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1
Multicriteria Optimisation of Small Hybrid Solar Power System
Kane M., Favrat D.
Institute
of Energy Sciences, Swiss
Federal lnstitute of Technology of Lausanne,
CHl0l5
Lausanne, Switzerland,tel+41
21 693
25l,fax+41 21 693 3502,
Daniel.Favrat@epfl.ch,
malick.kane@epfl.ch
Abstract: A new concept of small hybrid solar
power
system
(HSPS)
has been successfully
demonstrated
in the context of a project
called SPS (Solar
Power
System).
This plant integrates
two rows of solar collecûors,
two superposed
Organic
Rankine
Cycles (ORC) each
equipped
with a scroll
hermetic expandergenerator
and a heat
engine.
In operation with solar energy
only,
the heat is supplied
by a thermal fluid (presently
pressurized
water) heated in the vacuum
insulated
focal tubes
of sun following, flat concenfrators
made of series
of thin plate mirrors
(CEP).
In hybrid mode
additional heat
is supplied by heat rccovery
from the exhaust
gases
of
the engine
in series
with the solar
network and by a separate
network recovering
heat from the
cooling of the engine
block at an intermediate temperature
level. This paper
presents
the results
of a multicriteria optimization of a 22 kWe HSPS, including aspects such as energy
performance,
economic
and financial
analysis, and environmental
aspects. The so called
mini
maxi methodological
approach with genetic
algorithm
is used considering three
principal
siteria
such as the energy
efficiency of the superposed
ORCs, the minimal cost of the installation
and
the
minimum emission of COr. Taking into account
of the solar
radiation time dependence,
the
electricity supply variation and the change of configuration
(night and day operation),
the
performance analysis is based essentially on the yearly energy simulation
in which the off
design
physical models
of components
are considered.
A comparison
of HSPS with pure fossil
fuelled
Plants
(DEPUDiesel
Engine Power Unit) is reported
for the same
electrical
power
load
curve,
with an
economic
sensitivity
analysis. Results show
that the solar
elecnicity costs
are still
high and depend considerably
on the size of the Solar Field (the HSPS lævelized Electicity
Cost with 5 to l6Vo of annual solar share
is about ITVo to 49Vo
higher than a similar size
Diesel
Engine PowerUni.However,
areduction
of CO,
emission
tp to 26Vo could be obtained
when
replacing the Diesel
Engine Unit by a similar HSPS. Those
hybrid solar
thermal
power systems
may already be compettive
if a tax of about 42 Swiss cts /kgCO, would be considered.
Keywords: Hybrid solar
thermal
power plant,
solar
concentators,
turbine sctoll, thermal
engine,
Organic
Rankine Cycle,
minimaxi
muticriteria optimization,
genetic
algorithms.
1. Introduction
Elecûicity
generation
from low temperature
heat sources
generally
imply the use of so
called
organic
fluids working in Rankine cycles equipped
with vapour
turbines or expanders.
Hence the name
of Organic Rankine cycles (ORC) used in this context.
Those fluids have
thermodynamic
propenies,
which are adequate
for this application, such as their low specific
volume,
high molar
mass as well as
a saturated
vapour slope
which is often
positive
in a Log Ph
diagram,
which
prevents
condensation
at the
end
of the expansion.
This last factor simplifies the
design
of the turbines
for applications in the mid to large
power
range
(some
hundreds
of k'We
and more). Only a few studies
both theoretical
and experimental
(Prigmore
and Barber, 1975;
Giampaolo
et
a1., 1991;
rù/olpert
and Riffat,
1996; Yamamoto etal.,200I) have been done
in ttrc
low pôwer
range
going
from a few kWe to a few tens of kWe. The main limitations
in the latter
power range are the unavailability of turbines or expanders
with adequate efficiencies,
in
particular
when having to cope with reasonably
high expansion
ratios and variable operating
2
conditions. Economic considerations also considerably restrain the possibility to use dedicated
technological developments with high specific costs considering the low initial production
quantities. This therefore tend to favour the exploration of the potential of adaptation of
components produced in large quantities for other duties like is done in this paper. Moreover
there exists a sfong incentive to avoid as much as possible open systems with shaft seals, which
are sources of leakage and a burden on the maintenance. Those are the considerations, which
initiated our work on hermetic scroll expandergenerators
(hnelli et Favrat, 1994) for low power
ORC units. The expandergenerators, which we presently use, are obtained by modifications of
actual hermetic compressors produced at large scale for refrigeration and airconditioning
worldwide, hence with low specific costs. These units are not only hermetic but, provided an
adequate oil management
is intoduced, present the advantage
of a weak sensitivity to liquid
fractions, which could result from an imperfect evaporation and twophase
expansion.
