Renewable energy is a safe and limitless energy source that can be utilized for heating, cooling, and other purposes. Wind energy is one of the most important renewable energy sources. Power fluctuation of wind turbines occurs due to variation of wind velocity. A wind cube is used to decrease power fluctuation and increase the wind turbine’s power. The optimum design for a wind cube is the main contribution of this work. The decisive design parameters used to optimize the wind cube are its inner and outer radius, the roughness factor, and the height of the wind turbine hub. A Gradient-Based Optimizer (GBO) is used as a new metaheuristic algorithm in this problem. The objective function of this research includes two parts: the first part is to minimize the probability of generated energy loss, and the second is to minimize the cost of the wind turbine and wind cube. The Gradient-Based Optimizer (GBO) is applied to optimize the variables of two wind turbine types and the design of the wind cube. The metrological data of the Red Sea governorate of Egypt is used as a case study for this analysis. Based on the results, the optimum design of a wind cube is achieved, and an improvement in energy produced from the wind turbine with a wind cube will be compared with energy generated without a wind cube. The energy generated from a wind turbine with the optimized cube is more than 20 times that of a wind turbine without a wind cube for all cases studied.
Quality of life improvements are necessary as an economy and society develop. One corresponding challenge is to decrease environmental pollution. Replacing fossil fuels with clean energy is one of the main components to decrease environmental pollution. Renewable energy utilized at a large scale can help to meet daily energy demands [
The following items summarize the contributions of this paper:
Increasing the power generated from the wind turbine over a year using the wind cube. The inner and outer radius of the wind cube, roughness factor and the height of the wind turbine hub are the decision variables extracted using a new optimization algorithm (Gradient-Based Optimizer). Comparison between the proposed GBO algorithm with Tunicate swarm algorithm (TSA) and Chimp optimization algorithm (ChOA) is performed for the same wind turbine. Minimizing the probability generated energy loss. Minimizing the wind turbine and wind cube cost using the meter cubic function. Comparison between the power generated from the wind turbine with and without a wind cube.
The paper organization is as follows, Section two explains the problem formulation and metrological data. The objective function is illustrated also in Section 2. Section 3 dissects the Gradient-Based Optimizer algorithm. The study cases are illustrated in Section 4. The conclusion and future work is in Section 5.
The variation of wind speed is the main factor affecting the power generated from the wind turbine. The characteristics of wind turbine output power are dependent on the boundaries of the wind speed (cut-in speed
where
where
Based on Bernoulli’s theory and continuity equation, the main equation for the wind cube is shown as follows:
where
where
Hurghada City in the Red Sea governate of Egypt is the site used in this work to simulate the power output improvement. The latitude is
The improvement to the power generated from the wind turbine corresponds with decreasing the loss of energy generated probability (LEGP) with the maximum speed out from the outer radius of the wind cube not increasing 80% of the cut-off speed for the turbine. The decision variables required for optimal sizing are the two radiuses of the wind cube, the wind turbine hub’s height, and the roughness factor. The mathematical equation for the LEGP is as follows:
