Question

Some advocate for small scale wind turbines, for instance, on buildings in urban areas etc. An advantage would be more distributed generation, close to usage (reduced transmission loss etc.) Comment on ‘micro-wind’ projects from an engineering perspective (scaling, physics etc.)

Answer 1

Yes, It would be a great idea to install small wind turbines at individual residences to make energy generation distributed (unlike centralized) to overcome transmission losses.

Since conventional wind turbines are humongous (15 m blade length) they cannot me installed in urban areas due to n number of reasons eg: air-traffic issues, safety issues and many more.

Firstly we need to know the dimensions & statistics of an actual wind turbine.

• height(average) =466 ft
• power output = (2.5 to 3) MW capacity =6 million KWh in a year
• blade span = 15m each .i.e. 30m diameter

In order to make a prototype for use in urban areas and that too for individual use we need to do dimensional analysis.

Dimensional analysis is just a way of setting proportions and ratios of actual model in a prototype.

since our basic requirement is power(P)

A conventional one produces 6 million KWh in a year that is dufficient to power 1500 houses thus for 1 house we will need 6million KWh /1500

= 6000000/1500

= 4000 KWh in a year

for one day requirement = 4000/365 =10.95 KWh.

Power generated is calculated by calculating power of wind before entering the turbine and after exiting the turbine.

The reduction in power at exit is counted as effective power(P_eff) which is further multiplied with the factors affecting generation of power then after that the actual power generated(P) is calculated which is always less then effective power(P_eff).

and effective power P_eff is given by

From equation we can clearly see that P_eff depends on density of air(rho),temperature change(delta T) and velocities of entrance and exit (V₁ & V₂ ) respectively.

If the difference between both speeds is zero, we have no net efficiency. If the difference is too big, the air flow through the rotor is hindered too much. Power coefficient (C_p)characterizes the relative drawing power:

by practical experiments it was observed that maximum drawing of power occurred when V₂= (V₁)/3

.i.e. X=1/3

Thus ideal power coefficient is obtained as C_p =59%

Dimension is a necessary blade span & height

Since it would we installed on top of tall buildings only where wind speed is decent there would not be any need to place them further high on a tower but for small houses having 1 to 6 floors it would become necessary to raise the turbine high which would not be economical.so, for now lets just design for high rise buildings only.

since P_eff is directly proportional to area(A)

and A=4*pi*r²

thus P_eff is directly proportional to length of blade .i.e. r

and for an ideal condition C_p=59% =0.59.

C_p =P_eff / P_wind

P_{wind =} P_{eff /} C_p .............................(you can do calculations based on your region getting forecast data from meteriological departement)

and thus find out the ideal blade length in terms of radius(r). and again calculate effective power.

Also, the installed capacity or rated power of a wind turbine corresponds to an electrical power output of a speed between 12 and 16 m/s, with optimal wind conditions. For safety reasons, the plant does not produce greater power at the high wind conditions than those for which it is designed. During storms, the plant is switched off.

I have given all the parameters needed to make a prototype wind turbine and you can now easily find the velocities and length of blade(r).