One of the major limitations of standard
scroll compressor
units is the low builtin volume
ratio, which restricts the effrcient expansion ratio to values lower than typically 8 within a
pressure domain from 25 to 3 bars. However this can be compensated by considering
superposed ORCs using each a different fluid to keep a high specific power within the pressure
rangaof the scrolls and avoid sub atmospheric pressures (Favrat, 1995; Kane et a7.
1999). This
solution allows an efficiency improvement compared to single cycles, while avoiding the large
specific volume of equipment
required at the lower end of a twostage, single fluid cycle, which
is another potential alternative.
The small and modular ORCs open the possibility of not only
converting solar energy in hybrid solar power plants, in particular in developing countries, but
also of converting waste heat or heat from small boilers. In this conûext the feasibility of a small
pilot power plant (HSPS: Hybrid Solar Power System), of 22 kWe nominal power has been
demonsffated within the project SPS (Solar Power System). This hybrid plant includes two
superposed
cycles each equipped wittr its own expandergenerator
(figures 1 and 2). The hot
source
is provided by sun following solar concenfration linear collectors with vacuum insulated
tubes. The concentrators
are made of series of thin plaæ mirrors (CEP) of different width and
fixed at calculated
angles
on linear supports
to offer a reduced wind resistance
and allow an easy
replacement in case of failure. The thermal source is complemented with the heat from both the
combustion gases and the block cooling of a cogeneration Diesel engine of 13 kWe. This
integraæd
powerplant mainly designed for demonsffation purposes has been tested both in the
laboratory using heat from a thermal oil boiler and then on site where pressurized water wa.s
used in the collector tubes. Information relative to the design choices and the description of the
preliminary tests have been presented
in earlier papers (Kane et al., L999; Kane et al., 2m1).
Some of the insitu results (Martin et al., 2N2; Kme ?I02) will be briefly commented
undemeath. The present study also deals with the formal design and operation optimisation,
accounting
for energetic, economic and environmental considerations. The original method used
is based dn a formulation for a minimæri multicriæria optimization using génetic algorithmsr.
Results are presented for various solutions of optimal configurations.
2. HSPS prototype and results
Insitu tests
have been done over a period of several
months from May to October 2001 on a siæ
at EPFL (Lausanne,
Switzerland). This allowed performances to be measured over a broad and
variable operational range of conditions. Direct sun radiation varied from day to day between
500 and 8^00
W/' foù colector area of 100m2. When used, the power range of il\e engine
varied between 11 and 13 kWe, due in particular to variations in the air æmperaflue,
and gave a
heat recovery of the order of 20 kWth on the engine block and 7 kWth on the exhaust gases.
For all tests covering a cumulated duration of 110 hours, the power plant produced about 800
rThe approach
is part of iglobal methodology developped
in a recent thesis
(Kane,
2002) for
the systemic
optimisation of hybrid
thermal solar
power
plants
in general.
3
klVh including
500 kWh from the turbines. Some of the operational
conditions
as well as the
results obtained
for two operational
modes
(solar only and hybrid) are summarized
in Table I
and Table
2.
