*7.1. Wind Turbines*

The simulation's main goal is to carry out a comparison between the results calculated theoretically and the results calculated through the simulations performed.

After several simulations were made, where the main goal was to calculate the wind speed at the exit of the rotor, the calculations were carried out to calculate the power generated by the wind turbine.

Through the theoretical equations and with the data taken from the simulations performed, it is possible to calculate the power generated through Equation (2).

To calculate the power generated by the wind turbine, it is necessary to use the following data: *p* = 1.225 kg/m3 and A = 21,124 m2.

Using the data from Table 11, the generated power was calculated. A wind speed of 5.97 m/s corresponds to a power of 1.184 MW, a wind speed of 8.28 m/s corresponds to a power of 3.222 MW, and a wind speed of 11.20 m/s corresponds to a power of 7.970 MW.


**Table 11.** Values of wind speed before and after the rotor.

To find the power coefficient *Cp* at a given wind speed, all you have to do is divide the power produced by the total power available in the wind at that speed. Thus, through the simulations and the generated power calculations, we were able to calculate the power coefficient. A wind speed of 5.97 m/s corresponds to a power coefficient of 0.43, a wind speed of 8.28 m/s corresponds to a power coefficient of 0.44, and a wind speed of 11.20 m/s corresponds to a power coefficient of 0.44.

Calculating the energy produced during a year, a maintenance period of 15 days was considered when the turbines are not working. At average power (3.222 MW), the energy produced would be 11909 MWh.

Table 12 shows a comparison between the results obtained theoretically and the results obtained through simulations.


**Table 12.** Comparison of theoretical and simulated results.

Analyzing the results obtained, we can see that the theoretical results and those obtained through the simulations are quite similar, which allows us to say that the designed structure has a very close approximation to the real one.

There are several factors that influence the efficiency of a wind turbine. Many aerodynamic factors affect wind turbine power generation, such as wind speed, air density, temperature, air pressure, area swept, and height, etc.

The typical cut-in, rated and cut-out wind-speed values are in the range of 3–5, 10–15 and 25–30 m/s, respectively. The wind turbine chosen has a cut-in wind speed of 4 m/s, a rated wind speed of 13 m/s and a cut-out wind speed of 25 m/s. For the wind speed below the cut-in value, the turbine will produce worthless power. When this happens, the turbines usually enter a parking mode. The turbine is also shut down and kept in parking mode when wind speed is above the cut-out value or during emergency conditions due to

security. For wind-speed values between the cut-in and rated, the power P curve maintains a cubic relationship with respect to wind speed [16]. Figure 14 presents a power curve of a Vestas V164-8.0 turbine.

**Figure 14.** Power Curve of Vestas V164-8.0 (from [17]).

Therefore, the location chosen for the installation of these turbines is a good location since the wind speeds practiced in this location are suitable for a good operation of the turbines.

The wind turbine's characteristics are usually related to the degree of air density. The energy produced by the wind is directly commensurate to the degree of air density [16].

Air pressure and temperature affect the air density; they are directly proportional to the pressure and inversely proportional to the temperature. The scale of the pressure and temperature decreases with increasing elevation [16]. However, we saw that the air density does not have a significant change due to temperature and pressure and, therefore, in the simulations, the value of air density was always the same, 1.225 kg/m3.

It is also concluded that the produced power is directly proportional to the rotor-swept area. When the swept area and the diameter of the rotor are large, an increase in energy produced will be earned from the wind.

The tower height is another important factor in the power generated by the turbine. The energy available in the wind is proportional to the cube of the wind speed so any small increase in wind speed will result in an impact on the economic factor. An efficient method to get the turbine in stronger winds is to mount them on taller towers [16].

Near the Earth's surface, friction reduces the wind speed. Frictionless surfaces, such as a quiet sea, offer small amounts of resistance, so the difference in the wind speed with the height is not high. On the other hand, wind undergoes a major change by irregular surfaces, such as forests and buildings [16]. Obstacles such as structures and trees can significantly affect wind speed. They often create turbulence in their neighborhood. The slowdown effect on the wind from an obstacle increases with the height and length of the obstacle. This effect is more pronounced close to the obstacle and close to the ground. It is a good thing to have few major obstacles close to wind turbines, especially in the case they are upwind in the prevailing wind direction, i.e., "in front of" the turbine [16]. Thus, a similar turbine installed at sea or on land with buildings or trees around it will have different efficiency.

