# Evaluation of Regional Elevation and Blade Density Effects on the Efficiency of a 1-kW Wind Turbine for Operation in Low-Wind Counties in Iran

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## Abstract

**:**

_{s}) and power coefficient (C

_{p}) of a 1-kW two-bladed wind turbine. The study uses three Iranian hardwoods as the blade material and four counties of Iran with low wind speeds and different elevations as the case studies. The BW-3 airfoil is considered as the blade profile. A multi-objective optimization process with the aid of the differential evolution (DE) algorithm is utilized to specify the chord length and twist angle. The findings demonstrate that, while the maximum C

_{p}of the optimal blades designed with all three types of wood is high and equal to 0.48, the average T

_{s}of the optimal blades designed with oak and hornbeam wood is 84% and 108% higher than that of alder wood, respectively. It is also observed that, while raising the elevation to 2250 m decreases the C

_{p}by only 2.5%, the ideal blade designed to work at sea level could not manage to start rotating at a height of 1607 m and above. Finally, an improvement in the T

_{s}and C

_{p}was observed by performing optimization based on the local atmospheric conditions associated with the incrementing blade chord length at high elevations.

## 1. Introduction

^{5}, the flow around an airfoil might separate while the boundary layer is still laminar and before the transition to turbulent. This laminar separation might lead to the formation of air bubbles, which are known as laminar separation bubbles. These bubbles result in extra drag in airfoils, which is defined by the bubble drag. Figure 1 shows a schematic of laminar separation bubbles. A typical airfoil not designed for operating at low Reynolds numbers will suffer from a loss in performance in this condition; however, some thin airfoils are designed to operate at low Reynolds numbers and reduce the impact of the separation bubble. The BW-3 airfoil is one of these airfoils [18].

_{p}) is employed to design the blades of these turbines [29].

_{c}) that must be overcome by the generated startup torque (M

_{s}) [19]. Studies have shown that the M values generated by the root elements of the blade have a vital role in starting the blade rotation from the stationary state, and the startup process of the blade is mostly contributed by these elements. As the rotational speed of the turbine rises, the AOA along the blade reduces, so that the aerodynamic moment generated by the elements near the blade tip is much larger than that of the root elements. Thus, these elements have a greater contribution to the amount of power output from the turbine.

_{r}is the local tip speed ratio, α is the AOA in which the lift-to-drag ratio is the maximum, B is the number of blades, and C

_{l}is the lift coefficient. Research studies have suggested that, while using the nonlinear distribution obtained from Equations (2) and (3) provides the maximum C

_{p}, it causes a significant reduction in the M

_{s}and therefore leads to an increment in the rotor startup time [32]. Similar results have been presented for the application of the ideal equations provided by Burton et al. [33] for the design of SWT blades [34]. Thus, if any other objectives besides the C

_{p}are considered for the blade design, optimization methods should be employed [35]. In general, optimization techniques fall into two groups: gradient, and nongradient [36]. In gradient techniques, the derivative of the objective function with respect to the design variables is acquired, and then, the optimization process is carried out using them. The solving techniques of adjoint [37] and second-order sequential quadratic equations [38], as well as the finite difference method [39], are some of the gradient techniques. Nongradient methods are independent from the objective function characteristics, such as continuity and differentiability. In this regard, the optimal solution is determined by calculating the values of the objective function and comparing to with each other in an evolutionary process. Genetic algorithm (GA) [40], differential evolution (DE) [41], and particle swarm optimization (PSO) [42] are among the most famous nongradient algorithms. Robustness, rapidness, and convergence rate are the most fundamental features of the optimization methods, in which evolutionary algorithms, especially the DE algorithm, have been very successful [43].

