Engineering, 2013, 5, 26-31
doi:10.4236/eng.2013.51b005 Published Online January 2013 (http://www.SciRP.org/journal/eng)
Figure of Merit Analysis of a Hybrid Solar-Geothermal
Power Plant
Cheng Zhou1, Elham Doroodchi2, Behdad Moghtad eri1
1Centre for Energy, Discipline of Chemical Engineering, School of Engineering,
Faculty of Engineering and Built Environment, The University of Newcastle, Callaghan, NSW, Australia
2Centre for Advanced Particle Processing and Transport, Discipline of Chemical Engineering, School of Engineering,
Faculty of Engineering and Built Environment, The University of Newcastle, Callaghan, NSW, Australia
Received 2013
ABSTRACT
Figure of merit analysis is a general methodology used to evaluate whether a hybrid power plant could produce more
po wer than t wo st and-alone power plants. In this paper, the assessment methodology using figure of merit analysis was
re-examined for a hybrid solar-geothermal power plant. A new definition of the figure of merit was introduced specifi-
cally for a solar boosted geothermal plant to include both the technical and economic factors. The new definition was
then applied in a case study of a hypothetical demonstration hybrid solar-geothermal power plant in Australia. The
power plant was considered to have a typical net power output of 2.2 MW with a solar energy fraction of 27%. The
analysis was performed to compare the power output and capital cost of the hybrid plant with the state-of-the-art (SoA)
and e xist ing sta nd -alo ne sol ar and geothe r mal pl ant s. Ba sed on the ne w defi nitio n, the h ybr id plant was found to gener-
ally outperform the two existing stand-alone plants. Moreover, at an ambient temperature of 5˚C, the hybrid plant was
found to outperform the SoA stand-alone plants when the geothermal temperature was greater than 150˚C. For geo-
thermal temperature of 180˚C on the other hand, the hybrid plant outperformed the SoA stand-alone plants at ambient
temperatures lower than 33˚C.
Keywords: Figure of Merit; Hybrid Renewable Energy System; Solar; Geothermal; Power Generation
1. Introduction
In general, a hybrid power generation system can gener-
ate more power than two stand-alone power plants main-
ly due to an increase in efficiency. Such a syner g istic
effect alone, in most cases, makes the hybrid system
more attractive than the stand-alone systems, not to men-
tion other benefits that may be achieved simultaneously,
for example, pro viding reliability to certain po wer gener-
ation systems (e.g. solar thermal power plant), prolong-
ing plant service lifetime, and saving capital cost as well
as operating and maintenance costs.
However, not all hybrid systems are inherited with a
synergy, rather an improperly hybridised power genera-
tion system may even promote inefficiency. Thus, a me-
thodology should be established to assess the availability
and strength of the synergy. The figure of merit analysis
developed by Khalifa et al. (1978) for a hybrid geother-
mal–fossil fuel plant is commonly used for such assess-
ment s [1]. However, Khalifa and his co-workers only
provided the figure of merit analysis on a technical basis
and therefore in their definition of figure of merits the
economic factors were not considered. In the analysis of
hybrid solar-geother mal syst ems, however, the economic
factors cannot be ignored simply because sharing of
power generation facilities in these plants is expected to
greatly reduce their cap ital and o perating costs relative to
those of two stand-alone plants. Here we introduced a
new definition of the figure of merit taking into account
of both technical and economic synergies particularly in
the context of a hybrid solar-geothermal system. Specif-
ically a case study of the hybrid system was carried out
to validate the new methodology.