PftRllæbfCoËûdr{ Superposêd ORC cyd€ê
J
L
À
UI
t
J
È
g
o
=
Figwe 1: Simplified
flowsheet of the
HSPS
power plant
Figure
2: Components of the SPS
power
plant
SoIarDirect solar
radiation : 500...800 W I rn2
Collector area : 100 rr12
Motor
Elechical
power : 11...13 kWe
Engine cooling rate : 20 kWth
Cooling
temperature : 82.5 oC
Combustion
gas hest rate : 5...7 kwth
Superposed ORCs
Hotsource temperature : 120...150 oC
Cold source
temperature : 7 .. .9 oC
Condensation
pressure : 5...6.5 bar
SPS
power plant
Number of hours
of test : 110 Hours
Electricitv produced : 800 kWh
Table 1: Insitu test
conditions
and number of produced
kwh (Site EPFLLausanne)
Dates 29.05.01 14.08.01
Direct solar radiation .W
lm2) 8æ 742
Ooeratins mode solar hvbrid
Iotal elecvtricalpower .kWe) 6.52 78.57
Iurbine electrical power .kWe) 6.52 7.32
Motor elechical power lkwe) 011.25
Cvde energy efficiency (lst Law) %) L3.7 73.67
Cyde exergy efficiency "%) 46.57 57.26
Overall svstem efficiencv %) 7.74 15.88
Fossil efficiencv %) 41'1
Table 2: Insitu test results for 2 operutional
points
(mode solar only and hybrid, Site EPFLLausanne)
Considering the fact that there are different input ûemperature
levels for the ORCs, it is best to
express them exergetically
for both operational modes (solar only without engine inpul or
trybrid mode with engine).Curves of ORC exergy effrciencies and electrical energy produced by
the sctoll turbines are given in Figure 3 and Figure 4. The exergy efficiency is the ratio btween
4
ïoRc = 
The two distinct curves obtained in hybrid mode correspond
to series of measures
with different
values of solar radiation. Even if a number of improvement opportunities have been deæcted, the
performance
reached
are encouraging
for a thermodynamic conversion cycle in this power range
and with such a low level of ûemperature.
The superposed cycle exergy effîciency reached a
maximum value of 487o n solar mode only and 577o n hybrid solar mode. The decrease
of
exergy effrciency observed in hybrid mode can be attributed to losses linked to an inctease of
the condensing
pressure.
The latter is due to a limitation of the cooling flow, which was observed
following construction works which affected the cooling network.
(1)
ExEIgy
perlurmances
to 11 1?
Éxcrgy
Dovci
Input
(IWl
Figure
3: Exergy eff,rciency
Exeruy
perfurfianEes
9 lt 11 1? 13
Erêrly povGr
input
(fI{}
Figure 4: Elecfical power delivered by the
scroll expanders
'lo
Ès
3/
I
Ê6
!s
E
E+
15
:l it
t4
1?
It is inæresting to note that the energy efficiency (First Law) in hybrid mode and referred to ttre
fuel only (total electrical power/fuelLHV) reaches 4l.IVo, which represents
an increase of 50Vo
compared to the electical efficiency of 27Vo of the original Diesel unit. However the solar
electical efficiency alone (ORC elecfiical power/solar radiation) is of the order of 7.'Vo, which
is35Vo lower than
the l2%o
illnttally, expected.
It is important to noûe that the tests reported here have been realised in very partial operational
conditions of the cycles. Figure 4 illustrates the load level of the turbines (9 kWe maximum for
an installed power of 12 kWe). These operations
at partial loads are due to an over sizing of the
turbine relative to the solar fîeld and to the fact that the solar field did not yet achieve the
expected effrciencies,
about 53Vo onTy
for an initial value estimated at 75Vo ,(corresponding
to 60
tfittr direct solar radiation of 800 Wmt). Moreover the characteristics
of the heat exchangers
and particularly the evaporatorcondenser
are very sensitive to oil trapping. The minimum pinch
is located at the end of evaporation, which inherently limits the heat fransfer capacity.
Nevertheless
these tests did allow the experimental validation of the concept
of hybrid solar plant
HSPS and its interest for the solar thermal electric conversion.