_{s}. By raising the β and the c at r/R < 0.52 and following the Schmitz formula at r/R ≥ 0.52, they managed to obtain a 140% increment in the M

_{s}by losing only 1.5% of the C

_{p}value. This resulted in reducing the startup speed from 6 to 4 m/s. Pourrajabian et al. [44] investigated the chord and twist variables in three SWTs with power outputs of 0.5, 0.75, and 1 kW. They focused on enhancing the turbines’ operation during low wind conditions at the startup time. Enlarging the c and β values at the root section of the blades was found to be essential for reaching a better performance in low-wind scenarios. Their findings indicate that using more blades or enlarging the existing ones contributes to both a better startup process and greater power generation. Abdelsalam et al. [45] conducted experimental research on the aerodynamic efficiency of two distinct small HAWT rotors. The first rotor possessed nonlinear chord and twist distributions, while the second one had a novel linearized pattern that was designed using the BEM theory. The RISØ-A-24 airfoil was used as the blade profile. The findings exhibited that the maximum C

_{p}of the nonlinear model was higher; however, the linear model had a better startup performance. In the study carried out by Rahgozar et al. [21], a one-meter wooden HAWT blade was developed by taking both the startup time and power output into account. They tested four potential combinations of linear/nonlinear c and β distributions utilizing the BEM theory. They made use of the SG6043 airfoil as the uniform profile along the blade. They concluded that employing a linear distribution enhances the startup performance with a minimal impact on the power output. By choosing ten airfoils that are prominently used in the SWT industry, Akbari et al. [34] recommended the application of Bergey BW-3 and SG6043 airfoils as blade profiles for use in less and more windy regions, respectively. The reduced inertia presented in the blades featuring the Bergey BW-3 profile, along with the impressive lift-to-drag proportion exhibited by the SG6043 design, represent some of the noteworthy benefits of these aerodynamic structures.

_{s}, respectively. On the other hand, with the rise in elevation and the kinematic viscosity of the air, the Reynolds number (Re) on the blade is reduced and can decrease the lift value and, as a result, decrease the C

_{p}of the turbine. Considering the increase in the application of SWTs and the requirement to improve their performance, especially at low V values, the importance of these parameters can be well perceived. For this purpose, in the current study, three hardwoods with different densities that grow in Iran and also four low-wind counties with different elevations from the sea level up to 2250 m were selected as case studies. In the subsequent sections of the study, by designing and optimizing a low-cost two-bladed SWT, the impact of the blade density and elevation on the startup behavior and the power extraction coefficient will be investigated.

## 2. Wind and Timber Resources in Iran

^{3}of wood annually [63]. In the present study, three types of hardwood grown in this area, namely alder, oak, and hornbeam, which physical properties were presented in the work of Kiaei and Samariha [64], were used for the SWT blades.

## 3. Aerodynamic Analysis

## 4. Analyzing the Startup Time

_{s}) generated by the blade during the startup process:

_{h}is the hub radius. It is also worth noting that all speeds and lengths in this equation have been nondimensionalized by V and R, respectively. The important point in Equation (21) is the independence of the M

_{s}from the Re, which is due to using generic flat plate expressions to determine the aerodynamic coefficients at high AOAs. Also, c and r represent the chord length and the radial coordinate along the blade, respectively. During the startup process of the blade from a static condition, the changes in the tip speed ratio (λ) with time can be written as follows:

_{b}is the blade density, and A is the area of the airfoil by assuming c = 1. Solving the differential Equation (22) from the static condition λ = 0 to λ = 1 determines the turbine startup time. Experimental studies have affirmed the reliability of Equation (22), and this correlation has been used by many researchers for computing the startup time of SWTs [9,21].

## 5. Multi-Objective Optimization and Input Parameters

- Initialization of the population and selecting the algorithm settings, including evolution administration and termination criterion.
- Arbitrarily generating the population and computing objective function value for each member of the population.
- Continuing these substeps unless the termination criteria are reached:
- 3.1
- Mutating with the difference vectors (${x}_{r1.g}$, ${x}_{r2.g},$ and ${x}_{r3.g}$) according to the mutation factor (F) and generating another vector (${V}_{G}={x}_{r1.g}+F\left({x}_{r2.g}-{x}_{r3.g}\right)$).
- 3.2
- Crossing over based on the crossover constant (C
_{r}). - 3.3
- Computing the objective function for the members of the population after the evolution.
- 3.4
- Selecting the optimal members based on the greatest value of the objective function.

- Returning to the third step.

