Build-up an analysis model to evaluate wind potential for selecting suitable turbine configurations and proposing research to optimize wind farm design

Abstract

Before a wind farm is constructed, the assessment of wind potential in the proposed turbine installation area must be carried out as a prerequisite. To achieve the highest efficiency, the key concepts and a deep understanding of wind energy evaluation must be mastered by the design engineers. The article of study applies Weibull distribution theory and aerodynamics fundamental to build an analytical model for evaluating standards and estimating annual electricity output based on raw input data collected over a year. The calculation results for the wind characteristics, including shape and scale factor and power density at the surveyed area corresponding to an 80m height, are determined in detail by simulation software. The analysis results also indicate that the wind potential here is classified as very high (class 6), and a minimum II-A type turbine configuration must be selected to withstand these wind conditions.

Since the initial investment cost of a wind farm will be determined by the simulation results, the study aims to combine the calculation methods used in this research with the application of digital twin solutions and machine learning for wind farms to create an accurately digital replica of a physical system. In this way, real-time system operations will be monitored and continuously updated into the simulation model to understand and predict its behavior. From there, optimal design and operation adjustments will be made to enhance the overall system's efficiency and minimize errors and risks for investors.

Introduction

Recently, within the national strategy on Climate Change, the Vietnamese government has announced the goal of reducing emissions by 43.5% by 2030, with practical proposal and effective international support. Emission targets have been set for each sector for the years 2030 and 2050, alongside several qualitative proposals to achieve these goals. Among these proposals are policies to support the development of wind power projects in Vietnam 1 .

To construct a wind power plant, the first requirement is to have a basic knowledge of wind energy. Specifically, whether a wind power project is grid-connected or standalone, the core activity to assess the feasibility of the project is the Wind Resource Assessment (WRA) process 2 . The output data from WRA will be used and serve as the input for financial analysis and the overall feasibility assessment of entire project 3 .

Currently, wind farms are increasingly being developed, offering significant opportunities to enhance autonomous operation and optimize system productivity. In light of these, the research has developed an annual energy production (AEP) analysis model to select suitable turbine configurations 4 .

This analytical model plays a vital role in providing estimated electricity generation results with high reliability and accuracy of 100% when the characteristic parameters of the input wind dataset are identified. Additionally, the model also assists in predicting energy sources at different altitudes when planning designs to aid in feasibility assessments. The research results will provide a more detailed and intuitive perspective on providing useful scientific information that serves as a valuable reference for future wind power projects.

INPUT DATA AND METHODOLOGY

Data source

The input data consist of wind speed measurements taken every 10 minutes continuously over one year at the Con Dao telecommunications station as in Figure 1 at altitudes of 30m, 50m, and 60m above ground level respectively.

Figure 1 . The Con Dao Island map and picture of installation of anemometer at altitudes of60m, 50m & 30m

Based on these gathered wind speed data series, which to be presented in the form of Table 1 and chart as shown in Figure 2 to analyze and evaluate the characteristic of the avarage hourly wind speed at diffferent elevation.

Table 1 Hourly average wind speed at different elevation

Figure 2 . Hourly average wind speed in year (from 0h to 23h) at observed heights.

Methodology

In this study, an experimental method is proposed by collecting and processing data along with a mathematical method of probabilistic statistical analysis. According to the Weibull distribution is used to determine the importantly characteristic parameters of wind. Thermodynamic properties of moist air also is applied to build a simulation model by using MATLAB software to provide predictive results and potential assessment.

The classification of turbines according to the IEC-1400-1 standard is determined by average wind speed and turbulence intensity. The IEC-1400-1 standard defines four standard classes: I, II, III, IV, and an additional class S. For class S, all wind field parameters must be specified by the manufacturer. The average wind speeds for classes I through IV correspond to 10 m/s, 8.5 m/s, 7.5 m/s, and 6 m/s, respectively. In addition to these standard classes, turbulence intensity is categorized into high, medium, and low (classes A, B, and C).

THE ANALYSIS MODEL FOR EVALUATION AND ESTIMATING ANNUAL ELECTRICITY OUTPUT

The kinetic energy (E) of the wind in moving can be determined as the formular 5

(3-1)

where m is the mass of air passing through a circular plane perpendicular to the wind direction and ν is the mean wind speed over a suitable time period that can be seen in Figure 3 .