3. Multicriteria optimisation and Results
The tests of the SPS prototype allowed the identiFrcation and model validation of the most
significant operational patameters (Kane, 2002). However the actual size of the different
components
(motor, turbine) as well as the type and number of installed turbines ar9 not optimal
when considering the yearly operation. This is due to the facq in the timing of this particular
Mo*
.&o* * M"* .ak"w
5
project, the optimisation tools were not yet ready when the prototype power plant had to be
clesigned
and built. For example the configuration with one turbine by stage was chosen for
simplicity as the night operation (coupling of cogeneration
engine and superposed
ORCs) was
notâ major objective at the time. But furttrer optimisation is seen
as an important element for the
future progress
of this type of plants.
3.1 Methodological approach and optimization
The idea of a multiobjective optimisation is applied to determine one or several efficient
solutions,
which can serye as a basis for tradeoff analysis between several
different criæria. In
many cases
in energy systems,
the objectives present different trends or even opposite trends in
funciion of the evolution of the different key variables. A typical example in power plant design
is to look for a compromise betrveen objectives such as: to maximise the effrciency whilrc
. Such a compromise can be obtained either by
rge number of decision vectors or based on the
all the objectives in a single scalar criterion. In
:ighted functions is used (Lightner et Director,
It consists
in using a utility function, which is
made of the algebraic sum of the different objectives,
each
associated with its own predetermined
weight. An adequate
adjustnent of the weighting parameters allows the identification of several
feasible solutions (dominating solutions, pareto optima). In this work we use a socalled
minimaxi formulation based on canonic weights. According to this formulation the
optimisation is done on the basis of a utility function, which is represented by_the normalized
distance between an ideal point of reference (R) and another feasible point (F) (Lightrer et
Director,
1981):
f(x)=
),0, {:t^'
tO:'""
i JI'vnP "l,oPt (1)
where:
.(t)i
.x
. f(x)
' /,(x)
' f.oot
' /t,""n
pnority level relative to the objective
fi(x).
vector of independent
variables
C to the decision
space
Q.
utilitv function.
ih objective
function
C to the function
space
/(Q).
optimal
value
of the objective
fimction
f,(x).
nonpreferred
value of the objective
function
f,(x).
co, being a reference
coefficient assigned to each objective to define its priority level compared to
the other objectives (Hiller et Lieberman, 1990). Hence the order of priority is identical for all
objectives
itall the q parameters are chosen equal to unity. The aim of the optimisation is then
to minimise f(x) in the space of functions. It is necessarJ
to distinguish between the decision
space Q, describing all vectors of the independent variables from the gpace of the objectile
functions /(O). A point in the space of functions f(A) can correspond to a unigge decision
vector (feasible solution) or to several
different points in the space of the vectors of the decision
variables
(nonfeasible
solution). For example
the ideal reference
point çR=11.spr Ïz,opt
... /n,oo,)
represented,
in the solution space, by the best scores of all the considered objdctives is a noh
feàsible solution as the optimal value of each individual objective corresponds to a unique
decisionvector.
Similarlythepoint (P=/r.uno,
fr.uno
... .fo."no)
represented by the worst scores of
the objectives
(boundary
non preferred
scilutions)is
also nôt feasible.
The optimisation consists then in the search of the feasible solutions, which are the closest as
2
the operator of comparaison
is itself a function.
6
possible
from the
ideal reference
point (or the most far away
from the non preferred
boundary).
Figure 5 describes
the iterative stucture of the multiobjective optimisation.
Tûbine power mgi! (qT)
Solar Multiple (SM)
Petralty load (cblvD
bll{ff facûor (kJ
Fossil udt efrciercy (EF)
Operrtioml vûiables (Op)
Ilte8er vtiÂbles (BD)
Bilry vuiables (Bn)
Figure 5: Iærative structure
of the multiobjective optimisation undertaken
The main objectives considered in this study, are the minimisation of the costs of equipments
(CAE), the minimisation of CO, emissions (q"o) and the maximisation of the yeady energy
efficiency of the superposed
cycles
(eo*").As expecûed these
three criæria
show different ffends
relative to the decision variables.
The decision vector is made of different groups of variables:
. The variables associated with the size of components represented by the thermal margin
of the flnbine, the socalled solar multiple.
. The integer variables corresponding to the type and number of turbines implemenûed
at
each ORC. These turbines
can be chosen
among three different types: TI,T2 and T3. Each
type corresponds
to a different serial model and hence to a different catalogue of machines.
