}wind turbine recently installed at the NERC campus.

## 5. Conclusions

- A higher and multi-anemometer mast wind station must be installed locally to facilitate the vertical extrapolation of wind speed in heights compatible with utility-scale power production.
- Figure 15 demonstrates the high capacity of stochastic methods, in particular the swarm intelligence algorithms, in predicting the wind speed in the region, making this technique the best choice for domestic meteorological and forecasting research.
- Private sector participation in power generation from clean energy resources such as wind can fill the energy demand gap in Sudan. Hence, soft financing means provided by the stakeholders and international institutions will be the base for such contributions.
- Wind turbine manufacturers need to deploy pilot projects in the country, preferably under the supervision of the NERC, to inspect the prospects of this investment.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

$c$ | Scale parameter |

$\widehat{c}$ | Scale estimator |

$f\left(V\right)$ | Probability density function |

$F\left(V\right)$ | Cumulative density function |

$k$ | Shape parameter |

$\widehat{k}$ | Shape estimator |

$v$ | Wind speed (m/s) |

$\mu $ | Arithmetic mean |

${\sigma}^{2}$ | variance |

$\mathsf{\Gamma}\left(\mathrm{x}\right)$ | Gamma function |

EM | Empirical method |

EPFM | Energy pattern factor method |

FA | Firefly algorithm |

GM | Graphical method |

MLM | Maximum likelihood method |

MMLM | Modified maximum likelihood method |

MOM | Method of moments |

LSM | Least square method |

NERC | National Energy Research Center |

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**Figure 2.**Distribution of wind potential. Reprinted with permission from Ref. [4]. 2022, IRENA.

**Figure 5.**Wind speed time series chart as recorded by the NERC meteorological mast station between March 2017 and January 2018.

**Figure 6.**Frequency histogram of wind speed as recorded by the NERC meteorological mast station between March 2017 and January 2018.

**Figure 7.**Weibull probability density function at different $k$ values.Reprinted with permission from Ref. [43]. 2006, Springer Nature.

**Figure 8.**Typical Weibull cumulative density function. Reprinted with permission from Ref. [43]. 2006, Springer Nature.

**Table 1.**Wind energy potential for different cities in Sudan. Adapted with permission from Ref. [20]. 2008, Elsevier.

City | Altitude (m) | Annual Wind Speed Based on Weibull Distribution (m/s) | Shape Parameter (k) |
---|---|---|---|

Abu Na’ama | 445 | 3.1 | 2.2 |

Atbara | 345 | 4.2 | 1.75 |

El Fasher | 733 | 3.4 | 1.15 |

El Geneina | 805 | 3.1 | 1.9 |

El Obeid | 570 | 3.4 | 1.9 |

Karima | 250 | 4.7 | 1.7 |

Kassala | 500 | 4 | 1.95 |

Khartoum | 380 | 4.8 | 1.9 |

Kosti | 380 | 4 | 1.8 |

Port Sudan | 5 | 5 | 1.6 |

Shambat ^{1} | 380 | 4.8 | 2.1 |

Wadi Halfa | 190 | 4.6 | 1.8 |

Wad Madani | 405 | 4.8 | 1.8 |

^{1}Shambat is a station within Khartoum North city.

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

Stopping criterion | $t$ | 1000 iterations |

Population size | $n$ | 16 fireflies |

Lower bound | $lb$. | 0 |

Upper bound | $ub$ | 10 |

Scaling factor | ${\alpha}_{0}$ | 0.1 |

Cooling factor | $\delta $ | 0.95 to 0.97 |

Attractiveness | ${\beta}_{0}$ | 1 |

$\gamma $ | 0.316 | |

Random number | rand | 0 to 1 |

Wind Speed Class (m/s) | Average Wind Speed (m/s) | Frequency | Frequency Percentage | Cumulative Frequency Percentage |
---|---|---|---|---|

