What is the power coefficient?

The efficiency of a wind turbine is defined as the power coefficient (C_p), which is specific to the design of each turbine. The efficiency of a wind turbine is calculated as the ratio between the mechanical power generated by the blades (P_mec) and the wind power (P_w). The wind power is defined as the kinetic energy per mass of wind moving (V_w) across a blade-swept surface (A), which is defined by the air density (). The air density is approximately equal to 1,225 kg/m³ at sea level and at a temperature of 15°C.

The maximum theoretical value of the power coefficient is obtained through the application of Betz’s law, which indicates that the maximum value is approximately equal to 59%. This implies that the wind turbine is capable of converting a maximum of 59% of the kinetic energy of the wind into mechanical energy.

Mathematical model of the Power Coefficient

The power coefficient surface of an individual wind turbine model can be described as a function of its aerodynamic characteristics, the tip-speed ratio (λ), and the pitch angle (β). Commonly used models for defining the power coefficient (C_p) include the exponential model, which is outlined as follows:

The tip speed ratio is defined as the ratio between the magnitude of the tangential velocity and the magnitude of the wind speed.

Where is the angular velocity of the wind turbine and R_t is the radius of the wind turbine.

The figure below shows the power coefficient surface as a function of λ (rad) from 0 to 15 rad and β (sexagesimal degrees) varying from 0° to 45°. The maximum value of the power coefficient is approximately equal to 0.425 and is given for a pitch angle (β) equal to 0° and a tip-speed ratio (λ) equal to 6.9.

It can be observed that an increase in pitch angle (β) results in a reduction in power coefficient. This establishes the fundamental concept of mechanical power control by pitch angle in zone 4 of the wind turbine power curve.

Each power coefficient curve generated by different values of beta exhibits a maximum value. When the wind turbine is operating at partial load, the angle β is equal to zero.   

Relationship between the number of blades and wind turbine efficiency

Figure 3 depicts the distinct power coefficient curves for various categories of wind turbines. In a series of wind tunnel experiments, Poul La Cour reached the following conclusion: “More blades does not mean more power”. This shows that an increase in the number of blades on a wind turbine results in a corresponding decrease in efficiency. American multi-bladed wind turbines are the least efficient, whereas the most efficient are three-bladed and two-bladed wind turbines. The rationale for selecting a three-bladed wind turbine, despite its slightly lower efficiency compared to the two-bladed, is based on technical and economic considerations. For example, to generate the same power, a three-bladed wind turbine requires a lower rotational speed than a two-bladed one.

For different rotor types, the optimum tip-speed ratio varies. For multi-bladed wind turbines, λ has a value of approximately one, and as the number of blades decreases, λ increases. For example, the power coefficient curves in Figure 2 correspond to a three-bladed wind turbine. This type of wind turbines, which are the most widely used at the industrial level, have an optimum tip speed between 6 and 8 rad.

Conclusion

The power coefficient (C_p) is a fundamental parameter for evaluating the efficiency of a wind turbine, as it quantifies the fraction of wind energy that is converted into mechanical energy. According to Betz’s Law, the theoretical maximum value of C_p is 59%. Various factors, including the tip-speed ratio (λ) and pitch angle (β), exert a direct influence on C_p. Three-bladed wind turbines exhibit the highest efficiency at the industrial scale. By optimizing C_p through rigorous design and control, it is possible to maximize wind power generation.

Reference

[1] Burton, T., etc., Sharpe, D., Jenkins, N., & Bossanyi, E. (2001). Wind Energy Handbook. John Wiley & Sons.

[2] Ackermann, T. (Ed.). (2012b). Wind Power in Power Systems: Ackermann/Wind Power in Power Systems. Wiley-Blackwell.

Reference frame theory uses mathematical transformations to simplify the modeling, analysis and simulation of balanced three-phase circuits, power converters and electrical machines. Three main types of reference frames are widely used in electrical engineering. These reference frames are classified according to the speed of the reference frame and the nature of the variables involved.

Natural reference frame abc

The reference frame has an electric angular velocity (ω) equal to zero and is referred to as a three-phase stationary frame. The three-phase variables exhibit a time-varying nature (AC) with a phase shift of 120 degrees. This frame represents the actual correlation between the machine or power converter construction and the corresponding mathematical model.

The generic balanced three-phase variables are considered as follows:

Where 𝐹 is the peak amplitude (V, A or Wb), 𝜔 is the angular frequency (rad/s), θ₀ is the initial phase and 𝑡 is the time.

The three-phase function is represented by a phasor in the equivalent natural reference frame space, as shown below:

Where a is the Fortescue operator:

Stationary reference frame αβ: Clarke transform

The Clarke transform is a mathematical tool used in electrical engineering, and in particular for vector control, to model a three-phase system using a two-phase model. It was proposed by Edith Clarke, one of the first female pioneers in the field of electrical engineering. She invented a graphing calculator that facilitated the solving of electrical equations. She was the first woman to present a scientific paper at the annual meeting of the American Institute of Electrical Engineers (AIEE) in 1926. Furthermore, she was also the first woman to earn a Master of Science degree in electrical engineering from MIT and the first professor of electrical engineering at the University of Texas at Austin.

The Clarke transform is also known as the αβ transform, and it is precisely these complex coordinates (α as the real component and β as the imaginary component of the two-phase system) onto which we project our three-phase system (a, b, c) of phase voltages or currents.

The phasor in the natural reference frame space, 𝑓_𝑎𝑏𝑐(𝑡), is decomposed into real and imaginary components to form a phasor in the stationary reference frame space.

The angle between the α and β component is calculated as follows:

Clarke’s transformation matrix is applied as follows:

Synchronous reference frame dq: Park transform

The Park transform, also known as the dq-axis transform, is a mathematical tool used in electrical machine theory to simplify the analysis and control of alternating current (AC) machines, such as synchronous or induction motors and generators. Robert H. Park is remembered for developing the “Park equations”, presented in 1929, which greatly simplified the calculation of the dynamic performance of alternating current generators and motors, and which have been fundamental in the engineering of electric power systems. His work allowed a practical and efficient analysis of the stability and reliability of electrical systems in the face of disturbances. In addition, during World War II, he developed magnetic mines for the U.S. Navy, earning multiple patents. Throughout his life, Park was a prolific innovator, with 64 patents, and his contribution remains key in the field of electrical engineering. Park submitted his paper to the AIEE entitled “Two reactions theory of synchronous machines” in which he presented a generalization and extension of the work of Blondel, Dreyfus and Doherthy and Nickle. This paper established general methods for calculating current, power, and torque in salient-pole and smooth-break synchronous machines under both steady-state and transient conditions.

