Innovative Physics Pedagogy Using Ant Colony Optimization for Wind Power System Methodologies ^†

Abstract

This paper introduces an innovative approach to physics education by integrating the Ant Colony Optimization (ACO) algorithm within a simulation-based learning environment to optimize wind turbine blade angles. Using a simulated wind farm model, students analyze the impact of blade angle adjustments on energy output. The results demonstrate that the ACO algorithm effectively determines optimal blade angles, maximizing energy production. Compared to traditional instructional methods, this approach enhances students’ understanding of wind energy principles and the practical application of metaheuristic optimization techniques in physics and engineering. Furthermore, the study highlights the potential of combining ACO with active learning strategies in STEM education to cultivate advanced problem-solving skills and foster deeper engagement with complex energy systems.

1. Introduction

The global shift towards renewable energy has accelerated advancements in wind energy technologies, positioning wind power as a cornerstone of sustainable energy systems. Maximizing the energy capture of wind turbines is essential for improving the economic viability of wind farms, yet this objective is hindered by challenges associated with complex aerodynamic forces, turbulent wind conditions, and design parameters. Addressing these challenges demands advanced computational tools capable of solving non-linear optimization problems [1]. Beyond technical advancements, these challenges also present an opportunity to integrate optimization techniques into physics education, enabling students to connect theoretical principles with real-world applications.

Traditional optimization methods often fail to adapt to the dynamic and stochastic nature of wind resources, leading to suboptimal energy production and a lack of practical engagement for students. This gap underscores the significance of incorporating innovative computational methods, such as metaheuristic algorithms, into both engineering research and educational practices. Among these, Ant Colony Optimization (ACO), inspired by the foraging behavior of ants, has demonstrated exceptional performance in solving optimization problems, particularly in energy systems [2,3,4]. Despite its proven technical potential, the integration of ACO into physics education remains underexplored, especially in the context of renewable energy.

This study aims to address this gap by integrating ACO with an Inquiry-Based Learning Framework (IBLF) to enhance physics education and optimize wind turbine performance. Specifically, the research focuses on applying ACO to optimize blade pitch control in wind turbines, thereby maximizing energy capture under varying wind conditions. The study evaluates the effectiveness of this approach as both an optimization strategy and an educational tool, providing students with hands-on experience in applying advanced algorithms to real-world energy challenges [5,6,7].

2. Proposes and Materials

This section introduces a hybrid methodology employing the Ant Colony Optimization (ACO) algorithm, integrated with the Inquiry-Based Learning Framework (IBLF) and Teaching–Learning-Based Optimization (TLBO), to advance problem-solving capabilities in wind energy physics education. The conceptual architecture of this research is represented in Figure 1.

In Figure 1, this model depicts the process of enhancing physics education through STEM activities. Students are pre-tested and then exposed to STEM activities informed by reviewed teaching methods. Application learning focuses on physics, renewable energy, and engineering. A post-test evaluates the impact, contributing to improved physics pedagogy.

2.1. Metaheuristic Algorithm

This section reviews the relevant literature on metaheuristic algorithms, the Ant Colony Optimization (ACO) technique, and their applications in teaching wind energy physics. Metaheuristic algorithms, such as the Genetic Algorithms (GA) and Particle Swarm Optimization (PSO), are widely utilized due to their effectiveness in addressing complex, multi-objective optimization problems. The GA, inspired by the principles of natural selection, and PSO, based on the social behaviors observed in nature, have demonstrated significant advancements in optimizing wind turbine layouts and improving energy production efficiency. Studies indicate that these algorithms often outperform traditional methods by providing flexible and adaptive optimization techniques for wind farm layouts, mitigating wind shadow effects, and enhancing energy output [8,9].

Moreover, this research highlights the critical need for real-time optimization to address dynamic environmental conditions, such as fluctuating wind speeds and directions, which significantly influence turbine efficiency. However, most studies primarily emphasize technical advancements without exploring their potential for integration into educational practices. For instance, while Project-Based Learning (PBL) has been applied in STEM education to enhance critical thinking and problem-solving skills, these efforts largely focus on traditional physics topics and fail to incorporate advanced computational tools, such as metaheuristic algorithms. The integration of such tools into STEM curricula remains underexplored, particularly in the context of renewable energy education [10].

2.2. Ant Colony Optimization

ACO is a metaheuristic algorithm inspired by the natural path-finding behavior of ants, developed to solve various optimization problems, particularly for finding the shortest path in networks, such as transportation routes and the Traveling Salesman Problem. In this study, ACO is applied to optimize wind energy.

