Op imum design and pe o mance o a sola dish
mic o u bine using ailo ed componen cha ac e is ics
Giacomo Ga agnina, Se gio Rechb, Da id Sáncheza,∗, And ea Lazza e oc
aUni e si y o Se ille, Camino de los descub imien os s/n, 41092 Se ille, Spain
bIn e depa men al Cen e “Gio gio Le i Cases” o Ene gy Economics and Technology -
Uni e si y o Pado a, ia Ma zolo 9, 35131 Pado a, I aly
cDepa men o Indus ial Enginee ing - Uni e si y o Pado a, ia Venezia 1,
35131,Pado a, I aly
Abs ac
The aim o he pape is o ind he op imum design and pe o mance o
sola mic o u bines powe ed by pa abolic dish collec o s using an inno a i e
me hodology which in eg a es he design and o -design models o he o al
sys em. In con as o he common p ac ice o assigning an es ima ed e -
iciency o he engine u bomachine y (gene alized pe o mance maps), he
p ocedu e he eina e p oduces he speci ic geome y and he cha ac e is ic
maps o comp esso and u bine, acco ding o hei inle /ou le he mody-
namic s a es and wo king cycle bounda y condi ions.
Wi h his global app oach, a sensi i i y analysis is pe o med o sea ch
o he p essu e a io ha maximizes he sola - o-elec ic e iciency a design
poin o a cons an ai mass low a e and u bine inle empe a u e. Max-
imum alues in he ange 18.0% o 21.7% a e ob ained o a p essu e a io
o 3.2 when he u bine inle empe a u e changes be ween 800°C (base-case
sys em) and 900°C.
The me hodology allows also o simula e he pe o mance o he sys em
when di e en design DNIs a e conside ed wi h he aim o maximize he
annual yield o he sys em. Simula ions pe o med o Beijing, Se ille and
San Diego showed ha qui e di e en DNIs (610 o 815 W/m2) a e o be
chosen o ge he maximum annual (a e age) e iciency: 11% o 16% o he
base-case sys em and 14% o 19% o a mo e ad anced design.
∗Co esponding au ho
Email add ess: [email p o ec ed] (Da id Sánchez)
P ep in submi ed o Applied Ene gy Sep embe 11, 2018
Keywo ds: Mic o u bine, Sola dish, Volume ic ca i y ecei e , Design
and o -design
NOMENCLATURE
αAbso p i i y
¯ηglobal Mean annual e iciency
(global)
¯
Tai A e age empe a u e o ai in
he ca i y o he sola ecei e
∆hsIsen opic en halpy change
δcl Clea ance gap
˙
CHea capaci y
˙mMass low a e
˙
Qin Recei e g oss hea inpu
˙ Volume ic low a e
Emissi i y
ηE iciency
ΓFlux cap u e ac ion
γHea capaci y a io
ν s, To al- o-s a ic eloci y a io
ωAngula o a ional speed
φTo al adian lux
ψRim angle
ρDensi y
σS e an-Bol zmann cons an
τT ansmissi i y
εE ec i eness
ςRe lec i i y
ξInclina ion angle
AApe u e a ea
amb Ambien
bblade Blade heigh
C∗Hea capaci y a io
c0,is Spou ing eloci y
dDiame e
dsSpeci ic diame e
DNI Di ec No mal I adiance
DP Design Poin
EEne gy
e o To al concen a ion e o
pP essu e loss ac o
capaci y Capaci y ac o
dish Focal dis ance o dish
dumped Dumped ene gy ac o
GSpeci ic low a e
hEn halpy
HTA ec Hea T ans e A ea o ecu-
pe a o
2
ISpeci ic i adiance
kc ,ex Ex e nal con ec i e hea
ans e coe icien o ecei e
window
kc ,in In e nal con ec i e hea ans-
e coe icien o ecei e win-
dow
kdep De a ing ac o
mGT mic o Gas Tu bine
NRo a ional speed
nsSpeci ic speed
NTU Numbe o T ans e Uni s
PPowe
pP essu e
Pmech Sha powe
cComp esso p essu e a io
eTu bine p essu e a io
c Recei e
ec Recupe a o
el Rela i e
SR Simple ecupe a ed
TTempe a u e
TwTempe a u e o glass window
o sola ecei e
TIT Tu bine Inle Tempe a u e
TMY Typical Me eo olgical Yea
TOT Tu bine Ou le Tempe a u e
s To al- o-s a ic
To al- o- o al
UHea ans e coe icien
uBlade speed
c C i ical speed
WSpeci ic powe
1. In oduc ion
Sola powe is he mos abundan and dis ibu ed p ima y ene gy sou ce
on Ea h. In he las decades, academic and go e nmen al o ganiza ions
ha e a emp ed o de elop powe sys ems able o collec and con e his
ene gy in o elec ici y. Many o hese e o s we e aimed a demons a ing
he echnical and economic easibili y o sys ems ha in eg a e sola ene gy
collec ion and concen a ion de ices wi h well es ablished powe gene a ion
sys ems. Among hese con en ional echnologies, he ocus has always been
on he u iliza ion o gas u bines o hei small oo p in and low capi al
cos [1–5].