_{p}and startup time, are different. While the C

_{p}has a numerical value of less than one, the startup time can possess any value. Thus, by nondimensionalizing and using the weighting coefficients method, which is one of the techniques for determining the Pareto front, the following objective function was considered for the optimization process, so that the DE algorithm tried to maximize this function [16]:

_{f}≤ 1 is the weighting ratio that specifies the contribution of each of the design goals. Moreover, C

_{P}is the power coefficient corresponding to the blades in the population matrix, and max(C

_{P}) is the highest power coefficient in each generation. On the other hand, T

_{s}is the startup time corresponding to the blades in the population matrix, and min(T

_{s}) is the minimum startup time in each generation. With the aid of this objective function, the C

_{p}and startup time in each generation are nondimensionalized, and the value of the objective function is between zero and one. The objective function constants, max(C

_{P}) and min(T

_{s}), are variable during the execution of the algorithm, and therefore, the objective function also changes. The input parameters of the DE algorithm are given in Table 2. It is necessary to explain that, in the present study, a numerical code written using MATLAB R2014a software was used for the optimization.

_{c}values, as well as its inertia, are among the characteristics of the selected one-kilowatt generator [44]. Since the selected counties do not have a significant wind potential [69], the startup wind speed (V

_{s}) of the turbine was selected to be 4 m/s. On the other hand, it is suggested that the rated speed in the design should not be less than twice the V

_{s}value [9]. Thus, the design wind speed was chosen to be 8 m/s. The multi-objective optimization algorithm used in the present study is shown in Figure 6 in the form of a flowchart.

## 6. Validation

_{p}results, and in the second part, the startup time (T

_{s}) values, are validated.

#### 6.1. Validation of the C_{p}

_{p}values calculated from the numerical code have been compared against the experimental values in Figure 7. It can be perceived that the numerical results are in agreement with the reference data, having a maximum deviation of less than 6.5%.

#### 6.2. Validation of the T_{s}

^{3}, the T

_{s}was calculated. It is necessary to explain that, in Reference [16], the V

_{s}was considered to be 5 m/s, and the SG6043 airfoil was used as the blade profile. Table 4 compares the T

_{s}results. It is conspicuous that the results are significantly close to an absolute error of less than 2%.

## 7. Results and Discussion

#### 7.1. Designing a Blade for Operating at Sea Level and Evaluating Its Efficiency in the Selected Counties

_{p}and tip speed ratio of the turbine design can be acquired in terms of the blade length:

_{p}and λ are acquired. However, it should be noted that the value of C

_{p}cannot exceed the Betz–Joukowsky limit ($\frac{16}{27}$). The achievable C

_{p}value in SWTs is reported to be 0.48 [9]. Considering this value for the C

_{p}, the corresponding λ and R values are found to be 9.9 and 1.68 m, respectively (Figure 8). As was stated before, for the current research, a two-bladed turbine was chosen, the reasons for which are presented as follows:

_{p}and optimal T

_{s}for each of the selected timbers.

_{f}in the objective function (Equation (24)), both the C

_{p}and the T

_{s}are decreased, but the reduction of the T

_{s}is more considerable than the decrement in the C

_{p}, so that, for the blade made of alder timber, by reducing the C

_{p}by 7%, a 74% enhancement in the T

_{s}is observed. The improvement of the T

_{s}for the blades designed to be made of oak and hornbeam timbers is around 85%. This point underlines the significance of considering the T

_{s}in the design of SWT blades, which do not possess a pitch control mechanism. According to Table 5, even though the blade density does not influence the turbine C

_{p}, it substantially affects the T

_{s}. Figure 10 depicts the average T

_{s}of the optimal blades made of the selected timbers.

_{c}, the M

_{s}and the blade inertia are two factors that affect the startup behavior of SWTs. Based on Figure 9, as the value of W

_{f}is reduced, the β and c values increase in the root elements. Raising the β values reduces the AOA of the root elements and increases the lift coefficient. On the other hand, based on Equation (21), the increment of the c also raises the M

_{s}. In this regard, Figure 12 demonstrates that, for the blades made of alder timber, by reducing the value of W

_{f}, the M

_{s}increases.