The results obtained for these turbines were as expected. Since these turbines are installed in the chosen location, the calculations and results obtained are only a confirmation of the results of the operation of these turbines.

Data provided to the public by EDP (Energias de Portugal) say that a turbine installed at the chosen location generates around 25 GWh during a year. Through our calculations, this result is a little lower, about 12 GWh a year. This difference is due to the fact that we do not use results from real wind speeds and only approximations. The wind speeds used are annual averages of the wind speeds practiced annually and, therefore, there are wind speeds that we were not able to consider in the calculations performed.

### *7.2. Tidal Turbines*

As with the simulations for the wind turbine, the main goal was to calculate the wind speed at the exit of the rotor to calculate the power generated by the currents.

The power equation is the same as for the wind turbine, only changing the data: *p* = 999 kg/m3 and *A* = 254.469 m2.

Using the data from Table 13, the generated power was calculated. A current speed of 0.912 corresponds to a power of 38.492 kW, and a current speed of 1.902 m/s corresponds to a power of 371.006 kW.

**Table 13.** Values of current speed before and after the rotor.


To find the power coefficient *Cp* at a given current speed, all you have to do is divide the power produced by the total power available in the current at that speed. Thus, through the simulations and the generated power calculations, we were able to calculate the power coefficient. A current speed of 1.512 corresponds to a power coefficient of 0.40 and a current speed of 1.902 m/s corresponds to a power coefficient of 0.42.

Calculating the energy produced during a year, a maintenance period of 15 days was considered when the turbines are not working. At average power (1.512 m/s), the energy produced would be 575.744 MWh.

Table 14 shows a comparison between the results obtained theoretically and the results obtained through simulations.

**Table 14.** Comparison of theoretical and simulated results. \* This value of Cp is just an approximation due to lack of data.


Analyzing the results obtained, we can see that the theoretical results and those obtained through the simulations are quite similar, like the wind turbine, which allows us to say that the designed structure has a very close approximation to the real one.

Unlike wind turbines, tidal turbines do not have much information. However, we know that its efficiency is also affected by some factors such as current speed, water density, temperature, water pressure, area swept and height, etc.

The tidal turbine chosen has a cut-in current speed of less than 1 m/s, a rated current speed of 3 m/s and a cut-out current speed of 5 m/s. Like the wind turbine, in a current speed below the cut-in value, the turbine will produce negligible power and is usually shut down and entered into parking mode. The turbine will also shut down and be kept in parking mode when current speed is above the cut-out value or during emergency conditions due to security. For current speed values between the cut-in and rated, the power P curve maintains a cubic relationship with respect to the current speed. In Figure 15 is a power curve of a AR1500 tidal turbine.

The location chosen for the installation of these turbines is not the best since the current speeds practiced in this location are usually lower than the rated current speed. These turbines are normally placed in places where the currents are stronger. However, the current speed in this location is enough for the turbines to properly work.

The energy produced by the current is directly commensurate to the degree of water density. The water density considered was 999 kg/m3. The density does increase with depth, but only to a tiny extent. At the bottom of the deepest ocean, the density is only increased by about 5%, so the change can be ignored in most situations.

It is also concluded that the produced power is directly proportional to the rotor-swept area, just like the wind turbine. When the swept area and the diameter of the rotor are large, an increase in energy produced will be earned from the current.

The current speed changes with depth. Up to a 50 m depth, the current is influenced by the wind. The current speed is normally greatest near the surface.

The tidal turbine's operation is also influenced by the presence of obstacles, and the current speed will be less in the presence of them. However, at sea, the presence of obstacles that influence the operation of the turbines is less likely.

Unlike wind turbines, there is no data on the operation of these tidal turbines in the chosen location. Thus, the results obtained cannot be compared; they can only be analyzed.