Park’s transformation converts the three-phase current and voltage variables (which vary sinusoidally in time) to a rotating reference coordinate system (direct “d” and quadrature “q” axes), where these variables become constant or of lower frequency. This facilitates the analysis of electrical machines and the design of controllers.

The phasor in natural reference frame space, 𝑓_𝑎𝑏𝑐 (𝑡), is decomposed into real and imaginary components to form a phasor in synchronous reference frame space.

When the a-axis is aligned to the q-axis the equation is:

When the a-axis is aligned to the d-axis the equation is:

Where θ (In both cases, θ = ωt) is the angle between the a and q axes for the q-axis alignment or the angle between the a and d axes for the d-axis alignment, ω is the rotational speed of the dq reference frame, t is the time, from the initial alignment.

Example

A three-phase RMS voltage signal of 220 V and 60 Hz is shown for 0.45 seconds at reference frames abc, αβ0 and dq0 under three conditions. Between instants t=0 and t=0.15, the system is three-phase balanced. Between instants t=0.15 and t=0.3, phase “a” undergoes a 60% decrease in the RMS value of the voltage. Finally, between instants t=0.30 and t=0.45, harmonics of the 5th and 7th positive sequences are introduced, with an amplitude of 20% and 15% of the RMS voltage value, respectively.

Applications

Clarke and Park transformations were originally developed to facilitate the analysis and modeling of electrical machines. Today, dq0-based models are used in a wide range of applications, such as electrical control and drive, modeling of multiple machines and power converters, electric vehicles, microgrid simulation, phase-locked loops (PLLs) and active power filters. In addition, these transformations are essential in the field of renewable energy. In numerous instances, dq components are no longer limited to the direct and quadrature axes of an electrical machine, suggesting a broader interpretation of reference frames, decoupled from specific technologies or applications.

Conclusion

The Clarke and Park transforms are essential mathematical tools for the analysis and control of three-phase electrical systems, and they simplify the study of electrical signals. The Clarke transform converts three-phase signals into a two-phase system, allowing for the identification of symmetrical and unbalanced components. The Park transform, however, brings these components into a rotating reference frame, which is useful for precise control of electrical machines and power converters. These transformations are applied to various areas, such as motor control, converters, microgrids, and renewable energy, allowing for a more general interpretation of reference frames for complex electrical analysis.

Reference

[1] O’Rourke, C. J., Qasim, M. M., Overlin, M. R., & Kirtley, J. L. (2019). A geometric interpretation of reference frames and transformations: Dq0, Clarke, and park. IEEE transactions on energy conversion, 34(4), 2070–2083. https://doi.org/10.1109/tec.2019.2941175

What is a wind rose?

The wind rose is a polar diagram that defines wind magnitude, frequency, power, and energy for different directions. It analyzes the origin of the wind and its characteristics. Typically, the wind rose is divided into 12 sectors, each spanning 30°, 16 sectors, each spanning 22.5° or for greater precision in 24 sectors, each covering 15°.

Wind magnitude and direction data

The simulation data can be downloaded from the following repository: https://data.mendeley.com/preview/zrr487ry6x

It is important to note that wind direction measurements are taken with geographical north as the reference and in a clockwise direction.

Types of wind roses

The wind energy sector employs the following types of wind roses, which have been calculated at a height of 50 meters:

a) Frequency rose

The polar diagram shows the frequency of wind magnitudes for each range of wind directions.

b) Speed rose

The polar diagram shows the average wind speeds (m/s) for each wind direction range.

c) Power rose

The polar diagram shows the average power per square meter (W/m²) for each wind direction range. The power data is directly proportional to the cube of the wind speed in the direction, with representing the air density.

d) Energy rose

The polar diagram shows the energy per square meter (kWh/m²) for each wind direction range. The energy for each direction is given by the wind turbine power j in the direction and the time for each time stamp of one hour.

Which type of wind rose is used in the design of a wind farm?

All types of wind roses provide us with specific information, but the type that is most relevant to optimizing the design of a wind farm is the so-called “energy rose.” This provides us with the directions that concentrate the most annual energy, i.e., the directions from which the wind blows for the most hours per year and with the most power.

Reference

[1] Cucó Pardillos, S. (2017). Manual de energía eólica. Desarrollo de proyectos e instalaciones. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/77752.

[2] R. Byrne, N.J. Hewitt, P. Griffiths, P. MacArtain, “Observed site obstacle impacts on the energy performance of a large scale urban wind turbine using an electrical energy rose”, Energy for Sustainable Development: The Journal of the International Energy Initiative, Volume 43, 2018, Pages 23-37, ISSN 0973-0826. https://doi.org/10.1016/j.esd.2017.12.002.

The parts that make up a wind turbine are as follows:

1. Blades

The blades of a wind turbine are the components that directly interact with the wind, which is why they are designed with a profile that maximizes their aerodynamic efficiency. Most blades are manufactured using polyester or epoxy reinforced with fiberglass. This material consists of a matrix of synthetic resin and fiberglass fibers, providing the blades with lightness, durability, and resistance to corrosion and moisture. Carbon fiber can also be used as a reinforcement material to enhance the strength and rigidity of the blades. However, carbon fiber comes at a higher cost and poses challenges in terms of recycling.

Transporting the blades can be a major challenge. Larger wind turbines require longer blades, which can complicate their transport to the wind farm.

2. Hub

The hub of a wind turbine is the component responsible for connecting the blades to the shaft that transmits motion to the gearbox in the case of a Doubly Fed Induction Generator (DFIG) or to the generator shaft in the case of a Direct-Drive Permanent Magnet Synchronous Generator (PMSG). The hub contains mechanisms for changing the pitch angle of the blades. The hub is typically made of steel or cast iron and is aerodynamically designed to prevent the formation of turbulence and allow for maximum free airflow.

3. Blade orientation system

It consists of a series of mechanical, electrical, or hydraulic mechanisms that allow for adjusting the pitch angle of the blades. Their purpose is to maintain constant mechanical power when the wind speed exceeds the nominal value (as can be seen in the wind turbine’s power curve). This system can also be considered a protective measure to prevent the wind turbine from exceeding its nominal speed.