The maximum number of turbines per ORC stage
is limited to two, which can only be set in
parallel and not in series.
. The real variables of the load curve of the fossil unit (rolloff coeffrcient, penalisation load),
of the sizing of the heat exchangers
(pinches) and of the operation of the thermodynamic
cycles (boiling and condensation
pressures,
subcooling and superheating
temperatures).
By optimising separately
each of the three objectives (CAE, eçe2,
teaç), we get the three exfieme
decision vectors QÇAE,
&or, 4*") and their corresponding scores which form the ideal
reference. To determine the limit point of the nonpreferred objectives, the simulation is then
successively
launched for the vectors (X"*, &or, 4*"). The worst score is then noticed for
each objective. On the basis of these two points, characteristics of solar radiation, and of the
economic parameters
(economic life time, interest rates, amortisation, etc.), the simulation code
calculates
all the thermodynamic points of the hybrid cycle and sizes all equipments. It also
deærmines
the energetic,
economical and environmental performances of the whole power plant
and gives back the values of the different objectives (score). The utility function is established
and the optimisation at this stage is reduced to searching a new decision vector \", tlnt
minimizes the Euclidian distance relative to the ideal point of reference (R). For each iteration
step, the values of the independent variables are modified on the basis of characteristic
rules of
the algorithm being used, in this case a genetic algorithm. The optimisation constraints are
managed at the level of the simulation model. The latter allows the avoidance of penalty
functiôns, which are fiaditionally slowing convergence.
The advantage of such a process is that
at the end of the optimisation, the engineer
has optimal solutions for each individual objective as
well as one or several solutions, which are compromises.
There are no intrinsic limitations on the
number of objective functions, which can be considered by opposition to multiobjective
optimisation based on a criterion of comparison of the different scores.
3.2 Performance analysis and Results
The multicriæria optimisation model presented
above has been applied to an HSPS of 22 kWe.
The yearly energy performance
is calculated on the basis of the hypothesis of a solar profile by
7 
correlation
(Kane,
70fl2)
and
of a classification of the direct solar radiation
in the plan of a sun
following NS collector
field. The region of Gabes
in Tunisia3
(Minder, Cogener
1996) has
been chosen
as an example.
The quantity
of emitæd
CO, and the effrciency
of the ORCs are
averaged over
a full year,
optimising
in each case, the load cur"rre with a maximum
electic power
constraint of 22 kWe. The
Diesel
fuel considered
has a lower heating value
(LHV) of 11.86
kWhlkg and a density of the order of 840 kg/m3. The engine cooling water is supposed
not to
exceæd
a temperature of 90"C although there exists engines which could toleraæ higher
temperatures.
Input temperature
limits of the ORCs
are
of the order
of I70"C for the hot source
and 10oC for the cold source.
At nighL the power
unit is supposed to work only with the lower
temperature
cycle,
which works with R134a. The transition to the superposed
cycle
mode from
the single ORC mode is supposed
to take place
when the input heat raûe at the evapoxator
reaches
507o
of the
nominal
value.
However
and
even
if the simulation
model includes an option
to operate
with variable
speed turbines
(case
of an isolaæd region), we limit our considerations
in
this
paper
to turbines directly
linked to the electric
net
which corresponds to a speed of the order
of 3000
rpm. Table 3 shows
the corresponding
optimum values of objectives.
)biectives decision
vectors
\ame Symbol Units &nr Xcoe Xonc bpr
Eouioment cost :AE (kcHF) 1
18.5 149.9 206.6 157.5
Amount
of CO2 emitted lcoz (to) 120.3 100.8 1 15.9 r
01.0
)RCs
efficiency toRc 8.83 r
0.84 12.35 11.23
Table
3:
values of the objectives
for an HSPS22kW
(Site
of GabesTunisia, G,.o=!00
Wm2)
SM=l.16, 86 m2,
65%,
159'C qF2.20, 11 kwe 19.14 bar
147"C
18.99 bar,
78"C
4.87kwe, 46 cm3
vRi4.8
Figure 6: optimum configuration minimaxi (multicriteria optimisation, HSPS22kWe)
The final optimal solution Xopr (minimaxi optimum) corresponds to a confrguration with two
turbines percycle, type T3 foi the high temperature
cycle and T2for the low temperature
cycle.
