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. Cp–λ curves
• The power coefficient Cp, 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:

9. 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.

10. • 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

11. • . 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

12. • 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.

13. 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%.