where
Recently, Ahmadianfar et al. [
In the GBO, the control parameters α and the probability rate are used to balance and switch from exploration to exploitation. Furthermore, the population size and iteration numbers are due to the problem’s complexity. In the GBO, N vectors in a D-dimensional search space can be defined as:
Usually, the initial vectors of the GBO are randomly generated in the D-dimensional search domain, which can be defined as:
where
In the GBO algorithm, to guarantee a balance between exploration of significant search space regions and exploitation to reach near optimum and global points, a significant factor
where
The concept of GSR is to provide the GBO algorithm with a random behavior through iterations, therefore strengthening exploration behavior and escape from local optima. In
where
Moreover, Direction Movement (DM) is employed to converge around the solution area
where, rand is a uniform distributed number within the range [0, 1], and
Finally, depending on these terms GSR and DM,
where,
where
while
Specifically, the GBO algorithm aims to enhance the exploration and exploitation phases using
where
The LEO is introduced to strengthen the performance of the optimization algorithm to solve complex problems. The LEO can effectively update the position of the solution, to assist an algorithm to exit local optima points and speed the convergence of the optimization algorithm. The LEO targets generate a new solution with a superior performance
where
where
where
where
and
For fair benchmark comparison, the simulation settings are the same for all algorithms. furthermore, the algorithm parameter is set to their default values. This section presents the analysis of the proposed algorithm's results for the wind turbine explained in
Type | Rated power | Rotor radius | Cut-in speed | Cut-off speed | Rated speed |
---|---|---|---|---|---|
6 kW | 6000 | 3.05 | 3.6 | 25 | 9.8 |
30 kW | 30000 | 5.5 | 3.6 | 25 | 13.4 |
Type | Lower boundaries | Upper boundaries | ||
---|---|---|---|---|
6 kW | 30 kW | 6 kW | 30 kW | |
4.96 | 6.5 | 6 | 15 | |
3.1 | 5.55 | 3.5 | 5.95 | |
30 | 30 | 60 | 60 | |
0.14 | 0.14 | 0.25 | 0.25 |
Based on analysis described in Section 2 and data reported in
Based on analysis described in Section 2 and data reported in
Run | A | ||||
---|---|---|---|---|---|
1 | 57.40128 | 0.157887 | 3.311413 | 5.942579 | 1129.561463 |
2 | 45.26694 | 0.152597 | 3.226155 | 5.8442 | 853.4763615 |
3 | 48.98618 | 0.222489 | 3.157694 | 5.918605 | 915.509757 |
4 | 32.27097 | 0.194206 | 3.217166 | 5.97835 | 620.6787187 |
5 | 57.46627 | 0.214215 | 3.119393 | 5.748713 | 1030.513524 |
6 | 40.41741 | 0.157574 | 3.114831 | 5.703932 | 718.0874355 |
7 | 50.6326 | 0.169845 | 3.297265 | 5.90975 | 986.6271951 |
8 | 54.04965 | 0.220564 | 3.195539 | 5.836084 | 1007.995303 |
9 | 46.48875 | 0.245294 | 3.189204 | 5.851694 | 867.5845803 |
10 | 51.28276 | 0.179077 | 3.178343 | 5.976067 | 974.0640628 |
11 | 56.23774 | 0.152181 | 3.256936 | 5.863454 | 1073.966373 |
12 | 42.95625 | 0.174857 | 3.102174 | 5.894946 | 785.5472124 |
13 | 52.33389 | 0.155133 | 3.33319 | 5.951809 | 1038.226451 |
14 | 54.72452 | 0.221956 | 3.376278 | 5.98674 | 1106.141125 |
15 | 47.29105 | 0.191712 | 3.128933 | 5.646466 | 835.510537 |
16 | 48.00857 | 0.166523 | 3.295603 | 5.905486 | 934.3494325 |
17 | 56.98286 | 0.218793 | 3.285613 | 5.866266 | 1098.303595 |
18 | 56.9222 | 0.144987 | 3.125514 | 5.91272 | 1051.938866 |
19 | 46.19192 | 0.193511 | 3.111921 | 5.582244 | 802.4229603 |
20 | 31.96327 | 0.160249 | 3.125179 | 5.952396 | 594.5903487 |
21 | 52.14464 | 0.229889 | 3.328248 | 5.888502 | 1021.951462 |
22 | 49.90867 | 0.233568 | 3.133448 | 5.86657 | 917.4507097 |
23 | 49.84812 | 0.140284 | 3.116203 | 5.631328 | 874.7529775 |