Figure 3 . Kinetic energy and swept area of wind turbine

The wind power can be obtained by differentiating the kinetic energy in wind with respect to time:

However, only a small portion of wind power can be converted into electrical power. When wind passes through a wind turbine and drives blades to rotate, the corresponding wind mass flowrate is:

Where ρ is density of a moist air (kg/m ³ ) and A is the swept area of blades (m ² )

From above formula of (3-2) and (3-3), simplifying this we get a power (P) can be expressed as 5 :

The effective power through a wind turbine for electricity generation is significantly less than the energy in the air stream. According to Betz’s law, theoretically, only a maximum of 59,3% of the energy in the air stream can be captured because the wind speed behind a turbine cannot be fully absorbed and reduced to zero.

Statistical modeling of wind speed data

The statistical modeling method is applied the Weibull probability distribution as a crucial form to describe the statistical appearance of extreme values in meteorology, hydrology and weather forecasting. The Weibull distribution provides a reasonable mathematical description for wind speed graphs. This distributon is used to analyze probability, predict operational time, and estimate the electricity generation.

The Weibull probability density function :

Where:

k: Shape factor

A: Scale factor

Below frequency distribution graphs are created by grouping wind speeds. The shape parameter k and the scale parameter A allow the Weibull function to be fitted to the measured frequency distributions. Each region will have different k and A values, as illustrated in Figure 4 , Figure 5 .

Figure 4 . Weibull probability density function according to k-values

Figure 5 . Weibull probability density function according to A-values

Power density of wind speed

To understand the inpact of the statistical distribution of wind speed on power generation, we need to calculate this power density of wind speed.

Power density (PD) is defined as follow:

However, this PD value must be applied integral function to achieve result more accurate:

Where: v is wind speed (m/s), pd(v) is Weibull probability density function

Conventionally, wind intensity in the surveyed area is classified based on power density to evaluate the wind energy potential of that specific area. To assess this potential, wind speeds are categorized into 7 levels according to Table 2 . Based on the calculated power density using formula 3-6, we can determine whether that area has wind potential or not.

Table 2 Wind classification at reference heights 10m & 50m 6

Air density correction according to ambient temperature

Typically, wind energy is surveyed at ambient temperature. Air density (ρ) is also a factor that affects power density (PD). The relationship between PD and ρ is linear. Air density depends on pressure, temperature and relative humidity, both pressure and temperature decrease with altitude. The formula for calculating air density is obeyed the perfect gas equation of state as follows 7 :

Where:

• p: atmospheric pressure, (atm)

• V: total mixture volume (i.e dry air & water vapor), (m ³ )

• n: number of moles of air (mol)

• R: universal gas constant, 8,314 J/(mol.K)

• T: absolute temperature, (K)

With ρ = n/V, molecular weight per volume unit.

Hence, the term M (gam) represents the molecular weight of air. Air density is defined in below formula:

Otherwise, the pressure depends on altitude. The pressure value may be calculated from 5 , 8 :

Where:

M: the molecular weight of air, (M = 28.97 g/mol)

Z: altitude, m

This correction is necessary for wind energy assessment at different altitudes.

Wind speed distribution by Altitude

Wind speed is typically measured at a specific altitude above the sea level as indicated in Figure 6 . However, to enhance the efficiency of wind energy utilization, it is sometimes necessary to consider wind speeds at various heights. The equation for velocity as a function of altitude is expressed by the formula:

Where:

v ₁ ,v ₂ is the wind speed at height h ₁ , h ₂ , respectively

γ is the wind shear exponent, which varies depending on the terrain and atmospheric conditions.

Figure 6 . Wind speed distribution by height

In case of considering to extrapolate wind speed, γ-coefficient may be determined as follows:

Additionally, in cases of lacking observational input data, we can refer to the Table 3 to find γ coefficient for each specific condition.

Table 3 Terrain’s roughness classification & wind shear coefficient

Correlation between characteristic parameters of the Weibull

In addition to the two characteristic parameters k and A factor of Weibull distribution. We may establish other relationship of wind speed as follow:

Where: Γ(x) is gamma function, if x is an integer then Γ(x) = x!

To simplify this, we may apply the approximate formula as below:

ANALYTICAL RESULT OF WIND POTENTIAL ASSESSMENT AND TURBINE CONFIGURATION SELECTION

Frequency of wind speed levels

Frequency of wind speed levels

Frequency of wind speed levels

Statistical characteristics of the data series for

Statistical characteristics of the data series for

Statistical characteristics of the data series for

Wind Speed Data Conversion

Since the statistical data series of wind speed is not available at 80m, it is necessary to extrapolate and convert from the surveyed data series at other heights.