14 kWe, 27o/o,
ch=80%, kr=0.0
3 This site was chosen in ?elation with another hybrid combined cycle
d'Aménagement
Energétique Solaire lttttgté) which has also been used to test
described
in this paper.
5.84kwe,
60 cm3
VRI=2.6
project called PAESI (Projet
the optimisation methodology
14.4 m2
55 kW
HCFC123
8.4m2.5'l
kW4.33
bar
99.5'C
0.8m2
17 kW
HFC134a
7ÆIW s.osbar
8
Figure 6 shows the capacity of the different components and the thermodynamic conditions for
daylight operation.
One such configuration is favourable from the energy efficiency point of view by minimising the
effrciency drop at part load, but is of course far from being the most economical with present
day economics.
Tableau 4 shows the investment costs
for this minimaxi optimum in comparison
with optima obtained
for each
of the other criteria.
Figure 7 shows the distibution of the different costs
for the minimaxi optimum.
Tableau
4: Investment cost optima
(multiobjective
criterion,
HSPS22 kWe, Site GabesTunisia)
Manufacturing
&
Engineering
10%
cMl engineering
5%
Solar
unit
39%
ORcs
unit
35%
fossil unit
11%
Figure 8: Distribution of the investrnent costs
(optimum minimaxi configuration,
HSPS22 k\Ve, Site GabesTunisia)
We can see the significant impact of the solar freld and of the ORCs on the global HSPS cost.
The solar unit represents
in it already 39Vo
of the total equipment costs. The ORC porver unit
represents
35Vo fot a maximum power rating of 11 kWe compared
to only IIVo for the motor
Diesel unit rated at 14 kWea. It is however important to note that the cost values used for the
ORCsaredeterminedfromtwodifferentprototypes
(ORClOkWe, 1999 and ORCNC21kWe,
a The total rating is 25 kWe
nominal operational power is
daylight mode.
g1 kWe for the superposed ORC and 14 kWe for the engine).
However,
22 kWe accounting
for the fact that the engine is operated
at partial load in the
the
early collected solarenergy
44',575
20'ss3
53'357
6'970
13'939
73',384
12'153
24',30s
73',225
20'1
56
64',122
9'265
unit
(CAEs)
unit
(CAEm)
conversion unit (CAEu)
9
2001). Note that no effort was made to imp'rove the present pumps, which at present have a
higher unitary cost than the scroll expandergenerator
themselves
and therefore offer 3 poûential
foiimprovement. Moreover a unitary solar c6l1ector
price of 850 CIJFlflf pour 86 m2 lias been
considered. This price is determined on the basis of cylinderparabolic LES3 collectors, which
are commercialised
for large power plant and negatively corrected by a factor of scale (Kane,
2002). Actual price of the solar field was higher (Allani etal.2002)
The specific cost depends on the configuration and on the component sizing. It is of the order of
8543 CHF/kW for the minimaxi optimum of an HSPS of 22 kWe. This results from a tradeoff
between the most economical (hence the least efficien (6458 CHFlkW, 8.83Vo)
and the most
expansive
and
efflrcient
solution
(10803
CHF/kW, 12.357o). The specific cost increases wittt tlrc
size of the solar field. For the most efficient solution we have a tatal solar field of the order of
137 flf instead of 49 rt obtained for the minimum cost solution. The maximum energy solution
corresponds
to a solar multiple SM of I.20, corresponding
to a design radiation of 775W/m'
compared to the maximum value of 900Wnt'. The incident solar energy is in this case of the
orde? of 1647 kWVmt/y compared to a maximum solar radiation availâble of 1934 kWh/m2.
Table 5 shows the optima of the unitary production costs for the different confrgurations
resulting from the multi objective optimisation. An economic lifetime of 20 years is considered
for the reimbursement of capital at an interest rate of 4.5Vo.
