**1. Introduction**

The power of designed and built wind farms in the world is constantly increasing and reaches the value of MW. This pursuit is economically justified as larger turbines achieve higher efficiency of generated power. Modern commercial wind farms mostly have a horizontal axis of rotation and a three-blade turbine. The most frequently used generators are asynchronous machines and synchronous machines with permanent magnets (PMSG) together with power electronic converters and control systems. Modern wind turbines with a horizontal axis of rotation are usually adapted to work at wind speeds not exceeding 25 m/s. These turbines achieve their rated power at wind speeds between 10 and 15 m/s [1]. PMSG generators made of neodymium magnets are most often used in low-power wind turbines with high rotational speed, while in larger power plants, induction generators with a mechanical gear are used [2]. In modern wind turbines, several methods of adjusting the rotor speed and the generator power related to it are used in several ways, depending on the instantaneous wind speed [2]. To reduce mechanical power on the shaft in large turbines, pitch control is used, while in small and medium-sized ones, mainly passive stall control is used, breaking the laminar air stream [3,4].

The European Parliament issued a directive 2010/31/UE on the energy performance of buildings, introducing the nearly zero-energy building concept (zero-energy building). According to this directive, new buildings must meet the requirement that a significant amount of energy comes from renewable sources, including sources integrated with the building [5]. As a result, there is a growing interest in micro wind turbines that would supplement the electricity demand of small households [6–8]. The manufacturers' offer includes wind microturbines with a nominal power from 100 W to several kW. Miniature wind turbines can also often be seen on small yachts, recreational plots, and street-lighting lamps where there is no access to the power grid—Figure 1. Typically, such microturbines have three or more blades with as simple a profile as possible, are easy to manufacture, and directly mounted on the PMSG generator axis. Most often, the rated voltage of the generator is selected so that it charges the battery using an ordinary 6D rectifier.

**Citation:** Chudzik, S. Wind Microturbine with Adjustable Blade Pitch Angle. *Energies* **2023**, *16*, 945. https://doi.org/10.3390/en16020945

Academic Editor: Paweł Lig ˛eza

Received: 16 December 2022 Revised: 12 January 2023 Accepted: 13 January 2023 Published: 14 January 2023

**Copyright:** © 2023 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

**Figure 1.** Hybrid power supply from renewable energy sources: (**a**) street-lighting lamp; (**b**) on the yacht.

The belief that the cost of manufacturing a controller for the optimal operation of a microturbine is high in relation to the possible improvement of the efficiency of the microturbine means that there is no such controller on the market. In addition, control methods for larger wind turbines are not optimal for small turbines [9–11]. Therefore, the author designed and built a small test stand that allows for preliminary research related to the selection of the optimal wind turbine geometry, and the development and testing of the operation of the control algorithm for the operation of a simple converter charging the battery so as to optimally use the power of the wind turbine [12].

The presented research focuses mainly on determining the possibility of using wind turbines with an adjustable blade pitch angle depending on the rotational speed in microturbines. In larger wind turbines, changing the pitch angle is only used to limit their power at high wind speeds [10,11]. Currently, such solutions in micro wind farms are not used for economic reasons. Wind microturbines are very often located in places where wind conditions are unfavorable: low height from the ground, and terrain obstacles limiting the speed of the wind stream and causing its turbulence [1,9]—Figure 1a. The use of a simple blade pitch angle adjustment mechanism depending on the angular velocity of the turbine can increase its efficiency in a wider range of wind speeds.

The test stand with small dimensions enables quick and cheap development of initial prototypes of turbine blades due to the use of 3D printing technology.

#### **2. Materials and Methods**

#### *2.1. Working Principle of Wind Turbine*

The operation of the wind turbine depends on the setting of the blade angle φ (Figure 2): it is the angle between the blade chord and the apparent wind *V*, being the sum of the vectors of the blade linear velocity *Vω = ω*·*r* and the wind speed *V*. The value of the angle of attack α depends on the ratio of the linear blade speed *Vω* to the wind speed *V* and the blade position angle. Two forces act on the turbine blade: the lifting force *FL*, perpendicular to the direction of the resultant velocity *V*, and the thrust *FD*, corresponding to its direction. The rotation of the turbine causes the component *FT* of the resultant force *FL* in the direction of the blade rotation. The value of *FT* depends on the aerodynamic profile of the blade and is a non-linear function of the angle of attack. In the range of small values of the angle of attack, this force grows approximately linearly, but from a certain value of this angle it rapidly decreases; a stall state occurs [1,2,13]. Maintaining a constant value of the angle of attack, ensuring maximum aerodynamic efficiency, requires maintaining an

approximately constant ratio of the angular velocity of the rotor to the wind speed, i.e., the change in rotor speed in proportion to the wind speed.

The lift generated by the airfoil section is a function of the angle of attack to the incoming air stream. The angle of the air stream inflow depends on the rotational speed and the wind speed within a certain radius. The required twist angle of the blade depends on the ratio of the airfoil speed over a certain radius and the desired angle of attack of the airfoil. The part of the blade closer to the hub is tilted more against the wind due to the high ratio of wind speed to blade radial speed. The blade tip, on the other hand, will be almost perpendicular to the wind direction. In the case of blades with a constant angle of their setting, the optimal twist angle of the blade can be determined. However, when the angle of the blade is to be adjusted, the twist angle of the blade should also change. It would be too costly to build a wind turbine with variable-adjustable geometry and currently such solutions are not used in practice. Therefore, blade angle adjustment is only used in large turbines to limit their power. In the case of airplanes or helicopters where the adjustable pitch propeller is used as a drive, the blades of such propellers have a small or zero twist angle—this provides a wider speed range for effective operation of the propulsion [1,2]. For the purposes of the research on the impact of the adjustment of the blade angle on the operating efficiency range of a wind turbine, a propeller with a straight profile and a zero twist angle of the blade was made.