Figure 2 depicts the principles and flow chart of Ant Colony Optimization. (a) Illustration of ACO principles: Ants initially explore multiple paths between nest and food. Pheromone deposition and reinforcement lead to convergence on the shortest path over successive iterations. (b) ACO algorithm flowchart: The algorithm initializes parameters, generates a random global solution, calculates fitness, updates pheromone levels, applies transition rules, and evaluates the new path. This process iterates until a termination criterion is met. Pheromone update favors shorter paths while evaporation prevents premature convergence.

2.3. Blade Element Theory for Wind Turbines

Velocity vectors are analyzed in Figure 3, where ϕ represents the inflow angle, α denotes the angle of attack, and β corresponds to the pitch angle. These angles are critical in determining the aerodynamic forces acting on wind turbine blades, particularly the lift and drag forces, which influence the overall performance of the turbine.

The lift and drag forces projected onto the rotor plane combine to form the normal force, represented in Equation (1).

$$\mathrm{dT}=\mathrm{dLsinf}-\mathrm{dDcosf}$$

(1)

2.4. Tip-Speed Ratio

The tip-speed ratio represents the ratio of the blade tip speed to the wind speed, indicating the operational efficiency of the blade. It varies based on the blade design, as shown in Equation (2).

$$\mathsf{\lambda }={\displaystyle \frac{\mathrm{Tip}(\mathrm{speed},\mathrm{blade})}{\mathrm{Wind},\mathrm{speed}}}={\displaystyle \frac{\mathsf{\omega }\mathrm{R}}{v}}$$

(2)

where ω is the angular velocity (rotations per second), R is the rotor radius (meters), and v is the wind speed (meters per second).

Wind energy and power (E and P) are derived from the mass of air moving at a velocity over the earth’s surface. Wind energy is kinetic energy, with the kinetic energy of the air calculated using the cross-sectional area of the turbine’s rotational plane, as shown in Equation (3).

$$\mathrm{E}={\displaystyle \frac{1}{2}}{\mathsf{\rho }}_{\mathrm{a}}\mathrm{V}{\mathrm{v}}^2$$

(3)

where E is kinetic energy, ρ is air density (kg/m³), V is the volume of air mass passing through the rotor plane (m³), and v is wind speed (m/s).

$${\mathrm{P}}_{\mathrm{W}}={\displaystyle \frac{1}{2}}{\mathsf{\rho }}_{\mathrm{a}}\mathrm{A}{\mathrm{v}}^3$$

(4)

The wind power per unit area is expressed in Equation (5):

$${\mathrm{P}}_{\mathrm{v}}={\displaystyle \frac{{\mathrm{P}}_{\mathrm{w}}}{\mathrm{A}}}={\displaystyle \frac{1}{2}}{\mathsf{\rho }}_{\mathrm{a}}{\mathrm{v}}^3$$

(5)

where P_v represents power per area (W/m²).

3. Methods

This study integrates teaching techniques with the Ant Colony Optimization (ACO) algorithm. A program was developed to enhance wind turbine placement and performance using ACO, structuring teaching activities around its implementation. The research steps are outlined below.

3.1. Problem Definition

The objective is to optimize the placement and operation of wind turbines in a wind farm to achieve maximum power output while minimizing costs.

3.2. Data Collection

The ACO parameters include the number of ants, the number of iterations, the pheromone importance factor, and the blade angle search space, as presented in

Table 1. Parameters for wind turbine blade angles used in the ACO algorithm for determining optimal configurations.

Parameters	Value
minimum blade pitch angle in degrees	0
maximum blade pitch angle in degrees	30
number of discrete steps in angle search space	100

. The collected data includes wind resource variables such as wind speed, wind direction, and turbulence levels at the study location. Additionally,

Table 2. Wind energy parameters used in the ACO algorithm for calculating optimal values are as follows.

Parameters	Value
Wind speed in m/s	10
Air density in kg/m3	1.225
Blade radius in meters	20

presents the wind energy metrics.

3.3. Simulation Setup

MATLAB was used to model the wind farm layout, simulate wind flow, and evaluate wake effects between turbines.

3.4. Development of the Ant Colony Optimization Algorithm

The ACO algorithm was developed following the flowchart in Figure 2b and the design principles.

3.5. Algorithm Performance Testing

Simulate optimized wind farm layouts using periodic wind resource data to evaluate the effectiveness of the ACO settings implemented and developed in MATLAB as follows.

The algorithm describes the use of pheromone levels and heuristic information to determine the optimal blade angles using the ACO technique. As demonstrated in Algorithm 1, the main loop iterates through a predetermined number of repetitions, during which each ant selects an angle based on probabilistic computations derived from heuristic factors and pheromone influence. The optimal solution is updated by evaluating the power output of the selected angles using an objective function.

