full2011_inter.pdf - page 240

2011 International Conference on Alternative Energy in Developing Countries and Emerging Economies
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n Y n
i i i i
i 1 y 1 i 1
Y n
i i
y 1 i 1
C .N O&M .N
Minimize f (x)
R .N
ª º § · § ·
« » ¨ ¸ ¨ ¸
© ¹ « » © ¹
« »
§ ·
« »
¨ ¸
« »
© ¹ ¬ ¼
¦ ¦¦
¦¦
G (1)
Where:
n = the number of system components (unit)
Y = the number of years (year)
C i
N
= the initial capital investment cost (baht)
i
O & M
= the number of each system component (unit)
i
R
= the operation and maintenance cost (baht)
i = the replacement costs (baht)
General constraints: The hourly energy demand must
be satisfied by the amount of energy generated from all
distributed generation units. This constraint converts to
the following equation, for all hours i:
Y H Y H n
1 i
y 1 h 1 y 1 h i 1
Subject to g x EL EG 0,
i 1,2,.......,n
d ¦¦ ¦¦¦ G
(2)
Where:
EL = hourly energy demand (kWh)
EG = energy generated (kWh)
Y = the number of years (year)
H = the number of hours (h)
n = the number of energy generated sources (unit)
Decision variables and constraints: Table 2 summa-
rizes the decision variables and constraints of each
SAHPS model. For a more detailed description of all
algorithms, we refer the reader to the TRNSYS 16
manual. From Eq. 1-2 and Table 2, there are three
decision variables in the objective function: the rated
capacity of the PV array (W), the rated capacity of
WECS (W) and the battery capacity (Wh).
E. Implemented algorithms
We used the TRNSYS simulation program for the
minimization of the objective function that is evaluated
by the GenOpt optimization program to find the optimum
combination of the stand-alone hybrid power system. The
objective function is evaluated by TRNSYS that is
iteratively called up by GENOPT until the objective
function is minimized, as shown in Fig. 7. All computa-
tions were run on Windows computers with Pentium (R)
processors. With a 3.40 GHz processor, one simulation
of the SAHPS model takes 2 seconds. In the optional
search algorithm, we apply a particle swarm optimization
algorithm (PSO) to roughly explore the possible non-
convexity of the objective function. For a more detailed
description of all algorithms, we refer the reader to the
GenOpt manual.
TABLE II
OVERVIEW O VER THE DECISION VARIABLES AND C ONSTRAINTS IN THE
SAHPS M ODEL
Components Decision variables and constraints
PV array
T
cell cell L,ref Isc cell cell,ref
T,ref
cell cell s cell cell s
o
sh
G
P U I . T T
G
U I R U I R
I exp 1
R a
ª º
P « »
« » ¬ ¼
ª º ª º § · § ·
« » « » ¨ ¸ ¨ ¸
© ¹ © ¹ ¬ ¼ ¬ ¼
1 cell C / S h x P 0t G
WECS 3
W t g a p r P . .0.5. .C .A.VK K U
2 C / S h x A 0t G
Diesel generator diesel d V N . a bX
3 d C / S h x N 0t G
4 rate rate d h x 0.3P P P ,if N 0d d ! G
Battery
cell bs equ,0 equ,1
q,norm
ch ch ch q,norm
ch
U N U U SOC /100
I
U a 1 exp c I
b
ª º § ·
« » ¨ ¸
« » © ¹ ¬ ¼
5 bs C / S h x N 0t G
6 min cell max bs h x U U U ,if N 0d d ! G
For the numerical experiments, SAHPS optimizations
using the PSO on the mesh algorithm are investigated.
This algorithm uses the gbest topology, 3 particles, 200
generations, a seed of 0, a cognitive acceleration constant
of 2.8, a social acceleration constant of 1.3, velocity
clamping with a maximum velocity gain of 0.5, a mesh
size divider of 2 and an initial mesh size exponent of 0.
Fig. 7. Interface between GenOpt and the TRNSYS simulation
program that evaluates the cost function [5].
III. EXPERIMENTAL RESULTS
Fig. 8 shows a graphical representation of the distance
to the maximum obtained cost reduction and the required
number of simulations for PSO on the mesh algorithm.
The algorithms give the results close to the minimum
value, while using a low number of simulations (where
the number of generations in the algorithm is 46).
The results showed that the optimal system for Koh
Mak Noi village is a PV/diesel generator/battery hybrid
system (no wind turbine). This system consists of 56
kWp of a PV array, 100 kW of diesel generator, 302
kWh of batteries and 20 kW of bi-directional inverters
with a life cycle cost of 60.7 million baht.