0.01–1.00 | 0.749 | 540 | 1.20% | 1.20% |

1.01–2.00 | 1.603 | 4010 | 8.70% | 9.90% |

2.01–3.00 | 2.530 | 8309 | 18.10% | 28.00% |

3.01–4.00 | 3.491 | 9986 | 21.70% | 49.70% |

4.01–5.00 | 4.482 | 8460 | 18.40% | 68.10% |

5.01–6.00 | 5.472 | 6621 | 14.50% | 82.60% |

6.01–7.00 | 6.454 | 4328 | 9.40% | 92.00% |

7.01–8.00 | 7.436 | 2222 | 4.80% | 96.80% |

8.01–9.00 | 8.419 | 889 | 2.00% | 98.80% |

9.01–10.00 | 9.429 | 386 | 0.80% | 99.60% |

10.01–11.00 | 10.413 | 115 | 0.20% | 99.80% |

11.01–12.00 | 11.442 | 38 | 0.10% | 99.90% |

12.01–13.00 | 12.484 | 19 | 0.10% | 100.00% |

13.01–14.00 | 13.416 | 10 | 0.00% | 100.00% |

14.01–15.00 | 14.942 | 1 | 0.00% | 100.00% |

15.01–16.00 | 15.638 | 2 | 0.00% | 100.00% |

Method | $\mathit{k}$ | $\mathit{c}$ | Average Wind Speed | RMSE_{PP} | RMSE_{QQ} | R^{2}_{PP} | R^{2}_{QQ} | MAE_{PP} | MAE_{QQ} | KS |
---|---|---|---|---|---|---|---|---|---|---|

EPFM | 1.918 | 9.174 | 8.14 | 0.3176 | 0.0672 | 0.117 | 0.2109 | 0.2674 | 0.0559 | 0.5208 |

FA | 2.197 | 4.211 | 3.73 | 0.0056 | 0.0229 | 0.999 | 0.908 | 0.0033 | 0.014 | 0.0139 |

GM | 2.043 | 4.967 | 4.4 | 0.0631 | 0.0198 | 0.965 | 0.9316 | 0.0423 | 0.0142 | 0.1255 |

LSM | 1.213 | 6.869 | 6.44 | 0.1898 | 0.055 | 0.685 | 0.471 | 0.1643 | 0.0445 | 0.3157 |

MOM | 2.469 | 4.778 | 4.24 | 0.0529 | 0.0092 | 0.975 | 0.985 | 0.0315 | 0.0061 | 0.1278 |

Statistic | Value |
---|---|

R | 0.003 |

R^{2} | 0.000 |

Adjusted R^{2} | 0.000 |

Standard Error | 1.85 |

Significance F (ANOVA test) | 0.538 |

Wind Direction (Degree) | Wind Direction | Average Wind Speed | Frequency Percentage |
---|---|---|---|

345–15 | N | 4.2384 | 16.029% |

15–45 | NNE | 3.9889 | 4.075% |

45–75 | ENE | 2.88 | 1.398% |

75–105 | E | 3.23 | 1.431% |

105–135 | ESE | 4.066 | 2.494% |

135–165 | SSE | 3.997 | 8.411% |

165–195 | S | 4.285 | 13.903% |

195–225 | SSW | 4.51 | 10.669% |

225–255 | WSW | 3.686 | 3.500% |

255–285 | W | 2.763 | 1.727% |

285–315 | WNW | 3.213 | 7.339% |

315–345 | NNW | 4.567 | 29.046% |

Total | 100% |

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## Share and Cite

**MDPI and ACS Style**

Younis, A.; Elshiekh, H.; Osama, D.; Shaikh-Eldeen, G.; Elamir, A.; Yassin, Y.; Omer, A.; Biraima, E.
Wind Speed Forecast for Sudan Using the Two-Parameter Weibull Distribution: The Case of Khartoum City. *Wind* **2023**, *3*, 213-231.
https://doi.org/10.3390/wind3020013

**AMA Style**

Younis A, Elshiekh H, Osama D, Shaikh-Eldeen G, Elamir A, Yassin Y, Omer A, Biraima E.
Wind Speed Forecast for Sudan Using the Two-Parameter Weibull Distribution: The Case of Khartoum City. *Wind*. 2023; 3(2):213-231.
https://doi.org/10.3390/wind3020013

**Chicago/Turabian Style**

Younis, Abubaker, Hazim Elshiekh, Duaa Osama, Gamar Shaikh-Eldeen, Amin Elamir, Yassir Yassin, Ali Omer, and Elfadil Biraima.
2023. "Wind Speed Forecast for Sudan Using the Two-Parameter Weibull Distribution: The Case of Khartoum City" *Wind* 3, no. 2: 213-231.
https://doi.org/10.3390/wind3020013