A fund to renew defective material is
estabtshed at 1007o on the basis of the reserve capital generated
by ttre project. The return for
such a fund is done at the market rate of 3Vo and over an amortisation period of 20 years. The
unit price of Diesel fuel is taken equal to 0.62 CHF/kg.
Mean unitarv cost Optima
Nom Units Costs coz eoRc Tradeoff
Type of plant
Yearly collected energy
from solar
Solar
field
Rating
Tvoe of fuel
(kwh/m2)
(m2)
(kwe)
()
HSPS
1934
49
??
Diesnl
HSPS
1817
81
22
Diesel
HSPS
1647
137
22
Diesel
HSPS
1 647
86
22
Diesel
Hours
per year
Yearly electricity
production
yearly
solar
contribution
yearly
contribution
of waste heat
yearly
fossil contribution
Fuel Consumption
CO2
emissions
Reduction
of CO2
emissions
(hours)
(kwhe/y)
(%)
(%)
(%)
(ks/y)
(ks/y)
(%)
8'759
170'124
5.3
14.4
80.3
38'332
120'253
17
8'759
1 53'561
10.3
15.2
74.5
32',124
100'818
24
8'759
r 78',551
15.8
15.9
68.2
36'808
115'898
26
8'759
154'798
10.8
15.2
74.0
32',170
100'963
24
Caoital cost (Zt) {GHF/v\ 16'002 20'243 27'902 ?1',272
Depreciation
(CRM)
Reimbursement and
interest
(CPA)
Assurances
and Taxes
(TTA)
Srrhsidv (CTS'I
4'410
10'716
877
0
5'578
13'556
1'109
o
7'689
18'685
1'529
n
5'862
14',245
1'166
ô
0peration
and Maintenance
(OM) (CHF/v) 29'690 27',411 33'151 27',82'l
Resources
(Rs)
Maintenance
(KM) 23'766
5'924 r
9'9
r7
7',494 22'82'l
10'330 19',945
7'875
Mean vearlv cost (Costma) (CHF/v) 45'.692 47',653 61'0s3 49'093
Table 5: Optima
of the unitary
production
costs
(multiobjective
criterion,
HSPS22 kWe, Site GabesTunisia)
Figure
9 shows
the evolution
of the unitary/
cost (LEC) as well as the CO, emission
reduction
ratnG,æ)foreachof
thesolutions,thelatterbeingdefined
as the amount of CO, (qco, ) which
is not emitted
compared
to the emissions
(e8o, ) of a fossil reference
plant
satisfying
the same
load curve: acoz=(nS",
eco2)
lûo, (2)
10
As expected
the nend indicates
a unitary cost (LEC), which increases with the solar coverage
(yearly solar electicity produced). The latter reaches
I6Vo for the most efficient solution,
corresponding
to aLEC of the order of 34 Swiss
cts/kWhe, which is 49Vo
higher than the LEC
of a simple
reference Diesel engine
following the same
load curoe
(DEPUDiesel
Engine Power
Uilq22kWe, 23 Swiss
ctslkWh'). Consequently
a maximum
rate
of emission
reduction
of 26Vo
is reached for this
most
efficient
solution
(Xo*").
0.300
0.280
0.260
0.240
o.220
0.200 XCAE xco2
Decision
vectors
Figure 9: Unitary cost
LEC and
amount
of avoided CO, emissions
tt 12 13 14
Penalty period (hous)
278
249
.s
(E
21
.i
o
(J
.C
=
J
l!
I
()
()
uJ
18
15
Figure 10: Daily load curve (criterion
energy
efficiency, eo*")
Penalty
period (hours)
Figure ll:.Daily load curve (criterion
flrrllrmum elrusslon,
qco2)
It is worth mentioning
that the optimum for the absolute CO, emissions
(9co, ) corresponds
to
a configuration with a smaller fossil unit, here a smaller cogeneration engine, but does not
necessarily
represent the solution with a lower emission in relative terms (Figure 10 and Figure
11). This iesult can be explained by the fact that the reference
for CO, also varies in function of
s The calculation of the LEC for the DEPrJ22kWe
is done with the same hypotheses than the HSPS22kWe
power
plant.