The blades move relative to their axis to control the mechanical power. This type of control is called “pitch angle control”.

4. Wind turbine orientation system

The nacelle rotates along the vertical axis of the tower using an active and rotating orientation control system, which consists of electric actuators. The wind direction and speed are continuously monitored by sensors located on the nacelle’s cover, called anemometers and wind vanes. The aim is to align the wind turbines in the direction of the prevailing wind to maximize wind energy capture.

5. Gearbox

The function of the gearbox is to connect the shaft that joins the blades at the hub with the generator shaft. Its purpose is to multiply the turbine’s rotational speed to an efficient speed for the electrical generator. Without a gearbox, the electrical generator would need to rotate optimally between 10 and 25 rpm, meaning a generator with many poles would be required.

Therefore, the gearbox can be thought of as a mechanical transformer. It can multiply the wind turbine’s rotation speed, for example, 1:50, 1:70, 1:80, 1:90, 1:100, 1:110. The higher the multiplication factor, the more complex the gear system and gearbox stages will be. The gearbox provides a higher rotation speed for the electrical generator but lower mechanical torque.

6. Electric generator

6.1. Squirrel Cage Induction Generator (SCIG):

This configuration corresponds to the so-called “Danish concept”, which was very popular in the 1980s. This type of electric generator consumes reactive power, which it can absorb from the grid or a bank of capacitor batteries. To connect it to the grid, a soft-start system is used, based on thyristors, in order to limit the starting current. This generator can cause power oscillations that are directly transferred to the grid. Its main advantages are its smaller size, lower cost, and the simplicity of the control system.

6.2. Doubly Fed Induction Generator (DFIG):

It has been used since the year 2000. An electronic power converter is connected in a back-to-back configuration. Through the use of the electronic power converter, the frequency and current in the rotor can be flexibly controlled, thus extending the range of variable speeds to a satisfactory level. Control is achieved by injecting variable current into the rotor winding, both in magnitude and frequency. The speed variation range is about ± 30% of the rated speed. The stator is directly connected to the grid, while the rotor is connected through power converters with a fraction of power between 20% or 30% of the rated power. Disadvantages include having slip rings, requiring a multi-stage gearbox to connect to the wind turbine, incurring higher maintenance costs, and experiencing increased losses mainly due to the mechanical transmission train.

6.3. Permanent Magnet Synchronous Generator (PMSG):

This type of generator is the most commonly used alongside the DFIG generator. Unlike the DFIG, it integrates full-scale power electronic converters to connect to the electrical grid. This generator type has a greater capacity to support the electrical grid and requires less maintenance. It utilizes rare earth magnets in the rotor, which have a high magnetic flux density. Its primary disadvantage is the cost of the magnet, as it is subject to global uncertainty and can potentially demagnetize due to electrical faults in the generator.

7. Power electronics interface

The power electronics interface plays a crucial role in wind turbines. It is responsible for the transformation, control, and optimization of energy. Power converters are used to control the flow of active and reactive power in both steady and dynamic states, from the electric generator to the power grid. The rotational speed of variable-speed wind turbines is decoupled from the electrical frequency due to the electronic interface; in other words, they do not rotate in sync with the power grid, as a conventional synchronous generator would. The Back-to-back connection is the most commonly used and consists of two voltage-source converters (VSC).

These converters are composed of semiconductor devices such as the Insulated Gate Bipolar Transistor (IGBT), which functions as a controlled switch. IGBTs are controlled using pulse-width modulation techniques. The power converters, along with their control system, act as the “brain” of the wind turbine. It is vital that their operation is appropriate and optimal to ensure the proper functioning of the entire wind energy conversion system.

8. Transformer (LV-MV)

The electrical output power of the wind turbine is generally low voltage and is converted to medium voltage through a transformer to reduce transmission losses by connecting to the medium voltage grid. The transformer is installed either in the nacelle or at the base of the tower. It is a dry-type transformer with two windings.

Conclusion

In conclusion, wind turbines are complex systems as they encompass electrical, electronic, mechanical, aerodynamic, and structural subsystems. Wind turbines are the pillars of renewable energy generation due to their increased capacity in recent years. Each component, from the blades to the electrical generators, plays a vital role in capturing and transforming wind energy into electricity. The blades are aerodynamically designed and constructed with advanced materials to maximize efficiency and durability. The orientation systems ensure optimal operation by continuously adjusting the blades and nacelle based on wind conditions. The gearbox and various types of electrical generators, such as SCIG, DFIG, and PMSG, enable effective conversion of mechanical energy to electrical energy, each with its specific advantages.

The power electronics interface is the “brain” of the wind turbine, managing the power flow and decoupling the rotational speed of the wind turbine from the electrical grid frequency. This control and optimization capability is crucial for the overall system performance. Finally, the transformer raises the generated low voltage to a medium voltage level, minimizing transmission losses and ensuring efficient integration with the electrical grid.

Overall, the engineering behind each part of the wind turbine is fundamental to its efficiency and reliability, making these machines a key element in the transition to cleaner and more sustainable energy sources.

What is the wake effect in wind energy?

The wake effect in wind energy occurs when the wind flow is influenced by the presence of a wind turbine, which impacts nearby turbines. When the wind encounters a wind turbine, it creates a zone of low pressure behind it, resulting in slower and less energetic wind for the subsequent turbines. This situation reduces the efficiency and performance of downstream turbines, known as the wake effect.

Optimizing the arrangement of wind turbines is crucial to maximize the utilization of available space in a wind farm. On one hand, it is necessary to maintain an appropriate spacing between turbines to avoid the influence of wake shadows and generated turbulence, which can reduce the overall production of the wind farm. On the other hand, the turbines should be positioned close enough to optimize the available area and minimize the costs of the internal medium-voltage grid of the wind farm, as well as energy losses in the grid.

The design of wind farms poses a challenge due to the phenomenon of multiple wakes. Calculating the wake effect is a significant issue in wind farms and requires accurate modeling to minimize power losses caused by the wake effect both at close and far distances.

