Page 243 - Renewable Energy Devices and System with Simulations in MATLAB and ANSYS

230 Renewable Energy Devices and Systems with Simulations in MATLAB and ANSYS ®
®

Single-composite or multiple-objective function design optimization methods are now in use. In
a single-composite objective function optimization algorithm, more than one term may be included
(but normed to money/cost), such as active and passive material cost and capitalized cost of losses,
both of the wind generator plus transmission (in this case) and also that of the interfacing PWM
converter.
In a multiple-objective (e.g., DE) optimization algorithm, each objective function (say, mini-
mum losses) is followed through optimization versus [18, 19], say, initial cost or weight to build
the Pareto clouds and thus allow the designer more ways to choose the final solution while explain-
ing also the sensitivity/robustness of the design to various variables. In what follows, in short, the
modified Hooke–Jeeves algorithm is described, which is used with a single-composite objective
function [20].
The objective function as a cost function (in U.S. $) C is expressed as
t
C t = C a + C e + C f + C p (9.24)

where
C is the active material cost (lamination, copper, PMs)
a
C is the cost of energy loss during the expected life of PMSG for certain average-daily duty cycle
e
C is the frame, bearings, shaft, etc., costs
f
C is the penalty function cost
p
The cost of energy loss C (here only for the generator) is
e
 1 
C e ≈ P e  1 −  nn p (9.25)
hy ye
 η n 

where
n is the hours/year
hy
n is the year
y
p is the energy price USD/kWh
e
P and η are equivalent average power and efficiency
n
e
The energy loss cost C proves to be dominant in the objective function. It is thus feasible to
e
modify the energy loss cost C as
e
  1 1 
 P n  −  if η n < η 0

C e = n np P; P i =   0 η η n  (9.26)
ei
hyy

  0 if η n ≥ η 0
when η is the lower limit of the targeted efficiency.
0
In this way, the design is more flexible in computing cost versus efficiency while selecting appar-
ently the best cost solution above a certain efficiency level.
The frame cost C is C f ≈ p m a , where
f
f
• m —total mass of active materials,
a
• p —average price of frame and auxiliary components/kg.
f