2. Figure of Merit Definitions
The figure of merit developed by Khalifa, F, is defined in
Equation (1) as the ratio of the po wer output of a hybrid
power plant, Wh, to the sum of power outputs of stand-
alone power plants, Wi;
(1)
where . Ei is the exergy content of the
energy resource, and ηu,i is the utilisation efficiency of
the energy resource in a stand-alone power plant, i de-

C. ZHOU ET AL.
27
notes the energy resource, and n denotes the total nu mber
of t he sta nd -alone po wer plants. I n the de finition of Kha-
lifa, the figure o f merit o f lar ger than 1 indicate s that the
hybrid system outperforms the stand-alone systems in
terms of power generation; however, other factors, such
as resources availability, reliability of the hybrid system,
and its economics are not factor ed in this defi nition.
To develop a figure of merit which considers the eco-
nomic factors for a solar boosted geothermal plant, the
following parameters were considered. For a stand-alone
solar power plant,the overnight cost is largely for the
power cycle and the solar field. In contrast, in a hybrid
solar-geothermal plant for power generation, the over-
night cost mainly depends on the solar field with minor
costs ass°Ciated with the modification necessary for
sharing of the power cycle infrastructure. The ratio of the
total cost of solar in hybrid to the total cost of
stand-alone solar, ε, was fixed at 76% for all analyses.
The corresponding 24% cost reduction is largely attri-
buted to the shared cost of the main power cycle, cooling
system, engineering and management in a hybrid plant
[2]. Taking into account the above considerations we
define an economic figure of merit, Feco, which is the
ratio of the cost per power output of the stand-alone solar
po wer plant, Cap stand-alone solar t o the cost per power output
of the solar resource utilised in a hybrid plant, Capsolar in
hybrid (Equation (2));
(2)
where
and
Cstand-alone solar denotes the overnight cost of a
stand-alone solar power plant; Wstand-alone solar denotes the
power output of a stand-alone solar power plant; Wsolar in
hybrid denotes the equivalent power output attributed to the
solar resource in a hybrid plant (i.e. the boosted output);
ηstand-alone solar is the utilisation efficie ncy of solar re source
in a sta nd-alone solar plant and ηstand-alone geo is the utilisa-
tion efficiency of geothermal resource in a stand-alone
geothermal power plant. Substituting the definitions of
Capstand-alone solar and Cap solar in hybrid in Equation (2) gives;
(3)
In Equation (3) , the economic figure of merit of larger
than 1 indicates that the capital cost of utilising solar
resource in a hybrid plant is lower than that of a stand-
alone solar plant and hence, for the same power output,
the hybrid plant is economically more feasible than the
stand-alone power plants.
3. Approach and Methodology
Here both figure of merit definitions (i.e. Equations (1)
and (3)) are applied to the following three scenarios as
illustrated in Figure 1, in which the performance of a
hybrid solar-geothermal plant is compared with two
stand-alone reference power plants. These scenarios in-
clude, Scenario (a) where the two stand-alone reference
power plants are considered to be SoA power plants with
the maximum achievable utilisation efficiency, Scenario
(b) where the t wo st and -alone plants are considered to be
existing power plants ea ch with their own R ankine power
cycles (it should be noted that Rankine cycles generally
have a lower utilisation efficiency than the SoA utilisa-
tion efficiency), and Scenario (c) where the two stand-
alone plants are considered to be a combination of an
existing geothermal power plant with a rankine power
cycle and a SoA solar power plant with the maximum
achievable utilisation efficienc y. The latter Scenario spe-
cifically examines how well the solar resource is utilised
in a hybrid plant compared to otherwise utilised in a So A
stand-alone solar power plant. The above scenarios are
used to represent typical situations which can be encou-
netered in practice.
Corresponding to the three scenarios, figure of merits,
Fa, Feco,a, Fb, Feco,b, Fc, and Feco, c, were investigated, re-
spectively. As can be seen in Equations (1) and (3), the
calculation of figure of merit is a function of the utilisa-
tion efficiency of stand-alone reference power plants.