In this video, we will explore how Siemens Gamesa Renewable Energy is maximizing wind energy production through wake optimization. We will delve into their innovative approach to strategically placing wind turbines and utilizing cutting-edge technology, enabling them to generate more energy efficiently and profitably. With the use of NVIDIA Modulus and Omniverse, designers in the wind energy industry have the ability to merge traditional methods with physics-based super-resolution artificial intelligence models. This allows for the generation of high-resolution simulation data at significantly faster rates, resulting in the creation of more precise and detailed engineering wake models.

Impact of the wake effect on the performance of wind farms

The impact of the wake effect on a wind farm is significant and can have several consequences on the efficiency and overall performance of the system. Below are some of the main impacts:

a) Decrease in Energy Production:

The wake effect causes a reduction in the speed and energy of the wind reaching the downstream wind turbines due to the upstream wind turbines. This diminishes the energy production of the downstream wind turbines as they receive a less powerful wind flow. Moreover, the effect can be cumulative and detrimental to the wind turbines in the last row of the distribution within the wind farm.

b) Loss of Efficiency:

Due to the decrease in wind speed, wind turbines affected by the wake effect operate at suboptimal speeds. This results in a reduction in energy conversion efficiency, as they fail to fully harness the available wind potential. Efficiency (ɳ) can be defined as:

Where is the measured power output of turbine , is la power output for free stream conditions, and is the number of turbines.

c) Uneven Wear of Wind Turbines:

The wake effect can also lead to uneven wear on the turbines within the wind farm. The downstream wind turbines experience fluctuating wind loads and turbulence, meaning that the wind speed is not evenly distributed across the entire blade sweep area. This can result in increased mechanical wear and shorten the lifespan of the wind turbines.

d) Limitations in Wind Turbine Placement:

The wake effect imposes restrictions on the optimal placement of wind turbines within a wind farm. It is necessary to strike a balance between maximizing energy production and minimizing the impact of wake effect. This involves considering the distance and configuration of the turbines to avoid interference between the generated wakes. Moreover, it heavily depends on the geography of the installation site, as a particular location on the terrain may be optimal for wind resource, but not suitable for tower installation.

Criteria for Wind Turbine Distribution

Wind turbines are arranged in one or multiple alignments perpendicular to the most energetic component of the wind, as indicated by the energy wind rose. The following suggestions are commonly used as criteria for spacing between turbines:

• For the spacing between turbines within the same alignment, a distance ranging from 2 to 3 times the rotor diameter (D) is typically established.

• For the spacing between alignments, a distance of 6 to 8 times the rotor diameter (D) is applied.

The spacing between turbines is determined based on the “wind shadow” they may create, which depends on the prevailing wind direction.

In Figure 3, the distribution of 48 wind turbines in a 120 MW wind farm is shown with a row orientation of 25 degrees relative to the reference direction.

Conclusion

Wake effect in wind energy is a crucial factor that influences the performance of wind farms. Its impact results in decreased energy production, efficiency loss, and uneven wear on turbines. To maximize production and minimize negative effects, optimizing the strategic placement of wind turbines is essential. By combining traditional methods with high-resolution artificial intelligence models, such as those offered by NVIDIA Modulus and Omniverse, faster and more accurate simulation data can be generated, enhancing the ability to mitigate wake effect and maximize efficiency in wind energy generation. Proper turbine distribution, considering appropriate spacing and configuration, is crucial for optimizing wind farm performance and minimizing interference among wake patterns.

Example statement

We have available the data for the average magnitude of wind speeds, measured every hour at a height of 120 meters, for an entire year. This provides us with a total of 8,760 data points of wind speeds.

Wind data used in the application: Download

Figure 1 displays the magnitudes of wind speeds over the course of a year from the data obtained from the previous link. Analyzing wind speeds in this manner is complex and not suitable for analysis.

Figure 1: Magnitude of wind speed during one year, recorded hourly.

On the other hand, representing wind speeds in the form of a histogram with wind speed intervals of 1 m/s is much simpler and easier to understand.

Below, we obtain the k and c parameters of the Weibull distribution obtained using different numerical methods.

a) By the least squares estimation method

The 8760 data points are divided into equal wind speed ranges to calculate the wind speed distribution and the distribution of relative frequencies. Table 1 shows the established ranges and the calculations performed to determine the “k” and “c” parameters of the Weibull distribution.

Then, using the equations to calculate “a”, “b”, and “c”, the following values are obtained:

a = k = 3.334 ; b = -6.808 ; c = 7.707

Figure 3 shows the plot of the least squares linear fit.

Therefore, the Weibull distribution:

b) By the energy pattern factor method

The value of the Energy Pattern Factor is calculated using the wind speed data from the previous link.

The value of the shape parameter is calculated:

The value of the scale parameter is calculated:

Therefore, the Weibull distribution:

c) By the empirical method

The value of the shape parameter is calculated:

The value of the scale parameter is calculated:

Therefore, the Weibull distribution:

d) By the maximum likelihood method

For the maximum likelihood method, we use the MATLAB function wblfit(v), which is used to fit a Weibull distribution to a dataset and outputs a matrix containing the estimated values of the Weibull parameters. In another publication, the algorithm will be explained in more detail step by step. Below is the code to calculate the parameters:

Wind=xlsread('source of wind speed information');

% We calculate the parameters of the Weibull distribution
[parametros, intervalo] = wblfit(Wind);

% We display the results
disp(['The parameters of the Weibull distribution are:']);
disp(['c = ', num2str(parameters(1))]);
disp(['k = ', num2str(parameters(2))]);
disp(['The confidence interval for the parameters is:']);
disp(['[', num2str(interval(1)), ', ', num2str(interval(2)), ']']);

Therefore, the obtained Weibull parameters are:

c = 8.1721 ; k = 4.9566

Therefore, the Weibull distribution:

Method comparison

The following table shows a summary of the values obtained for the parameters c and k using the different methods mentioned earlier.

In Figure 4, the comparison of the Weibull probability curve is shown with the different parameters k and c obtained using the various numerical methods.

Conclusion

There are several methods to calculate the parameters of the Weibull distribution in wind speed analysis, such as least squares fitting, energy pattern factor, empirical methods, and maximum likelihood estimation. Generally, the maximum likelihood method tends to be the most accurate. Each method has its advantages and limitations, and the choice depends on the conditions and available data.

Types of Renewable Energy

The production of electrical energy from renewable sources refers to the production of energy through projects that utilize the energy produced by various renewable sources, such as hydroelectric, geothermal, wind, solar, bioenergy, and ocean energy, which includes the energy of tides, waves, and ocean currents. The following is a detailed explanation of how each of these renewable energy sources is captured and used to generate electricity.

