Vertical axis wind turbine analysis using MATLAB

Wind Turbines have become one of the feasible power plants to replaced fossil fuels. Because this plant is affordable cost and did not produce pollutants as an output. Vertical Axis Wind Turbine can be placed at points with high wind intensity such as; toll roads, ships, railroads, airports. The energy produced can be distributed for the civilian house light, the street lights, the fishing boats light, others. The hope is that wind turbines can generate 100 watts of power, so that charging time can be at least 6 hours. But, the average velocity data in the field is worth under 2.85 m/s (minimum wind speed to get 100 watt). Resulting in a turbine charging time more than 6 hours. In this case, The Turbine needed more than one accu as a place to store the energy even the accu take more than 6 hours to be charged.


Introduction
Energy is a basic human need that must be fulfilled, it continues to increase as time passes, it is directly proportional to human life. Fuel oil holds a very dominant position in meeting national energy needs. The current composition of energy consumption is fuel oil: 52.50%; Gas: 19.04%; Coal: 21.52%; Water: 3.73%; Geothermal: 3.01%; and Renewable Energy: 0.2%. [1] Indonesia is a tropical country located on the equator, as an archipelago with varied geological contours, has more than 100 mountains, and also beaches. One of the energies that can be utilized is wind. The movement of wind from the mountains which has high air pressure towards the coast with low air pressure can be utilized in the implementation of wind turbines, which convert mechanical energy into electrical energy. At an affordable cost, didn't produced pollutants as an output, Wind Turbines have become one of the feasible power plants to replace fossil fuels.
Generally, there are two types of Wind Power Plants; Horizontal Axis Wind Turbines, and Vertical Axis Wind Turbines. The Horizontal Axis Wind Turbine is a type of porous turbine parallel to the wind direction like a typical aircraft propeller, so it requires its own mechanism to adjust the blade to be able to follow the direction of the wind turbine rotating, with the generator placed behind the turbine. Meanwhile, the Vertical Axis Wind Turbine is a type of turbine with a axis perpendicular to the wind direction, easy for each blade to catch wind even though the direction changes, and the position of the generator is at the base of the turbine so that this will facilitate maintenance of the turbine. [3] Later, this Vertical Axis Wind Turbine can be placed at points with high wind intensity such as; toll roads, ships, railroads, airports, and so on. The energy produced can be distributed to lighting the civil house, lighting the street lights, lights on the fishing boats, and others.
There are various types of Vertical Axis Wind Turbines, and what is currently being analyzed is the Savonius type, although it generally moves more slowly than the Horizontal Axis Wind Turbine, but the torque produced is larger.  Figure 1 shows the design of the Savonius Type Vertical Axis Wind Turbine and its size. The length of the blade is 150 cm, the radius is 30 cm, and the blade is 120 degrees. This 4 kg wind turbine is made of lightweight stainless-steel material which is expected to be easy to rotate, and the design of the 3 blade that forms the letter S can catch the wind even though it blows from various directions. With this size, it is also expected to produce a power output of 100 watts if the intensity of the wind in the field fulfill the expected calculations.

Beltz Limit
Beltz Limit, in theory is the maximum efficiency value for a wind turbine, put forward by German Physicist Albert Beltz in 1919. The value of Beltz Limit is 16/27 or 59.3%, that is only 59.3% of the kinetic energy of the wind can drive the turbine. In fact, the turbine cannot reach Beltz Limit. And generally, the efficiency value of a turbine is between 35% and 45%. [5]

Turbine Power
Wind turbines work by converting the kinetic energy in the wind first into rotational kinetic energy in the turbine and then electrical energy that can be supplied.

Wind Speed Sample
In reality, the average wind speed based on the sample data taken below is: In table 2, it can be seen that in the morning and evening, the average wind speed does not reach 2,85 m/s. So at that time the battery takes longer to fill. Whereas at night from the range of 8 PM -9:30 PM, the average wind speed is above 2,85 m/s, it is possible to fill the battery faster and produce output power of more than 100 watts. For the calculation of battery usage and charging can be seen in the next sub-chapter.

Wind Torque
The wind torque and load torque can be expressed as follows equation 5 and 4 [6].

Wind Speed Sampling
Sampling of wind speed, as a reference in the process of calculation, Turbine Torque, Output Turbine Power, Time of Use (usage), Time of Charging on turbine batteries. The collection location is on the 7th Floor of Al-Azhar University in Indonesia.

Matlab Simulation
Simulated back in Matlab using data that has been obtained directly from the Field, or real data Data Analysis Analyze formulas to calculate power output, usage time, battery charging time, and turbine torque at each time; morning afternoon Evening Conclusion Conclusions can be obtained from the graph in matlab and calculation End End

MATLAB Code for Wind Torque Function
The plot result show below, This of course will affect many things, such as the value of the output power decreases, charging the battery will require more time, as explained in sub-section 2. Except, if the wind speed that drives the turbine can reach 2.85 m/s or more, the output power will be as desired, which is 100 watts, so charging the battery only takes 6 hours.

MATLAB Code with Power Function
The plot result show below,

Figure 5. Wind Speed Vs Power
According to the Power equation referred to equation 3, There are two things that can affect the value of output power. First is wind speed. The second is the cross-sectional area of the blade.
The relationship of Power to wind speed is, directly proportional to power 3, only at the speed of 2 m/s, the value of power will be 8. If the wind speed is 3 m/s, then the power value will be 27. The Power difference is very significant, even though the wind speed only increases by one number. And also, the greater the cross section, the more wind is captured, causing large torque, and the output power also increases.

Conclusions
As mentioned in the Chapter Introduction, that Vertical Axis Wind Turbine moves more slowly, but produces a large Torque. Which Turbine Torque Wind with a length of 1,5 m, and radius of 0,3 m, mass of will produce a torque of 0.27 Nm. Because the wind turbine has an efficiency value, commonly referred to as Beltz Limit, the torque value will decrease because the Turbine absorbed wind energy is only 59.3%, then the torque value when there is a load drops to 0.17 Nm. And even though the hope is that wind turbines can generate 100 watts of power, so that charging time at least 6 hours. The average velocity data in the field is worth under 2.85 m/s (minimum wind speed to get 100-watt output power), except the night time. Resulting in a turbine charging time is more than 6 hours. The solution of the Wind Turbine that is analysed is, the addition of batteries is needed, so that the capacity of the number of usages can be increased even the charging time take more than 6 hours. %wind speed, m/s rho = 1; %air density, assumption 1 kg/m^3 R = 1.5; %Lenght of blades,m A = pi.*R.^2; %Swept surface area, m^2 P = (1/2)*rho.*A.*(v.^3); %Power, watt plot (v,P); %graph, wind speed vs power