This efficiency varies from a high utilisation efficiency
of a SoA plant to a low utilisation efficiency of a non-
SoA pl ant u nder the above senar ios. G iven t hat the hybr-
id power cycle in this case study was limited to an air-
cooled binary Organic Rankine Cycle (ORC), we as-
sumed t hat the So A utilisa tion e fficienc y of solar r esourc e
was 15% (a typical value in a SoA solar parabolic trough
plant), and the SoA utilisation efficiency of geothermal
resource was 30% (a typical value in a SoA geothermal
Figure 1. Three scenarios of figure of merit analysis, i.e.
Scenario (a), Scenario (b), and Scenario (c).

C. ZHOU ET AL.
28
binary pla nt). It should be noted that i n practice this e ffi-
ciency varies widely ranging from 29.5% for a sin-
gle-flash power plant to 35.6% for a dual-pre ssur e b inar y
power plant, 46.7% for a double-flash power plant, and
57.6% for a dry steam power plant [3].
4. Hybrid Plant Model
The hybrid solar-geothermal plant model, as shown in
Figure 2, was established by using the Pr°Cess simula-
tion package, Aspen HYSYS. In this case study the pow-
er cycle of the hybrid system was selected to be an
air-cooled binary ORC. The plant was composed of a
basic air-cooled geothermal binary ORC and a solar heat-
ing system (i.e. the solar field) comprising a solar pump,
solar collectors, and a superheater. The solar heating
system was hybridised into the geothermal base power
cycle to boost thermal efficiency and power. The geo-
thermal base power plant used a demonstration power
unit fed by a single well with a productivity of 50 kg/s
and a reservoir temperature of 150˚C, which wa s capable
of producing a maximum available net power output of
1.5 MWe. The condensate entering the pump was always
sub-cooled by 2˚C. For the solar field, a parabolic trough
syste m with a heat tra nsfer fluid of Therminol VP -1 was
used. The solar field area was fixed to be 6000 m2,
representing 27% solar energy fraction of the total heat
input in the hybrid plant. The major parameters of the
hybrid plant are summarised in Table 1.
5. Results and Discussion
The two definitions of the figure of merit were analysed
under three predefined scenarios in the hybrid power
plant. To conduct the figure of merit analysis, first the
maximum available power output of the hybrid plant was
calculated. F igure 3 shows the maximum available power
output of the hybrid sola r-geothermal plant with differen t
solar field areas for geothermal reservoir temperaturs
ranging between 90˚C - 180˚C. In this figure the power
output results for a stand-alone geothermal plant (i.e.
solar field area = 0 m2) at corresponding reservoir tem-
peartures are also presented. Generally the solar heating
system always boosted the power generation of the hy-
brid plant compared with a stand-alone geothermal plant,
and the amount of boosted power was found to be di-
rectly proportional to the geothermal reservoir tempera-
ture and the solar field area. Moreover it can be see n that
at a given power output, lower geothermal reservoir
temperatures are needed as the solar field area increases.
For example to generate 2.2 MW power output shown by
the horiz ontal solid line, a lower reservoir temperature of
150˚C is needed at 6000 m2 solar field area compared
with 160˚C for solar field area of 2000 m2.
Figure 2. A di ag ra m of a hy p ot het ic al hy bri d solar-geothermal
power pl a nt.
Figure 3. Max i mum a va il able net p ow er output of t he hybri d
plant as a function of geothermal reservoir temperature,
Tgeo and solar field a r ea.
Table 1. Simulation conditions used in the st eady-state case study.
Parameters Va lue Pa r ameters Value
Prod uct ion well temperatu re and flow rate 150˚C, 50 kg/s Des ign -point solar irr adiance 1000 W/m2
Ambient temperatur e r ange 5˚C - 44˚C Solar field area 6000 m2
Organic working fluid Isopentane Optical efficiency of solar collectors 70%
Working fluid flow rat e 35.6 kg/s Solar working fluid high temperature 390˚C
Isen tropic ef ficiency of turbine 80% M ini mum temperatur e app r o ach of heat exc h angers 10˚C
Pum p efficien cy 70% Cost saving ratio of the hybrid plant, ε 76%
SoA utilisation efficiency of geothermal resource 30% SoA utilisation efficiency of solar resource 15%