Hydroelectric energy

This form of energy is derived from the energy in motion and the energy stored in the height of rivers and waterfalls. There are two main types of hydropower technology used to generate electricity: run-of-river and reservoir power plants. Reservoir power plants involve the construction of a reservoir to store water, while run-of-river power plants generally use the natural flow of the river. The main difference between the two types of hydroelectric plants is that reservoir plants are dispatchable, meaning that they can be scheduled to produce electricity, while run-of-river plants are not. In both types of power plants, water is directed toward turbines, creating a rotating motion that in turn generates electricity. Run-of-river plants use the kinetic energy of the river water, while reservoir plants use the potential energy of the water stored in the reservoir. To measure the performance of these plants, it is necessary to measure the water flow and the height of the water fall. The water flow measurement is used to determine the kinetic energy, while the water fall height measurement is used to determine the potential energy. To determine the hydroelectric potential, it is necessary to conduct field surveys to determine the available water resources.

Only run-of-river hydropower is considered a renewable energy source because it does not require a reservoir, which has an environmental impact.

Geothermal energy

Geothermal energy is derived from the heat found within the earth’s crust. To harness this energy, a fluid, such as water, is required to capture the thermal heat from within the earth’s crust. Typically, this fluid is found in the Earth’s crust, forming accumulations called reservoirs, which manifest outside the Earth’s crust in the form of geysers, hot springs, etc. By early 2021, available technologies will make it possible to harness the heat from these reservoirs as thermal and electrical energy, which depends on the temperature of the reservoir. The higher the temperature of the fluid, the greater its application in power generation plants. To determine the maximum power output of these plants, it is necessary to measure the temperature that could be reached in the fluid and also to identify the size of the reservoirs.

There are three types of geothermal power plants that can be identified: First, there are flash steam plants, which draw hot water at high pressure from deep within the earth and convert it to steam to drive the generator turbines. Then, as the steam cools, the water is condensed and returned to the well for reuse. Second, there are dry steam plants, which use dry steam to drive turbines and generate electricity through the generator. Finally, there are the binary cycle plants that transfer heat from hot water to another liquid that evaporates to power an electric generator.

To identify areas with geothermal potential, it is necessary to carry out exploration work, which is divided into three phases: geology, geophysics and geochemistry. Each of these phases is important in determining the presence of the geothermal resource and thus reducing the risk of discovering reservoirs that are technically infeasible to exploit. If, after the exploration phase, it is determined that there is geothermal potential, the exploitation phase can proceed, bearing in mind that there is still a risk that the reservoir may not be economically viable.

Wind energy

This form of energy is based on capturing the kinetic energy of the wind. It uses a technology that consists of an electric generator installed on a tower that harnesses the kinetic energy of the wind to produce electricity. The choice of the optimal size of the wind turbine blades and the appropriate height of the tower depends on the wind profile curve (which shows the wind speed as a function of height) and the geography of the terrain. Currently, the technology makes it possible to generate electricity both onshore and offshore. To measure the maximum power of these wind turbines, the wind speed and direction must be measured with an anemometer placed at the desired height.

Wind potential is calculated as a function of wind speed distribution. Wind turbines located at sites where the average wind speed is 8 meters per second at the height of the rotor axis produce between 75% and 100% more electricity than those where the average wind speed is 6 meters per second. A 1.8 MW wind turbine in a good location produces more than 4.7 GWh per year. This is enough to meet the annual electricity needs of more than 1,500 households.

There are three criteria for classifying wind turbines: turbine orientation (horizontal or vertical), installation characteristics (onshore or offshore), and grid connection (connected or unconnected). Horizontal axis wind turbines are the most popular and have an axis of rotation parallel to the ground. Typically, these turbines have three blades and can reach heights similar to a 20-story building. On the other hand, vertical axis wind turbines are less common and have an axis of rotation perpendicular to the ground. Depending on the shape of the turbine, they can be classified as “Darrieus” (2 or 3 arcs), “Panemonas” (4 or more semicircles) or “Sabonius” (2 or more rows of semicircles).

Solar energy

Solar energy is derived from the sun’s electromagnetic radiation. There are several ways to harness this energy, such as photovoltaic solar, which produces electricity, concentrating solar power, which also produces electricity, and solar thermal for domestic hot water, which produces heat. In photovoltaic solar technology, cells act as semiconductors that produce a physicochemical reaction that releases electrical energy in the form of direct current. Photovoltaic panels, which contain these cells with semiconductor material, are characteristic of this technology. There are several photovoltaic panel technologies on the market, with polycrystalline silicon cells being the most common due to their efficiency.

Concentrating solar thermal power technology works by using the reflection of the sun’s rays on mirrors to concentrate them on a fluid that is heated by absorbing the thermal energy generated by the sun’s rays. This thermal energy is then transferred to another fluid, usually water, which is turned into steam by the increase in temperature and drives a turbine to generate electricity. These systems operate at high temperatures, ranging from 400°C to 600°C. The most common concentrating solar thermal technologies are the concentrating tower, parabolic trough, and linear Fresnel reflector.

Finally, solar thermal technology for domestic hot water consists of a system that includes a tank and a solar panel containing a circuit through which water flows that absorbs the thermal energy provided by solar radiation, energy that is used in homes. These systems are designed to operate at low temperatures (up to 180°C) and are used for applications such as water heating, heating and swimming pools.

The efficiency of power generation in each of these technologies depends on climatic conditions such as cloud cover and the tilt of the sun’s rays relative to the Earth. To measure the maximum output of these systems, it is necessary to measure solar radiation, which is done using an instrument known as a pyranometer or solar meter.

Biomass energy (bioenergy)

Bioenergy is derived from biomass, which includes sustainable organic matter such as energy crops, agricultural and forestry wastes, animal wastes, and municipal and water treatment wastes. Biomass has multiple uses, such as fuel for combined heat and power, liquid biofuel production, and biogas production. The potential of biomass as a fuel and biofuel can be measured using satellite technology and cropland analysis. Biogas is produced by the biological decomposition of organic matter and can be recovered from landfills and wastewater treatment plants. Measuring biogas potential requires information on the amount and type of waste at production sites.