8910rt12131415161718
 11

the load curve. An inûeresting conclusion is that a tax of the order of 42 Swiss cts/kg"o, would
be required in the present economics to ensure the competitiveness of an HSPS 22 kWe
compared
to a Diesel of the same size (not accounting for any tax for additional pollutants).
4. Conclusions
A prototype unit of an original concept of minisolar hybrid plant has been manufactured and
tested
within the framework of a project called SPS (Solar Power System). Performances of the
thermodynamic cycle are satisfactory considering the low temperature
and power ranges and the
fact that obvious improvement measures have been identified. The First Iaw effrciency of
electricity
production
in hybrid mode is of the order
of 4lVo when considet
fuel input (total
electrical
power/
LHV of the
fuel). This already represents an mcrease
of close to 50Vo
compared to the Diesel engine alone. However due to an over of the
turbines and a lower solar collector efficiency than expected,
the conversion at very
paftial load and the efficiency in mode "solar
only" was only of 7.747o.
The latær is 35Vo below
the expected
performance
for operations, which wotrld be closer for the expected
nominal values.
Simulating a continuous operation of the hybrid plant over a full year (day and night), one
multicriteria optimisation based on a minimaxi formulation and using genetic algorithms was
done for a power plant HSPS of 22 kWe. Such an approach allowed the deûermination of
vmious optimal configurations in function of exteme criæria (thermodynamic, economical and
environmental) as well as a tradeofi solution. Results show that the solar electicity conversion
costs stay relæively high and considerably depend on the relative size of the solar field. For
example
the LEC of a HSPS22kWI plant with 6 to l6Vo of solar contribution is about 17 ûo
49Vo morc expansive
that a reference fossil unit (DEPUDiesel of 22 kWe,23 Swiss cts/kWh),
which would satisfy the same
load profile. However future potential reduction of the costs of the
solar field, identified improvements of the ORCs as well as the infroduction of credits for the
reduction of CO, emissions should open new prospects for hybrid solar power plants.
Nevertheless,
at prèsent,
atax of the order of 42 Swiss cts/kg"orwould
be required to ensure
the
competitivity of an HSPS22 kW with 16%o solar compared
to Diesel of the same
power.
Nomenclature
CAE Cost
of Equipment
CEP ExtraPlats Solar Collector
DEPU Diesel
Engine Power Unit
HSPS Hybrid Solar
Power System
ORC Organic Rankine Cycle
SPS Solar
Power
System
LHV Lower heating value
Ep
ET
/(x)
G
Mpt
Mc*
jcoz
93oz
o)i
x
Ah*
Ah"*
^ç
Electric
power
delivered to the pump
Electric
power
delivered
to the turbine
Utility function
Direct solar radiation
Pressurized water
mass flow of the hot source
Coolant
water mass
flow from the engine
to the
preheater
Yearly amount
of emitted CO,
Yearly amount of emitted
CO2
from a reference
power plant
Priority level with regards to the objective
/,(x).
Vector
of independent variables C to the decision
space
Q.
Enthalpy
difference on the pressurized
water
heating the evaporator
(kJ/kg)
Enthalpy
differcnce on the water
cooling the condenser (kJ/kg)
Coenthalpy
difference
(exergy)
of the water to the evaporator (kJ/kg)
(kJ
or H/ke)
(kw)
(kw)
twrrfl
(kg/s)
(kw)
[kgCOr/an]
[kgCO2/an]
12
Àk"* Coenthalpy
difference
(exergy)
of the coolant to the preheater (kJlkg)
e First Law efficiency tl
n Exergetic efficiency t1
Tcoz
Tcsa Reduction rate of emissions of CO2
Yearly solar contribution to electricity production tl
tl
5. Acknowledgments
The authors would like to acknowledge the financial support provided by the Swiss
Federal
Office of Energy (OFEN), the contribution of COGENER SA who designed
and
delivered
the solar
collectors
and the group of MIT Cadlab (Prof Wallace) who is at the
origin of some
the genetic
algorithms used
(part of a project of the Alliance of Global
Sustainability
between
MIT, the University of Tokyo and the Swiss Institutes of
Technology).
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