24 | 50.54733 | 0.226675 | 3.122786 | 5.923438 | 935.0056141 |
25 | 57.52945 | 0.163827 | 3.268732 | 5.759444 | 1083.053909 |
26 | 32.30148 | 0.157218 | 3.139406 | 5.784851 | 586.6271031 |
27 | 56.02531 | 0.201424 | 3.100072 | 5.971138 | 1037.081919 |
28 | 51.44141 | 0.168626 | 3.161804 | 5.712825 | 929.1776024 |
29 | 31.19217 | 0.169806 | 3.171518 | 5.947532 | 588.3686953 |
Algorithm | A | ||||
---|---|---|---|---|---|
GBO | 31.08461 | 0.168752 | 3.15661 | 5.929514 | |
TSA | 33.95042 | 0.151096 | 3.190784 | 5.859134 | 634.7109261 |
ChOA | 32.71091 | 0.164894 | 3.130075 | 5.811248 | 594.9997839 |
Run | α | ||||
---|---|---|---|---|---|
1 | 33.9903 | 0.168467 | 5.576217 | 10.58872 | 2006.95769 |
2 | 41.23584 | 0.176445 | 5.90803 | 11.04344 | 2690.430679 |
3 | 59.99437 | 0.249611 | 5.947948 | 10.66068 | 3804.191615 |
4 | 34.07007 | 0.150989 | 5.593785 | 10.59017 | 2018.280502 |
5 | 41.17549 | 0.160371 | 5.915031 | 11.0462 | 2690.349584 |
6 | 59.99185 | 0.24995 | 5.94891 | 10.66202 | 3805.125321 |
7 | 56.3486 | 0.17893 | 5.787966 | 10.52267 | 3431.904241 |
8 | 46.87051 | 0.153597 | 5.65338 | 10.44837 | 2768.576657 |
9 | 59.66264 | 0.243826 | 5.732932 | 10.28951 | 3519.441572 |
10 | 46.07201 | 0.21587 | 5.72789 | 10.60664 | 2799.044078 |
11 | 56.52102 | 0.155246 | 5.551946 | 10.11289 | 3173.441056 |
12 | 51.64603 | 0.24933 | 5.552197 | 10.13934 | 2907.444836 |
13 | 33.72516 | 0.205779 | 5.799582 | 11.08859 | 2168.836732 |
14 | 35.23807 | 0.212581 | 5.807014 | 11.06361 | 2263.924172 |
15 | 53.90231 | 0.147021 | 5.881671 | 10.75907 | 3411.007878 |
16 | 30.02507 | 0.223701 | 5.841212 | 11.34799 | 1990.24277 |
17 | 45.81277 | 0.17039 | 5.893233 | 10.91312 | 2946.381392 |
18 | 39.48589 | 0.229741 | 5.575304 | 10.51012 | 2313.7594 |
19 | 34.81782 | 0.249944 | 5.751105 | 11.03274 | 2209.204985 |
20 | 36.73943 | 0.15563 | 5.635884 | 10.61535 | 2198.004659 |
21 | 49.66252 | 0.155886 | 5.887991 | 10.83304 | 3167.716883 |
22 | 32.88174 | 0.18592 | 5.763045 | 11.00836 | 2086.072849 |
24 | 39.46348 | 0.149229 | 5.55141 | 10.39238 | 2276.742437 |
25 | 50.89265 | 0.169445 | 5.929976 | 10.88363 | 3284.594438 |
26 | 59.15301 | 0.175359 | 5.66672 | 10.26178 | 3439.786336 |
27 | 44.19609 | 0.154358 | 5.8718 | 10.90138 | 2829.023782 |
28 | 59.96046 | 0.24965 | 5.844689 | 10.47629 | 3671.418304 |
29 | 56.1891 | 0.216415 | 5.757975 | 10.43581 | 3376.356052 |
30 | 35.94489 | 0.190275 | 5.571909 | 10.56166 | 2115.30706 |
Algorithm | A | ||||
---|---|---|---|---|---|
GBO | 31.16894 | 0.199724 | 5.550141 | 10.68478 | |
TSA | 30.36002 | 0.170384 | 5.73696 | 11.00257 | 1916.363658 |
ChOA | 30 | 0.25 | 5.640492 | 11.02396 | 1865.416509 |
Increasing the generated energy from the wind turbine is important work. Wind cubes improve wind turbine output using an effective optimization technique. A GBO is used to estimate the roughness factor’s decision variable, the inner radius of the wind cube, the wind turbine hub's height, and the outer radius of the wind cube. The extraction of these parameters is dependent on minimizing the probability of a loss of generated energy and decreasing the decision variable to make these variables more cost-efficient. There is a tolerance of a 20% air speed increase for the site as compared with the speed recorded in this work. A comparison between wind turbine output power with and without the optimized wind cube was performed. Based on this comparison, the energy generated from a 30-kW wind turbine with the optimized wind cube as 55.7317 times the energy generated without the wind cube. The energy generated from a 6-kW wind turbine with the optimized wind cube is 23.8123 times the energy generated without the wind cube. The future work will concentrate on apply GBO for several problems such as power flow in power system, wind farm layout problem.