Ocean energy

There are several ways to extract energy from the oceans, such as tidal energy from the tides, wave energy from the waves, energy from ocean currents, and energy from the thermal gradient. Different technologies are available for each of these types of energy.
Although technologies are being developed to harness these forms of energy, they are still in the experimental phase due to their high development costs and the complexity of the marine environment. However, if cost-effective technologies can be developed to harness them, ocean energy could become an important source of renewable energy, helping to reduce greenhouse gas emissions and mitigate climate change.

The state of renewable energy in the world

Each year, more electricity is generated from renewable sources than the year before. By the end of 2021, installed renewable energy capacity was sufficient to provide approximately 28.3% of global electricity generation. However, projects continued to be impacted by supply chain issues, delivery delays, and rising global commodity prices. Below is the estimated global renewable energy capacity by type at the end of 2021 (Source: International Renewable Energy Agency’s Renewables 2021 Global Status Report):

Hydroelectric capacity includes only run-of-river power plants and excludes reservoir power plants, which are not considered renewable energy. The following figure shows the graph of the data from the previous table.

From the above table, it can be seen that hydropower remains the largest renewable energy source in terms of installed capacity, accounting for almost half of the total global renewable energy capacity by the end of 2021. However, wind and solar PV have also experienced significant growth in recent years and together account for more than 50% of total global renewable energy capacity. Bioenergy, geothermal and ocean energy are still a much smaller part of the renewable energy mix, but are expected to experience significant growth in the coming years as technologies continue to improve and costs continue to fall. Overall, the steady growth in global renewable energy capacity indicates a positive trend towards a transition to more sustainable energy sources and greater climate change mitigation.

Conclusion

In general, renewable energy is an increasingly important alternative to traditional energy sources that use fossil fuels and contribute significantly to climate change and pollution. Renewable energy, such as solar, wind, hydro, geothermal, and ocean power, uses inexhaustible and clean energy sources that do not emit greenhouse gases or other toxic pollutants.

The development and expansion of renewable energy has been driven by increased awareness and concern about climate change and the need to reduce greenhouse gas emissions to limit their impact on the environment. In addition, the declining cost of technologies such as solar panels, wind turbines, and batteries has made renewable energy increasingly cost-competitive with conventional energy sources.

Reference

[1] Environment, U. N. (2022, junio 16). Renewables 2022 Global Status Report. UNEP – UN Environment Programme. https://www.unep.org/resources/report/renewables-2022-global-status-report

[2] Carta González, José Antonio. Centrales de energías renovables : generación eléctrica con energías renovables, Madrid ES Pearson Educación 2013.

Advantages of wind energy

Renewable energy source

Wind energy is a renewable and sustainable energy source that does not emit greenhouse gases. It does not depend on fossil fuels and is therefore a clean form of energy that does not produce greenhouse gas emissions that contribute to climate change. In addition, wind energy is an inexhaustible source of energy because wind is always present in the atmosphere.

Reduced dependence on fossil fuels

Wind power reduces dependence on fossil fuels, thereby reducing a country’s exposure to price fluctuations and volatility in the global energy market. Wind power is becoming an increasingly important part of the energy mix in many countries, helping to reduce dependence on fossil fuels. This not only helps mitigate the effects of climate change, but can also provide energy security and reduce energy price volatility.

Low operating cost

Operating costs are the expenses necessary to keep the wind turbines in operation and in good working order. Operating costs include expenses such as wind turbine repair and maintenance, wind farm management and supervision, personnel safety, and site cleanup. Once installed, the cost of maintenance and operation is low compared to the operating costs of fossil fuel power plants.

Employment generation

Wind energy creates jobs at all stages of the supply chain, from manufacturing and installation to maintenance and operation. In addition, wind energy can be an important source of employment for local communities.
The manufacture of wind turbines and other wind energy components requires specialized skills and skilled labor, creating manufacturing jobs. Wind farm construction also creates jobs in areas such as civil engineering, electrical, tower and foundation construction.
Once the wind farms are operational, maintenance and operations technicians are needed to service the wind turbines and ensure their proper functioning. These workers may be hired by the wind energy company or by independent contractors.

Lower carbon footprint

Wind energy has a smaller carbon footprint than fossil fuel-based power generation. The manufacturing of wind turbines and the construction of wind farms have a carbon footprint, but this is quickly offset by the energy generated.
Wind energy has a lower carbon footprint because it does not emit greenhouse gases such as carbon dioxide (CO₂), methane (CH₄) and nitrous oxide (N₂O) during operation. Because wind turbines generate electricity from the kinetic energy of the wind, they do not require the burning of fossil fuels.

In addition, wind power has a smaller carbon footprint than other renewable energy sources, such as hydroelectricity and solar photovoltaics. Wind turbines do not require large dams, reservoirs, or solar panels, which require large amounts of materials and energy to manufacture.

Disadvantages of wind energy

Impact on wildlife

The construction of wind farms can have a negative impact on wildlife, particularly birds. Wind turbines can disrupt the migratory and feeding patterns of birds, which can have serious consequences for their populations. The construction of wind turbines and transmission lines may require the removal of vegetation and alteration of the landscape, which can affect local wildlife and their habitats. In addition, the construction of infrastructure can affect the migration of some species.
However, it is important to note that the impact of wind energy on wildlife is extremely low compared to other energy sources, such as fossil fuels, and other human activities.

Noise and vibration

Wind turbines can generate noise and vibration from the movement of the blades, the operation of the generator, and other components. Noise is generated as air passes over the blades and into the tower, which can create turbulence that produces an audible sound. In addition, mechanical movement of internal generator components and other electrical equipment can also generate noise and vibration. The level of noise and vibration depends on the type and size of the wind turbine and the environmental conditions. In general, larger wind turbines tend to be noisier and may generate more vibration due to the greater amount of energy they produce.
However, the impact of wind farms on ambient noise is extremely small. For example, a wind farm located 350 meters from a person has a noise level of approximately 35 to 45 decibels. This is much less than the 105 decibels produced by an airplane at 250 meters.

Wind power intermittency

Wind farms require consistent and strong winds to effectively generate electricity. Although winds can be affected by a number of factors such as topography, geographic location and altitude, the most important climatic conditions for wind farms are wind speed and wind direction.
Wind is a renewable resource, but it is not constant and can vary significantly at different times and locations. Wind farms are designed to operate within certain ranges of wind speed and direction, and wind farm design and construction engineers carefully consider these variables before installing wind turbines.
The intermittency of wind power can be a challenge to integrating wind power into the electric grid because it can create imbalances in the supply and demand of electricity. Electric power systems must adjust their output to maintain grid stability and ensure that electricity demand is met at all times.

