New small turbine technologies - Wind Power Generation and Wind Turbine Design - page 398

5.2.2 Optimization for maximum energy yield
An optimization is given by the condition that AEP will be maximum, i.e.:

AEP

→ Max (8 )

A rotor designer must fi nd the optimal power curve P ( V ) together with WT
operation modes. An optimal rotor geometry which comprises of chord and twist
distributions and aerofoil sections is found in combination with operation modes;
cut-in, cut-out and rated wind speed in principle. Thus an optimal rotor design is
site-dependent. Further, since every reliable operation mode depends on power/
speed control methods, conceptual design of control methods are also needed at
the initial stage.

5.2.3 One-point optimal rotor design
Simplest optimization of rotor design is “One-point design method”, in which an
optimal rotor geometry is determined for one operation point: one combination of
a design wind speed V D and a design rotor speed D by using BEM theory [2].

The optimization is given by the following condition for V = V D with selected rotor
speed

Ω

Ω D :

C → Max. At every axial position of rotor blade

(9 )

P

Algebraic solution determines the chord and twist distributions along its axis of
the blade. However, it must be noticed that “One-point design method” does not
always give the maximum AEP, because a maximum AEP is obtained under the best
combination of decided WT's operation mode and wind characteristics at the site.
The question is how to decide design wind speed V D .
The simplest design by BEM theory is conducted under the following
assumptions:

• Low Reynolds number effect is negligible

• Power curve is a function of tip speed ratio l only.

Then eqn (6) is expressed as:

⎧

V V

⎫

1

R out

⎪ ⎪

3

∫

3

∫

AEP = r Af VVC ( ) ( ) d l VVC + ( l ) f VV ( ) d

(10 )

⎨ ⎬

P R P R

2

⎪ ⎪

⎩ ⎭

V V

in R

where V R is rated wind speed and

R
V

Ω

R

l =

(11 )

R

R

Max(AEP) is derived as follows:
In case of variable-speed operation WT, an optimal l opt ≈ l R is defi ned and the

optimal value can be possibly in the manner:

ll ≈ for VVV ≤ ≤

(12 )

opt in R