Betz speed limit and tip speed ratio

THIS IS USEFUL FOR THE RTU B.TECH. 7TH SEMESTER STUDENTS
THIS PPT ALSO DESIGNED ACCORDING TO THE NEW SYLLABUS AND PATTERN

1. SOLAR AND WIND ENERGY TOPIC:-BETZ SPEED LIMIT AND TIP SPEED RATIO PRAPARED BY SONU KUMAR BAIRWA

2. Betz limit The  Betz limit  is the theoretical maximum  efficiency  for a  wind turbine , conjectured by German physicist Albert Betz in 1919. [2 ]  Betz concluded that this value is  59.3% , meaning that at most only 59.3% of the  kinetic energy  from  wind  can be used to spin the turbine and generate  electricity . In reality, turbines cannot reach the Betz limit, and common efficiencies are in the 35-45% range .

3. Wind turbines work by slowing down passing wind in order to extract  energy . If a wind turbine was 100% efficient, then all of the wind would have to stop completely upon contact with the turbine—which isn't possible by looking at a wind turbine (figure 1 ). In order to stop the wind completely, the air wouldn't move out of the way to the back of the turbine, which would prevent further air from coming in—causing the turbine to stop spinning.

4. Figure 1. A wind turbine. The Betz limit gives the maximum amount of power it can convert into motion and electricity

5. Tip speed ratio he  tip-speed ratio , λ, or  TSR  for  wind turbines  is the ratio between the tangential speed of the tip of a blade and the actual  speed  of the wind. The tip-speed ratio is related to efficiency, with the optimum varying with blade design .  Higher tip speeds result in higher noise levels and require stronger blades due to larger  centrifugal forces .

6. The tip speed of the blade can be calculated as  w times R, where  w is the rotational speed of the rotor in radians/second, and R is the rotor radius in metres . Therefore, we can also write. where   v is the wind speed in metres /second at the height of the blade hub.

7. C p – λ curves The power coefficient C p ,   is a quantity that expresses what fraction of the power in the wind is being extracted by the wind turbine. It is generally assumed to be a function of both tip-speed ratio and pitch angle. Below is a plot of the variation of the power coefficient with variations in the tip-speed ratio when the pitch is held constant:

8. The case for variable speed wind turbines Originally, wind turbines were fixed speed. This has the benefit that the rotor speed in the generator is constant, thus the frequency of the AC voltage is fixed. This allows the wind turbine to be directly connected to a transmission system. However , from the figure above, we can see that the power coefficient is a function of the tip-speed ratio . By extension, the efficiency of the wind turbine is a function of the tip-speed ratio.

9. Ideally, one would like to have a turbine operating at the maximum value of  Cp  at all wind speeds. This means that as the wind speed changes, the rotor speed must change to such that  Cp= Cmax . A wind turbine with a variable rotor speed is called a  variable speed wind turbine

10. . Whilst this does mean that the wind turbine operates at or close to  Cpmax for a range of wind speeds, the frequency of the AC voltage generator will not be constant. This can be seen in the following equation: N=120f/P where  N  is the rotor angular speed,  f  is the frequency of the AC voltage generated in the stator windings,  P is the number of poles in the  generator  inside the nacelle

11. That is, direct connection to a  transmission system  for a variable speed is not permissible . What is required is a power converter which converts the signal generated by the turbine generator into DC and then converts that signal to an AC signal with the grid/transmission system frequency .

12. The case against variable speed wind turbines As already mentioned, variable speed wind turbines cannot be directly connected to a transmission system. One of the drawbacks of this is that the inertia of the transmission system is reduced as more variable speed wind turbines are put online . This can result in more significant drops in the transmission system's voltage frequency in the event of the loss of a generating unit. Furthermore, variable speed wind turbines require power electronics, which increases the complexity of the turbine and introduces new sources of failures. It has also been suggested that additional energy capture achieved by comparing a variable speed wind turbine to a fixed speed wind turbine is approximately 2 %.

13. THANKS FOR YOUR ATTENTION