To mitigate the intermittency of wind power, energy control and storage technologies have been developed. For example, battery storage systems can help store energy produced by wind farms during periods of high production and provide power to the grid during periods of low production. Energy control systems can also be used to manage and regulate wind farm production based on grid demand.

Space requirements

Wind farms require a lot of space for their installation because the wind turbines are relatively large and need to be placed at an appropriate distance from each other to ensure efficiency and safety. In addition, wind farms must be located in areas with strong and consistent winds over a long period of time. This means that the selection of wind farm sites can be limited to specific areas with suitable wind conditions. These areas may be on public or private land, and often require the purchase of easements or property rights.
Wind farms must also consider other factors such as land topography, distance to electrical grids, and the presence of infrastructure such as roads and bridges to provide access to wind turbine installation and maintenance sites.

Visual impact

The visual impact of wind turbines depends on several factors, including the location of the wind farm, the size, height, and number of wind turbines installed. If wind turbines are located in open areas or on high ground, they may be more visible and have a greater visual impact on the landscape. To mitigate the visual impact of wind turbines, wind farm developers often seek locations that minimize the visual impact on the landscape and work closely with local governments, communities, and stakeholders to identify suitable areas and minimize the impact on the environment and the community.

High initial cost

The initial cost of building and commissioning a wind farm is significantly higher than that of building a fossil fuel power plant. In general, the initial cost of building a wind farm can range from a few million to several hundred million dollars. These initial costs may include land acquisition, construction of access infrastructure, installation of wind turbines, construction of electrical substations, and connection to the existing electrical grid.
However, operating costs are lower once the wind farm is operational.

Green transmission problem

Wind energy is typically generated in rural or remote areas where there is insufficient electricity transmission infrastructure. Given that one of the aspects that characterize the development of renewable energy (including wind energy) is that it is linked to the location where the resource is located. For this reason, it is necessary to develop the transmission system to get from where these resources (wind) are located to the centers of consumption. The problem of needing to build electric transmission lines to transport renewable energy that is distant from consumption centers is usually known as the green transmission problem.

Conclusion

Wind energy is a renewable energy source that has several advantages and disadvantages. It is a clean and sustainable source of energy that reduces dependence on fossil fuels, has low operating costs, and creates jobs in local communities. However, wind energy has an impact on wildlife and can be a problem for the visual aesthetics of the landscape, although its impact is very small. It is also dependent on weather conditions, which can affect the availability of energy. Despite these challenges, it remains an important alternative to fossil fuels and a viable solution for reducing greenhouse gas emissions and addressing climate change. Due to the characteristics of wind turbines, this type of renewable energy is expected to lead the shift to a modern, sustainable, low-fossil-fuel-consumption power system.

Reference

[1] Ackermann, T. (Ed.). (2012b). Wind Power in Power Systems: Ackermann/Wind Power in Power Systems. Wiley-Blackwell.

[2] Villarrubia López M. (2012). Ingeniería de la Energía Eólica. Facultad de Física, Universidad de Barcelona. Alfaomega Grupo Editor, S.A. de C.V.

[3] Amaro Pinazo, M., & Romeral Martinez, J. L. (2022). Intermittent power control in wind turbines integrated into a hybrid energy storage system based on a new state-of-charge management algorithm. Journal of Energy Storage, 54(105223), 105223. https://doi.org/10.1016/j.est.2022.105223

From Education to Invention: Early Life of Poul La Cour

Born into a farming family, La Cour showed a keen interest in science and technology from an early age. Despite his humble beginnings, he received a good education, attending the prestigious Sorø Academy and later the Technical University of Denmark.

It was during his time at the university that La Cour first became interested in the potential of wind power. He studied the work of earlier pioneers in the field, including Thomas P. Smith and Charles F. Brush, and began experimenting with his own designs for wind turbines.

The Discovery that Led La Cour to Wind Energy

While studying wind power, La Cour discovered that it had the potential to generate electricity. This was a groundbreaking discovery at the time, as wind power had previously only been used for mechanical purposes, such as grinding grain.

La Cour realized that wind turbines could be used to generate electricity on a large scale, providing a source of clean, renewable energy. He began to focus his research and experiments on developing wind turbines that could efficiently convert wind energy into electrical energy.

Designing the La Cour Rotor: La Cour’s Contribution to Wind Power Technology

La Cour’s most significant contribution to wind power technology was the development of the La Cour rotor. This innovative design featured a rotor with curved blades that allowed it to capture more wind energy than previous designs.

The La Cour rotor was a major breakthrough in wind power technology, and it remains the basis for many modern wind turbines. La Cour continued to refine his design over the years, creating larger and more efficient turbines that could generate more power.

The World’s First Electric Windmill

La Cour’s electric windmill was designed to produce electricity for the small town of Askov, Denmark. The windmill was built with a rotor diameter of 23 feet and was connected to a 2.5 kW dynamo. The dynamo was used to produce electricity which was then fed into the town’s power grid.

The electric windmill was a great success and provided the town of Askov with electricity for many years. La Cour’s invention was also an important milestone in the development of wind power technology, as it showed that wind power could be used to produce electricity on a large scale.

The Importance of La Cour’s Books and Articles on Wind Power

In addition to his practical work in wind power, La Cour was also a prolific writer on the subject. He published numerous articles and books on wind power technology, sharing his knowledge and insights with the wider scientific community.

La Cour’s books and articles were highly influential in the development of wind power, providing valuable guidance and inspiration to other scientists and engineers working in the field. Many of his ideas and concepts remain relevant today, and his writings continue to be studied and referenced by researchers in the wind energy industry. In 1900, La Cour published a book entitled “Windmills: Theory and Practice,” which became a reference for windmill engineers and designers around the world. In the book, La Cour presented a series of mathematical calculations and practical experiments that demonstrated the viability of windmills as an energy source.