C. ZHOU ET AL.
29
While this figure provides information on how greater
power outputs can be generated using a hybrid system, it
does not provide any information regarding its competi-
tiveness in terms of technical and economic benefits over
t wo s t and-alone geothermal and solar power plants. Such
an evaluation was then carried out using the figure of
merit analysis in Equations (1) and (3). The summary of
the results for geothermal reservoir temperatures of
150˚C and 180˚C are pr eseneted in Table 2 and Tab le 3,
respectively. At 150˚C the original figure o f merit showed
that the hybrid plant produces 9% more power than the
two existing sta nd-alone plants (i.e. Fb = 1.09). However
the hybrid plant failed to produce more power than two
SoA stand-alone plants (i.e. Fa = 0.85) as well as the
combination of solar SoA and the existing geothermal
plants (i.e. Fc = 0.90). Similar trend was observed using
the economic figure of merits where the hybrid plant
under investigation was found to be inferior to a SoA
stand-alone solar power plant or the combination of the
solar SoA and the existing geothermal plants (i.e. Feco =
0.94 in Scenario (a) and Scenario (c)), indicating that the
cost of the hybrid system was ma rgi nall y greater than the
stand-alone plant s under investigatio ns. The co st of solar
in hybrid on the other hand was found to be approx-
imately half of the cost of a existing stand- alone solar
plant (i.e. Feco.a = 1.91 in Scenario (b)).
For the geothermal reservoir temperature of 180˚C, the
calculated original figure of merits for Scenario (a) and
(c) were 0.96 and 0.99, respectively (Table 3 ) suggesting
that the hybrid plant underperforms the two SoA stand-
alone power plants (Scenario (a)) as well as the combina-
tion of the SoA solar and existing geothermal plants
(Scenario (c)). However, the economic figure of merit for
these scenarios (Feco,a and Feco,c) was calculated to be
1.27 indicating that from an economic perspective, the
hybrid plant actually outperforms the two stand-alone
power plants given in Scenario (a) and (c) overwriting
the previous conc lusion.
Also, the original and new figure of merit definitions
for the hybrid plants given in Scenario (a), (b), and (c)
were examined over a wide range of environmental con-
ditions namely the heat source and heat sink tempera-
tures. In this study, the geothermal reservoir temperature
was varied from 90˚C to 180˚C and the ambient te mper-
ature was varied from 5˚C to 44˚C. The comparative
analysis results were shown in Figure 4 and Figure 5,
respectively. In these figures the horizontal dashed line
represents the conditions at which the hybrid and two
stand-alone plants have the same performance.
Table 2. Simulation condi tions and o utput s f or the cas e study with a ge othermal reservoir temperature of 1 50˚C.
Power plants Type Exergy input (kW) Utilisation efficiency Maximum available net power output (kW)
Stand-alone solar power plant SoA 5706 15.0% 856
Existing 5706 10.4% 423
Stand-alone geothermal power plant SoA 5977 30.0% 1793
Existing 5977 27.2% 1627
Hybrid power plant 11683 19.2% 2241
Figure of merit for Scenari o (a), Fa 0.85 Economic fi gure of merit for Scenario (a), Feco,a 0.9 4
Figure of merit for Scenari o (b), Fb 1.09 Economic figure of merit for Scena rio (b), Feco, b 1.91
Figure of merit for Scenari o (c), Fc 0.90 Economic figure of merit for Scena rio (c), Feco,c 0.9 4
Table 3. Simulat ion conditions and outputs for the case study with a geothermal resource temperature of 180˚C.