Algorithms 1: Ant colony optimization for compute blade angles of wind turbine

1 % ACO main loop 2 for iter = 1:num_iterations 3    solutions = zeros(num_ants, 1); 4    power_values = zeros(num_ants, 1); 5    % Each ant selects an angle based on pheromone and heuristic info 6    for ant = 1:num_ants 7        probabilities = (pheromones .^ alpha) .* (heuristic_info .^ beta); 8        probabilities = probabilities/sum(probabilities); 9        cumulative_prob = cumsum(probabilities); 10        random_choice = rand; 11        selected_index = find(random_choice <= cumulative_prob, 1); 12        selected_angle = angles(selected_index); 13        % Store the solution and calculate its power 14        solutions(ant) = selected_angle; 15        power_values(ant) = objective_function(selected_angle); 16        % Update the best solution found 17        if power_values(ant) > best_power 18            best_power = power_values(ant); 19            best_angle = selected_angle; 20        end

4. Results and Discussions

4.1. Case Study

For the development of the ACO algorithm for wind energy physics, teaching activities using parameters of the wind energy system, including turbine blade size, blade angle, wind speed, and air density, the ACO algorithm was applied to calculate the optimal blade angle that maximizes power output.

4.2. Calculation Using the ACO Algorithm

Based on the parameters of blade angles the application of the ACO algorithm was used to determine the optimal blade angle for wind turbines. The parameters were set as follows: 10 ants, 50 iterations, a pheromone importance factor of 1, a heuristic information importance factor of 2, a pheromone evaporation rate of 0.5, and a pheromone update constant of 100. The analysis results indicate that setting the blade angle in the range of 0–30 degrees, divided into 100 steps, achieves the maximum power output when the blade angle is adjusted optimally under conditions of 10 m/s wind speed, an air density of 1.225 kg/m³, and a blade radius of 20 m. Figure 4 shows the graph of the optimal blade angle calculated using ACO, which was found to be 29.39 degrees, resulting in a maximum power output of 189 kW.

This section explains the Teaching–Learning-Based Optimization (TLBO), a novel and effective optimization technique that is suggested in this study for the optimization of optimal blade angles design challenges. This approach focuses on how a teacher’s influence affects students. Similar to other algorithms inspired by nature, TLBO is a population-based approach that employs a population of solutions to reach the global solution. This operation method yields the following results for student groups.

4.3. Evaluation and Assessment of Student Learning Outcomes

The analysis of

Table 3. T-test results regarding students pretest and post-test scores.

Test	N	$\overline{\mathbf{x}}$	S.D.	$∆\overline{\mathbf{x}}$	t
Pretest	20	8.45	2.16	7.40	−14.97
Post-test	20	15.85	4.87

revealed a statistically significant difference between students’ pretest and post-test scores, with higher scores on the post-test (p < 0.05). A paired-samples t-test confirmed this significant improvement from pre-test $(\overline{\mathbf{x}}$ = 8.45, SD = 2.16) and post-test scores ($\overline{\mathbf{x}}$ = 15.85, SD = 4.87), t = −14.97, indicating an enhanced understanding of wind energy principles and problem-solving skills after the intervention. Students also reported increased interest in the subject matter, the perceived relevance of the learning activities, and greater confidence in their problem-solving abilities.

4.4. Discussions

The effectiveness of integrating the Ant Colony Optimization (ACO) algorithm into an Inquiry-Based Learning Framework (IBLF) to enhance physics education in renewable energy. Additionally, it introduces Teaching–Learning-Based Optimization (TLBO) as a novel and promising approach for optimizing wind turbine blade angles. By applying ACO to blade angle optimization, students gain a deeper understanding of the relationship between theoretical principles and practical applications, thereby strengthening their problem-solving skills and fostering a positive attitude toward science. The findings underscore ACO’s potential as an educational tool for promoting critical thinking and active engagement in STEM learning. Future research should explore the scalability of this approach to more complex wind farm models and strategic wind farm decision-making. which could further validate its applicability and effectiveness in real-world scenarios [11].

5. Conclusions

This study demonstrates the effectiveness of integrating the Ant Colony Optimization (ACO) algorithm into an Inquiry-Based Learning Framework (IBLF) to enhance physics education in renewable energy. Using ACO to optimize wind turbine blade angles helps students to connect theory with real-world applications, improving problem-solving skills and fostering positive scientific attitudes. The findings highlight ACO potential as an educational tool to promote analytical thinking and engagement. Future work could explore several promising avenues. Investigating the scalability of this approach to larger and more complex wind farm simulations would be valuable. Adapting the ACO–IBLF framework to other areas of physics and STEM education, such as optics or electronics, could broaden its impact [12]. Finally, a longitudinal study could assess the long-term retention of learned concepts and the development of advanced problem-solving skills [13].