La Cour as an advocate for education and science

Throughout his life, La Cour was a strong supporter of education and scientific research. He believed that education was the key to progress and that scientific knowledge was essential to improving people’s lives. La Cour worked tirelessly to promote science and education, serving as director of the Danish Meteorological Institute and the Danish National Laboratory for Sustainable Energy. He was also a founding member of the Danish Academy of Technical Sciences, which continues to promote scientific research and innovation in Denmark today.

Poul La Cour’s 1904 class

Poul La Cour’s Class of 1904 was an important milestone in the history of wind energy. In this class, La Cour taught his students how to design and build wind turbines to generate electricity. This was a revolutionary concept at the time, as most wind turbines were used primarily to grind grain or pump water.

The class of 1904 met at the Copenhagen Polytechnic, where La Cour was a professor of physics. La Cour believed that wind power had great potential for generating electricity and was convinced that his students could help make this vision a reality. During the class, students learned the basic principles of wind energy and the physics behind wind turbines. They also received detailed instructions on how to design and build efficient and reliable wind turbines. La Cour and his students designed and built several wind turbines during the class, including one that generated enough electricity to power a small water pump. This demonstration was an impressive proof of the potential of wind energy and generated a lot of interest in the press and industry.

After the Class of 1904, La Cour continued to work on developing wind turbines and promoting their use in Denmark and around the world. In 1908 he founded the world’s first wind energy research institute in Askov, Denmark, and in 1918 he founded the International Wind Energy Society.

Poul La Cour’s Class of 1904 was an important milestone in the history of wind energy, laying the foundation for the development of efficient and reliable wind turbines for power generation. La Cour’s vision and dedication to wind energy have left a lasting impression on the industry and the world.

Johannes Juul: The outstanding engineer trained by Poul La Cour

Johannes Juul was a Danish engineer known for his work in the field of wind energy. He was a student of Poul La Cour at the Technical University of Denmark and worked closely with him for many years. Juul was one of the first engineers to design and build large wind turbines. In 1929, he designed and built a 200 kilowatt wind turbine in Gedser, Denmark, which was the largest wind turbine in the world at the time. The turbine was used to generate electricity for a local power grid.

Juul was also the founder and director of the wind energy company Vindmølleindustrien, which became one of the leading wind turbine manufacturers in Denmark. Under his leadership, the company developed several innovative technologies, including variable pitch control technology, which allowed wind turbines to operate more efficiently.

In addition to his work in wind energy, Juul was also an advocate for the use of renewable energy in general and for phasing out fossil fuels in favor of cleaner, more sustainable energy sources.

La Cour’s Legacy

La Cour’s contributions to wind power technology have had a lasting impact on the renewable energy industry. His work in the early 20th century laid the groundwork for the development of modern wind turbines, which have become an essential source of renewable energy worldwide.

Today, wind power is one of the fastest-growing sources of electricity globally, and the technology continues to advance. Large-scale wind farms are becoming increasingly common, and there are ongoing efforts to develop offshore wind turbines that can generate even more electricity.

La Cour was an advocate of wind power as a sustainable and renewable source of energy. In a 1908 speech, he stated that “wind power is the energy source of the future” and predicted that windmills would become a common feature of the landscape around the world. It seems that Poul La Cour’s predictions are coming true and it is possible that wind energy will lead the transition to a fossil fuel free energy matrix.

Reference

[1] Burton, T., etc., Sharpe, D., Jenkins, N., & Bossanyi, E. (2001). Wind Energy Handbook. John Wiley & Sons.

[2] https://bramminginfo.dk/poul-la-cour.html

[3] https://www.siemensgamesa.com/es-es/descubrir/revista/2019/11/siemens-gamesa-inventors-day

Preliminary Concepts

To calculate the annual energy produced by a wind turbine, the following concepts must be considered:

The power curve of the wind turbine (P(v)): This curve can be obtained from the manufacturer. It should be noted that the curve provided by the manufacturer is obtained under standard conditions (15°C and 1.01 bar), for which a wind density of 1,225 kg/m³ is obtained.

The Weibull distribution curve (p(v)): This curve is obtained by a statistical treatment of the wind speeds at the hub height of the wind turbine for one year. It is a versatile continuous distribution that can be used to mathematically model wind speeds. It can also be replaced by the probability distribution of wind speeds.

There are two ways to calculate the power produced by a wind turbine: discrete or numerical. Generally, the power curve (P-v) is not expressed in mathematical form, but is provided by the manufacturer in discrete form, i.e. in the form of a table with a series of points relating a given wind speed (m/s) to a given power (MW).

• To use the numerical method, it is necessary to obtain the mathematical equation of the power curve and the Weibull distribution curve for one year.
• To use the discrete method, it is necessary to obtain the manufacturer’s power curve in tabular form and the statistical treatment of wind speeds for one year.

For this reason, it is common to use the discrete method to calculate the energy produced by the wind turbine.

Energy Calculation (Discrete Method)

The annual energy production (E_a) of a wind turbine is calculated using the following equation:

P_i : Power at speed “i
f_i : Relative frequency “i”.
T : Production time period (8760 hours).

Capacity Factor (CF)

It is defined as the ratio between the electrical energy (E_a) produced during a period of time (T) and the energy that would have been produced if the unit had been operating continuously at rated power (P_n) during that period. It is also known as the capacity factor. It can be defined using the following equation:

Application

You have the recorded wind speed data at a given location. The data have been grouped into speed packets centered on intermediate values (1, 2, 3, 4, …, 20) because the manufacturer typically provides power data for values centered on natural numbers. Table 1 shows the statistical treatment of wind speeds for one year.

The P-V power curve is obtained from the manufacturer Goldwind GW121/2500 for standard conditions.

Figure 2 shows the power curve (P-V) from the manufacturer Goldwind.

The number of hours per year corresponding to a given speed is obtained by multiplying the frequency of occurrence (fi) by the number of hours in the year (8760 h). In this way, Table 3, which represents the Goldwind GW121/2500 power output of 2.5 MW under standard conditions, can be filled in.

The capacity factor of the wind turbine is calculated as follows:

A capacity factor (CF) of 56.5% indicates an excellent evaluation of the energy production of the wind turbine. This is only an example, as it depends on the choice of the machine.

Reference

[1] Goldwind GW121/2500 – Fabricantes y aerogeneradores – Acceso en línea – The Wind Power. (s/f). Thewindpower.net. Recuperado el 21 de enero de 2023, de https://www.thewindpower.net/turbine_es_1029_goldwind_gw121-2500.php.