Power plants Type Exergy input (kW) Utilisation efficiency Maximum available net power output (kW)
Stand-alone solar power plant SoA 5706 15.0% 856
Existing 5706 11.4% 652
Stand-alone geothermal power plant
SoA 8360 30.0% 2508
Existing 8360 28.7% 2400
Hybrid power plant 14066 23.0% 3228
Figure of merit for Scenari o (a) , Fa 0.9 6 Economic fi gure of merit for Scenari o (a), Feco,a 1.27
Figure of merit for Scenari o (b), Fb 1.06 Economic fi gure of merit for Scenari o (b), Feco,b 1.67
Figure of merit for Sc enario (c), Fc 0.99 Economic figure of merit for Sc enario (c), Feco,c 1.27

C. ZHOU ET AL.
30
Figure 4. Co mparison of figure of merits as a function of g eot hermal resource t emperat ure at ambie nt t emperature of 5 ˚C.
Figure 5. Comparison of variou s fi gure of merit s a s a f unction of ambient temperat ure at geother mal temperature of 180˚C.
Figure 4 shows that increasing the geothermal reser-
voir temperature in Scenario (a) and (c) increases the
value of b o th fi gur e of merits whil st the origi nal figure of
merit for Scenario (b) remains almost unchanged. These
results sho w that in a case of using two SoA stand -alone
power plants (Scenario (a)) or the combination of the
SoA solar and existing geothermal plant (Scenario (c)),
the hybrid plant became economically feasible at reser-
voir temperatures greater than 150˚C. However accord-
ing to the original definitio n of figure of merit, the hybrid
system requires a reservoir temperature of at least 170˚C
before it can outperform the stand-alone plants. The hy-
brid plant on the other hand was found to outperform,
both in terms of power generation and cost, the existing
stand-alone solar and geothermal plants.
As Figure 5 shows, an increase in ambient tempera-
ture reduces the values of both figure of merits in Scena-
rio (a) and (c). However the ambient temperature was
found to have a relatively negligible effect on the figure
of merits for the Scenario (b). For the two SoA stand-
alone power plants (Scenario (a)) or the combination of
the SoA solar and existing geothermal plant (Scenario
(c)), the hybrid plant became economically feasible at
ambient temperatures less than 33˚C. Based on the orig-
inal definition of figure of merit, however, the ambient
temperature should be less than 20˚C for the hybrid sys-
tem to outperform the two SoA power plants in terms of
power output. For the combination of the SoA solar and
existing geothermal plant, the ambient temperature
should reach sub zero temperatures before hybrid system
became viable. Moreover, based on both definition of
figure of merits, the hybrid system was found to outper-
form the two existing stand-alone power plants over the
ambient temperat ure r ange exa mi ned in this study.
Clearly the new defi nitio n of figure of merit p ro vides a
greater insight into the assessment of hybrid Solar-geo-
thermal power plants than the original definition of fig-
ure of merit simpl y by i ncludi ng the cost factor .
6. Conclusions
A new definition of figure of merit was developed con-
sidering both technical and economic parameters. The
original and new figure of merit definitions were then
applied to compare a hybrid solar-geot herma l power plant
with stand-alone plants using three scenarios. Based on
the new definition, the hybrid system was found to gen-
erally outperform the two existing stand-alone plants. In
a cold climate with an ambient temperature of 5˚C,
however, the hybrid plant could only perform better tha n
the two SoA stand-alone plants when the geothermal
reservoir temperature was greater than 150˚C. As the
geothermal reservoir temperature increased to 180˚C, the
critical ambient temperature below which the hybrid
system outperformed the SoA stand-alone plants raised
to 33˚C. The cost of solar power generation per MW

C. ZHOU ET AL.
31
electricit y in a hybrid power plant was predicted to be
greater than the SoA stand-alone solar power plant, but
48% less than the existing stand-alone solar power plant.
Overall, the results indic ated that the new fig ure of merit
provides a greater insight into the assessment of the hy-
brid system over the stand-alone power plants especially
in a solar-geothermal context.
7. Acknowledgements
The authors thanks to the financial supports received
from The University of Newcastle, Australia.
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