_{s}, it also increases the blade inertia, which can hurt the turbine T

_{s}; thus, there is a conflict between the inertia and the M

_{s}, for which the optimization algorithm tries to come up with a compromise by determining the optimal value for the c.

_{f}values) was investigated in the selected cities (Table 1), and the results are tabulated in Table 6.

_{p}is reduced while the T

_{s}rises. Even though the decrease in the C

_{p}due to the reduction in the Re (because of the increase in kinematic viscosity) can be up to 2.5%, the increase in the T

_{s}is notable, so that the ideal blade (W

_{f}= 1), which was designed to work at the sea level, cannot start to spin at V = 4 m/s in the cities of Asadabad and Sisakht, and it practically loses its performance. In these regions, the generated M

_{s}cannot conquer the M

_{c}, which has a meaningful value in SWTs (as compared to the M

_{s}generated in these turbines). This point affirms that, in the design and selection of SWT blades, the parameter of elevations above sea level should be considered.

#### 7.2. Redesigning the Blades for Each County

_{p}and prevent its drastic reduction by raising the c. On the other hand, as mentioned before, the increase in the c also results in an increment in the M

_{s}, which enables the blades to rotate at V = 4 m/s.

## 8. Conclusions

_{s}) was added to the main design goal, which was maximizing the power coefficient (C

_{p}) of the turbine. Then, based on these objectives, the geometric shape of the blades was determined with the aid of the DE algorithm. The BEM model (along with the Prandtl model for accounting for the blade tip losses) was utilized to compute the C

_{p}, and a quasi-steady version of the BEM model was employed to calculate the T

_{s}. The findings showed that the hardwood type utilized in the blade has no impact on the C

_{p}, but it utterly influences the T

_{s}, so that the average T

_{s}of the blades made of oak and hornbeam timbers are 84 and 108% higher than the average T

_{s}of the optimized blades made of alder timber. It is highly recommended to consider the T

_{s}for the design and optimization of wind turbine blades in less windy regions, because the results demonstrate that, with only about a 7% reduction in the C

_{p}, the T

_{s}of the blades made of alder improves by 74%, and the enhancement of the T

_{s}for the blades made of oak and hornbeam timbers is around 85%. This undeniable improvement stems from raising the twist angle and chord length in the root elements of the blades. In addition, it was observed that the performance of the turbine that was designed to work at sea level was weakened at greater elevations. Although the change in the C

_{p}can be ignored, the startup performance is prone to more severe impacts, and the reduction in the startup torque (M

_{s}) can be so drastic that it practically stops the turbine from operating in these regions, since the rotor cannot conquer the generator cogging torque (M

_{c}) and start rotating. In this case, the turbine loses its performance and cannot be used to generate power. This phenomenon was observed for the two-bladed turbine of the current research in Asadabad and Sisakht Counties, with elevations of 1607 and 2250 m above sea level. To solve this problem, the blade was redesigned based on the local atmospheric conditions in which the turbine was intended to be used, and improvements were observed in the C

_{p}and T

_{s}of the blades, especially the ideal blades.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**(

**a**) Topographic map of Iran. (

**b**) The location of the Hyrcanian forests in the north of Iran.

**Figure 7.**Comparing the values from the numerical code and Reference [70] data.

**Figure 11.**The inertia values for the blades made of the selected timbers with different W

_{f}values.

Case Study | County | Elevation (m) | Air Density (kg/m^{3}) | Air Kinematic Viscosity (m^{2}/s) | Coordinate E–N |
---|---|---|---|---|---|

Sea level | - | 0 | 1.225 | 1.460 × 10^{−5} | - |

1 | Dalgan | 392 | 1.1795 | 1.525 × 10^{−5} | 59°32′–27°26′ |

2 | Maku | 1182 | 1.0919 | 1.624 × 10^{−5} | 44°38′–39°29′ |

3 | Asadabad | 1607 | 1.0468 | 1.680 × 10^{−5} | 48°8′–34°47′ |

4 | Sisakht | 2250 | 0.9814 | 1.771 × 10^{−5} | 51°45′–30°86′ |

Parameter | Population | Generation | Mutation Factor | Crossover Constant |
---|---|---|---|---|