The aerodynamic properties of the wind turbine are determined by the power factor *Cp(λ*, *β)*, which depends on the tip speed ratio *λ* and the blade pitch angle *β*. The coefficient *λ* is defined as the ratio of the linear speed of the turbine blade tip to the wind speed,

$$
\lambda = \frac{\omega\_r \cdot R}{V\_{\text{av}}},
\tag{1}
$$

where ω*r* is the angular velocity of the turbine and *R* is the radius of the turbine.

The power factor corresponding to the aerodynamic efficiency of a wind turbine is given by the expression,

$$C\_P = \frac{P\_{\rm ff}}{P\_{\rm uv}} \,\tag{2}$$

where *Pm* is the mechanical power of the turbine and *Pw* is the wind power:

$$P\_w = 0,5\rho\pi R^2 V^3,\tag{3}$$

where *ρ* is the air density.

Figure 3 shows an example of the *Cp(λ*, *β)* characteristic of a wind turbine. The maximum power generated by the turbine at a given wind speed *Vw* is achieved for the maximum value of the efficiency coefficient corresponding to a certain optimal value *<sup>λ</sup>op<sup>t</sup>* of the tip speed ratio [1,2].

**Figure 3.** An example of the *Cp(λ*, *β)* characteristics.

The mechanical power of the turbine and the output of the electrical system *Pout* is described by Equation (4), where *Mt* is the frictional moment, *ω* is the turbine angular velocity, *J* is the moment of inertia of the rotating mass, *η* is the overall electrical efficiency of the system from the generator input to the inverter output.

$$P\_{\rm nt} = \frac{1}{\eta} P\_{\rm out} + \omega \cdot M\_t + \omega \cdot l \frac{d\omega}{dt},\tag{4}$$

The boundary layer is a thin layer of air and appears on the surface of objects in viscous flow. The boundary layer effect depends on the flow pattern which is related to the Reynolds number (5). Reynolds number is a function of fluid velocity,

*Re* = *ρ*·*V*·*C μ* , (5)

where *ρ* is the fluid density, *V* is the mean velocity of the fluid, *C* is a chord length, and *μ* is the dynamic viscosity of the fluid.

Airfoil efficiency decreases as the Reynolds number decreases. Reducing the Reynolds number means that viscous effects become more dominant, increasing viscous drag. In addition, the thickness of the boundary layer will increase as the Reynolds number decreases, leading to increased shape drag or less lift. Small wind turbines usually operate at Reynolds number less than 5 × 105. In this Reynolds number range, laminar flow gets separated at the upper surface of the airfoil and is reattached to the surface as turbulent causing laminar separation bubble, which increases the drag of the airfoil. Large-scale wind turbines have become the development trend of wind power. At present, the radius of wind turbine rotors ranges to one hundred meters, or even more, which extends Reynolds number of the airfoil profile from the order of 10<sup>6</sup> to 107.

#### *2.2. The Most Commonly Used Methods of Optimal Control of Wind Turbine Operation*

The algorithms used to achieve maximum power point tracking (MPPT) by wind turbines can be divided into three main control methods: tip speed ratio (TSR) control, power signal feedback (PSF) control and, search method maximum power (hill-climb search—HCS) [14–16]. The TSR control method regulates the rotational speed of the wind turbine in order to maintain the optimal value of the tip speed ratio, at which the achieved turbine power is the highest [17,18]. This method requires measuring or estimating both the wind speed and the rotational speed of the turbine, and also requires knowledge of the characteristicsoftheoptimaltipspeedratioforthedesignedturbine—Figure 4.

**Figure 4.** Tip speed ratio control.

In the PSF control method, it is required to know the maximum power characteristics of a wind turbine and to follow this curve with a control and measurement system [19,20]. The maximum power curves should be obtained by simulations or experiments with a disconnected wind turbine. In this method, the reference power is determined from the recorded maximum power curve or from the wind turbine power equation where the input speed is either wind speed or rotor speed—Figure 5.

**Figure 5.** Power signal feedback control.

The HCS control algorithm is constantly looking for the peak power of the wind turbine—Figure 6. The tracking algorithm, depending on the position of the operating point of the turbine and the relationship between changes in power and rotational speed of the turbine, calculates the optimal signal to bring the wind turbine to the point of maximum power [21–25]. Unfortunately, HCS control can only work well when the moment of inertia of the wind turbine is very small so that the change in turbine speed occurs almost "instantaneously" to the change in wind speed. For wind turbines with higher inertia, the instantaneous power output of the power plant is related to the mechanical power of the turbine and changes in kinetic energy stored in the rotating elements, which often makes

the HCS method ineffective. HCS control does not reach the maximum power points with rapid increases in wind speed and causes the so-called "stall" when wind speed decreases, which severely limits the usefulness of this method for wind turbines. Boundary layer flow characteristics are critical for determining inputs to control systems. The occurrence of the laminar-to-turbulent transition process, especially at high angles of attack and rapid changes of angles of attack, can significantly change the aerodynamic behavior of the blade and cause the phenomenon of stalling [26,27].

**Figure 6.** Hill-climb search algorithm.

It is therefore highly desirable to develop a maximum power output method for micro wind turbines that does not require measuring wind speed and turbine rotor speed, is independent of system characteristics, and is applicable to small wind turbines.
