Enhancement of the output power of a small horizontal axis wind turbine based on the optimization approach

2.1 Selecting the optimal airfoil for the blade

The airfoil is considered the main element in the design process of the wind turbine blade. When choosing the appropriate airfoil, the length of the blade, the speed of the blade (Reynolds number), and the energy to be extracted must be taken into account. Moreover, the shape of the airfoil has an impact on the structural strength and durability of the blade [10]. Therefore, there is no universal method for airfoil selection, often requiring a blend of experimentation and simulation.

However, specific standards and criteria exist for comparing airfoils and determining the most appropriate among them, such as assessing the lift-to-drag coefficient ratio. This analysis focused on enhancing small wind turbine blades designed for supplying electricity to homes and small agricultural operations. Thus, a 5 kW wind turbine was chosen, following the required specifications. Consequently, the choice of a suitable airfoil for smaller blades, including NACA4412, NACA4415, NACA4418, and NACA4421, is shown in Figure 1.

Figure 1

NACA airfoil to design the HAWT blade.

2.2 Chord and twist design

In this research, a blade design code [11] grounded in the blade element momentum theory is devised to delineate the geometric configuration of the turbine blade within MATLAB software. In addition, the aerodynamic behavior of the blade can be predicted from this code. From Equation (1), the blade radius can be determined, taking into account the expected wind power and speed [12]:

The following equations determine the chord length distributions for an airfoil and the twist angle in each section [11,13]:

One of the important parameters that affect the aerodynamic behavior of wind turbines is the tip speed ratio (TSR). TSR is the ratio of the tip speed of the blade to the wind speed. The TSR significantly affects the efficiency of the wind turbine, especially based on the power capture and aerodynamic loading. The TSR formula is [14]

Here, r represents the sectional radius of the blade; ω is the angular velocity of the turbine rotor; N _b denotes the number of blades; C _l stands for the lift coefficient; λ _r signifies the local TSR; and α d refers to the designed angle of attack. Figure 2 illustrates the relationship between the wind velocities U wind , angles of attack α, and forces acting on one of the blade sections’ normal forces F N , tangential force F T , including the chord length c, and the twist angle θ p . The lift coefficient (C _l) and the drag coefficient (C _d) are fundamental in aerodynamics and are used to assess and enhance the performance of aerodynamic shapes. These coefficients help engineers and designers achieve a balance between the lift and drag, leading to more efficient and safer designs.

Figure 2

Effect of velocities and forces on the blade section.

The lift coefficient (C _l) is the ratio of the lift generated by an airfoil or aerodynamic shape to the product of the density of fluid by the square of the velocity of fluid. C _l is expressed by the following formula [15]:

The drag coefficient (C _d) is the ratio of the drag force acting on an object to the product of the density of fluid by the square of the velocity of fluid. C _d is expressed by the following formula [15]:

where L is the lift force, V is the flow velocity, A is the blade area, and D is the drag force. Equations (2) and (3) were used to calculate the initial chord length and the angle of twist, which are presented in Table 1.

3.1 Types of generators

Generators are classified into two types: the first one is the synchronous generator, and the second one is the asynchronous generator. When the speed synchronized with the grid frequency is fixed, the synchronous generators operate. However, at variable speeds without the need for external synchronization, it can be used as an asynchronous generator. Both types have distinct characteristics and applications in various industries, including power generation and renewable energy systems.

3.1.3 Doubly fed induction generator (DFIG)

This type can be categorized within the WRIG. In a DFIG, it can be connected to the rotor and stator with the grid by separate converters. This allows for variable speed operation and enhanced control over active and reactive power output, as shown in Figure 5. Table 3 shows the difference between the other two types, as mentioned above [17].

Figure 5

The main elements of double-feed induction generators.

Table 3

Comparison between the induction generator and double-feed induction generator [18,19]

Aspect	DFIG	IG
Connection with grid	Rotor-side and grid-side converters	Directly connected to the grid
Scale of usage	Large-scale wind farms	Small-scale applications
Wind speed	Suitable for a wide range of wind speeds	Optimal performance at lower wind speeds
TSR	Adjustable for optimum performance	Fixed based on design specifications
Torque	Controlled and adjustable	Fixed based on wind speed
Control system	Sophisticated control for variable speed	Simple control for fixed-speed operation
Pitch angle	Adjustable for optimal power extraction	Not applicable

3.1.4 Electrical losses

In a wind turbine, there are several sources of electrical losses, as shown in Figure 6 [20,21].

• Copper losses: These are due to the windings of the generator because of the copper wire’s resistance. The loss that exists in the armature copper is as follows:

  (8) Armature copper loss = I a 2 R a ,

  where R _a is the armature resistance and represents 30–40% of full-load losses.

• Iron losses: Also called core losses, and occur in the generator’s iron core because of hysteresis and eddy currents. Hysteresis losses occur because the magnetic domains in the core material must constantly realign as the magnetic field changes. Eddy currents are induced currents that circulate within the core material, causing additional losses.