Value | 3000 | 500 | 0.8 | 0.1 |

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

Output Power | 1000 W | V_{s} | 4 m/s | R_{h} | 0.125 m |

B | 2 | V_{rated} | 8 m/s | ω | 450 rpm |

Min c/R | 0.01 | Max c/R | 0.2 | M_{c} | 0.5 Nm |

Min β | −5 | Max β | 25 | Generator inertia | 0.01 kg·m^{2} |

Parameter | Reference [16] | Current Research | Deviation (%) |
---|---|---|---|

Startup time (s) | 5.1 | 5.2 | 1.96 |

Timber | ρ_{b} (kg/m^{3}) | W_{f} = 1 | W_{f} = 0.9 | W_{f} = 0.8 | |||
---|---|---|---|---|---|---|---|

C_{p} | T_{s} (s) | C_{p} | T_{s} (s) | C_{p} | T_{s} (s) | ||

Alder | 490 | 0.480 | 8.08 | 0.469 | 2.75 | 0.446 | 2.12 |

Oak | 600 | 0.479 | 17.86 | 0.469 | 3.39 | 0.444 | 2.61 |

Hornbeam | 707 | 0.480 | 19.83 | 0.469 | 3.98 | 0.445 | 3.09 |

**Table 6.**The performance of the optimal blades for the sea level (made of alder timber) at different elevations.

Case Study | W_{f} = 1 | W_{f} = 0.9 | W_{f} = 0.8 | |||
---|---|---|---|---|---|---|

C_{p} | T_{s} (s) | C_{p} | T_{s} (s) | C_{p} | T_{s} (s) | |

Dalgan (392 m) | 0.477 | 20.71 | 0.466 | 2.95 | 0.443 | 2.26 |

Maku (1182 m) | 0.475 | 61.67 | 0.462 | 3.42 | 0.441 | 2.58 |

Asadabad (1607 m) | 0.471 | - | 0.460 | 3.72 | 0.439 | 2.77 |

Sisakht (2250 m) | 0.470 | - | 0.457 | 4.26 | 0.436 | 3.11 |

**Table 7.**The performance of the optimal blades for the sea level (made of alder timber) at different elevations.

Case Study | W_{f} = 1 | W_{f} = 0.9 | W_{f} = 0.8 | |||

C_{p} | T_{s} (s) | C_{p} | T_{s} (s) | C_{p} | T_{s} (s) | |

Dalgan (392 m) | 0.479 | 6.73 | 0.468 | 2.95 | 0.446 | 2.28 |

Maku (1182 m) | 0.479 | 9.35 | 0.467 | 3.39 | 0.444 | 2.58 |

Asadabad (1607 m) | 0.479 | 11.89 | 0.466 | 3.67 | 0.444 | 2.78 |

Sisakht (2250 m) | 0.478 | 17.76 | 0.465 | 4.22 | 0.442 | 3.27 |

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**MDPI and ACS Style**

Akbari, V.; Naghashzadegan, M.; Kouhikamali, R.; Yaïci, W.
Evaluation of Regional Elevation and Blade Density Effects on the Efficiency of a 1-kW Wind Turbine for Operation in Low-Wind Counties in Iran. *Wind* **2023**, *3*, 320-342.
https://doi.org/10.3390/wind3030019

**AMA Style**

Akbari V, Naghashzadegan M, Kouhikamali R, Yaïci W.
Evaluation of Regional Elevation and Blade Density Effects on the Efficiency of a 1-kW Wind Turbine for Operation in Low-Wind Counties in Iran. *Wind*. 2023; 3(3):320-342.
https://doi.org/10.3390/wind3030019

**Chicago/Turabian Style**

Akbari, Vahid, Mohammad Naghashzadegan, Ramin Kouhikamali, and Wahiba Yaïci.
2023. "Evaluation of Regional Elevation and Blade Density Effects on the Efficiency of a 1-kW Wind Turbine for Operation in Low-Wind Counties in Iran" *Wind* 3, no. 3: 320-342.
https://doi.org/10.3390/wind3030019