Based on the collected data series, applying formula 3-13 to find out γ value which allows for the conversion of wind speed. To verify the accuracy of γ-coefficient, the statistical data series at a height of 60m is used to convert wind speeds at 30m and 50m respectively. These converted data are then compared and evaluated against actual data at these heights to conclude the reasonableness of the chosen γ value. Using this method, the converted and statistical data values are listed in Table 4 and illustrated in Figure 9 .

Table 4 Average hourly windspeeds throughout the Year at observed heights of the statistical data seriesand calculated converted data

Figure 9 . Average hourly wind speeds throughout the year at observed heights and converted

As the result in Table 4 and Figure 9 , the error between the calculated converted data and actual collected data is negligible and entirely acceptable. All curve lines representing these data are almost coincident.

Conclusion: Using the formula to calculate γ-coefficient for converting wind speed at a height of 80m is accepted.

Variation of Average Hourly Wind Speed Throughout the Year at 80m Height

Table 5 Average Hourly Wind Speeds Throughout the Year at 80m Height, Extrapolated from the Statistical Data Series

Figure 10 . Average Hourly Wind Speeds Throughout the Year at 80m Height, Extrapolated from the Statistical Data Series

Characteristic Parameters of the Data Series for Calculation

Based on the 10-minute average wind speed data series collected at heights of 30m, 50m, and 60m, the extrapolation of wind data to a height of 80m was carried out as indicated in Table 5 and Figure 10 ). The wind data characteristics were derived using the Weibull distribution function, similar to the method used for the 60m height. The results are illustrated in Figure 11 and Figure 12 .

Figure 11 . The statistical frequency of converted wind speed at the height of 80m

Figure 12 . Characteristics of wind speed data at 80m follow Weibull Distribution

Where:

• Air density at 80m: ρ = 1,167 kg/m ³

• Shape factor: k = 2,23

• Scale factor: A = 9,55

• Average wind speed: 8,46 m/s

• Mode = 7.32 m/s

• Standard deviation: σ = 4.0 m/s

• Power density: PD = 608,29 W/m ²

Observation:

With an average power density of approximately 608.29 W/m² at a height of 80 meters, the wind potential of this area is very high and classified into class 6. Comparing the results at heights of 60m and 80m, it is evident that the higher the altitude, the greater the energy potential. Therefore, installing wind turbine at a height of 80 meters is very reasonable.

Selection of Turbine Based on Power Generation Capacity and Annual Electricity Production Estimation

Selection of Turbine Based on Power Generation Capacity and Annual Electricity Production Estimation

Selection of Turbine Based on Power Generation Capacity and Annual Electricity Production Estimation

Estimation of Annual Electricity Production

Estimation of Annual Electricity Production

Estimation of Annual Electricity Production

Estimation of Annual Electricity Production

Estimation of Annual Electricity Production

CONCLUSION AND DISCUSSION

To avoid inaccurate forecasts and increased experimental costs that waste resources, each wind farm project, both existing and planned for the future, must be performed in detailed analysis. By creating computational models as illustrated in Figure 22 , we establish a basis for assessing the wind energy potential of a given area and data, estimating the maximum annual electricity production a turbine can generate with highly reliable and accurate analysis results, and ultimately evaluating turbulence intensity conditions to select the appropriate turbine type for the intended installation site.

Figure 22 . The Analytical Modelof Annual Energy Potential Calculation.

Furthermore, to optimize the design and operation of the system in the future, the research proposes the development of digital twin (see Figure 23 ) and machine learning applications for wind farms 13 . This involves establishing Physics-based models to simulate operating conditions under various scenarios (what-if simulations) due to the continuous changes in input variables. Such analyses will enable appropriate adjustments to enhance the overall system efficiency. The benefits of digital twin somution include:

• Optimizing the placement of wind turbines to maximize wind energy capture.

• Increasing the electricity output of the wind farm.

• Reducing operational and maintenance costs.

• Extending the lifespan of the equipment.

Figure 23 . Digital twin modelcan predict failures and optimal design adjustment

Finally, the development of a hybrid model that combines Physics-based modeling and machine learning is proposed. This model will learn from actual operational data, improving and enabling an evaluation of the performance of system components and providing more accurate and optimal adjustment signals 14 , 15 .

Competing Interests

We hereby confirm that there are no conflicts of interest regarding the entire content of this paper.

Authors' Contributions

Truong Trong Hieu: Collected input data, processed and performed data analysis, developed algorithms, and built analytical software with graphical visualization, wrote and revised the manuscript.

Nguyen The Bao: Advise mathematical formulas and contributed to manuscript revision.