• Mechanical losses: These losses occur because of friction and mechanical resistance in the turbine’s moving parts, such as bearings, gears, and rotor blades. These losses reduce the mechanical energy available to drive the generator.

• Converter losses: In modern wind turbines, the electrical power induced by the generator is converted from AC to DC (for direct-drive turbines) or from AC to AC (for geared turbines) using power electronics. These conversions incur losses due to the switching of power semiconductors and other components.

• Transformer losses: If the generated power needs to be stepped up or down in voltage for transmission, losses occur in the transformer due to resistance in the windings and core losses.

• Electrical network losses: In grid-connected wind turbines, there are losses in the electrical network (transmission and distribution lines) that transport the generated power to consumers. These losses depend on the distance between the wind turbine and the consumers and the capacity of the electrical network.

Figure 6

Details of the electrical losses.

Minimizing these losses is crucial for improving the efficiency and overall performance of a wind turbine system. Strategies to reduce losses include using high-efficiency components, optimizing the design of the turbine and generator, and improving the control algorithms for power conversion and grid integration.

4.1 Design optimization of the HAWT blade

The Betz method initially offered guidance for designing the chord and twist angles of wind turbine blades, but its inherent nonlinearity in these design aspects presents a significant limitation, especially for practical applications. To overcome this, the current analysis introduces a linearization approach aimed at improving both the design efficiency and the manufacturability of the blades. To ensure the optimal distribution of dynamic forces along the blade span, a strategy of optimizing the angle of twist and chord, which has a linear decline from the blade root to the tip, was necessary. This strategy also aims to reduce the complexity of blade molds and tools by simplifying manufacturing processes, which leads to smooth production, reduced costs, and improved repeatability during manufacturing. The balance between structural integrity and aerodynamic efficiency is maintained across different air speeds through specific equations that determine the linear decline, which is considered part of the optimization process [2]:

where n represents the number of linearized chord lines, c i , n is the chord length at the nth linearized chord line for the blade element section, and θ i , n is the twist angle at the nth linearized twist line for the blade element section. The values c t , 0 , c r , 0 and θ t , 0 , θ r , 0 correspond to the initial blade chords and twist angles at the tip and root, respectively, while N denotes the total number of linearized lines. The optimal blade parameters are presented in Table 4.

A closer analysis of Figure 10 reveals that the optimized design shows a marked increase in the power coefficient, particularly at lower TSR values between 1 and 4. This suggests that the linearization method enhances blade performance at lower rotational speeds, where optimal aerodynamic shaping is crucial for capturing energy effectively. At intermediate TSR values, the power coefficient of the optimized design remains similar to the initial design, indicating stability and consistency across varying speeds. Notably, at TSR values above 6, the optimized design shows a significant increase in the power coefficient, highlighting its capacity to maintain efficiency even at high rotational speeds.

Figure 10

(a) Power coefficient with TSR, and (b) power output with wind speed.

Overall, this enhancement in power coefficient at both ends of the TSR range results in an average improvement of up to 8%, with a specific improvement of 6.38% in power output at the rated wind speed. These findings underscore the positive impact of the linearization method on aerodynamic efficiency and confirm its effectiveness in boosting overall power generation, particularly at moderate wind speeds starting from 8 m/s. This comprehensive optimization allows for a more consistent and higher energy yield across varying operational conditions.

4.2 Aeroelastic simulation of the HAWT blade

During the simulation, wind loading was generated using TurbSim and subsequently input into the InflowWind module within the FAST framework. QBlade incorporates a computational tool for generating these wind fields through stochastic temporospatial simulation. For this study, the following parameters were utilized: a complete turbulent wind field was generated employing the Kaimal spectral model and the power law wind profile. The mean wind velocity at the hub height was established at 10 m/s, with turbulence characteristics conforming to IEC characteristic B, representing a turbulence intensity of 14%. The wind field grid size was configured as 10 m × 10 m. The simulation duration of 600 s was chosen to derive results for a 10 min interval, with the initial 20 s excluded to allow for the dissipation of transient effects associated with starting from a stationary state. Figure 11 illustrates a time series of wind velocity fluctuations in the horizontal directions (x-direction) obtained by FAST software simulation. These fluctuations depict variations around 10 m/s in the x-direction, with the wind velocity remaining at zero in both the y- and z-directions.

Figure 11

Time and wind speed variation.

Figure 12 shows that when depicting power concerning wind speed over time, it forms clusters of closely spaced points due to wind speed fluctuations (both increases and decreases), as shown in Figure 13. Similarly, the power coefficient is influenced by the wind’s instability, marked by its periodic shifts in a manner dependent on the geographical location where the blade is positioned, as shown in Figure 14. Indeed, the power output from the analyzed model demonstrates a considerable range, reaching its peak at 13 kW when the wind speed hits 13 m/s, and decreasing to 0.5 kW during low wind speed conditions.

Figure 12

The output power of the wind turbine dependent on time.

Figure 13

Power extracted at variable wind speeds.

Figure 14

Power coefficient at various times.