One o he mos ecen a emp s o de elop small scale sola powe
gene a o s based on mic o gas u bine echnology is he OMSoP p ojec
(Op imised Mic o u bine Sola Powe Gene a o ), unded by he Eu opean
Commission wi hin he 7 h F amewo k P og amme [6]. The OMSoP con-
so ium has al eady published many wo ks ela ed o his ype o sys ems
3
[7–12]. Gio annelli [7, 8] p esen s a e iew o he cu en s a e o he a
in he a ea o small-scale concen a ed sola he mal powe sys ems based
on dish collec o s. Lanchi e al. [9] p esen he expe imen al sola uni de-
eloped by ENEA (I alian Na ional Agency o New Technologies, Ene gy
and Sui able Economic De elopmen ) o he OMSoP p ojec . Ce i e al.
[10] p opose he in eg a ion o sola dishes wi h ad anced semi-closed cycles
mic o- u bines. Sanchez e al. [11] analyze he po en ial o selec ed ma ke s
o he wo ldwide comme cial deploymen o OMSoP sys ems. Ga agnin e
al. e alua e he manu ac u ing, anspo a ion and ins alla ion cos s o he
simple ecupe a ed sola -only and hyb id sys ems in [12] and he economic
and inancial app aisal o he p ojec o simple ecupe a ed, in e cooled and
in e cooled/ ehea ed ad anced layou s in [13].
Mic o gas u bines (mGT) ha e powe ou pu s in he ange om a ew
kilowa s [14] o hal a megawa [15], e en i his uppe limi migh change
be ween 250 kW and 1 MW depending on he sou ce. They ypically include
single s age adial u bomachine y wi h mode a e p essu e a io ( hough
highe p essu e a ios a e possible in la ge engines in combina ion wi h
axial low machine y) and an in e nal hea eco e y de ice (compac hea
exchange [14]) o enhance e iciency. These componen s a e ypically a -
anged in a single sha con igu a ion al hough mul iple-sha layou s ha e
also been conside ed [16].
Sola mic o u bines ypically make use o pa abolic dish collec o s o col-
lec and concen a e sola ene gy on o a ecei e which in u n con e s i in o
hea . The concen a ion a io o hese collec o s is e y high and enables he
e y high empe a u e ha is needed o a ain high e iciency [17]. Wi h he
a o eci ed OMSoP p ojec , he Royal Ins i u e o Technology in S ockholm
(KTH) es ed wo di e en sola ecei e p o o ypes: a ca i y olume ic
p essu ized ecei e wi h oam abso be [18, 19] and an impingemen ca i y
ecei e [20]. The in eg a ion o olume ic ecei e s in se e al applica ions
such as sola sys ems o o -g id ene gy p oduc ion [21] and polygene a ion
in u al a eas [22], ei he in simple o combined cycle con igu a ion [23], was
s udied by Aichmaye e al. whils Wang e al. [24] in es iga ed an in eg a ed
dish-mGT design using sola sys ems wi h impingemen ecei e s. These ac-
i i ies add o he pas wo k on hese sys ems o space, mili a y and ci il
powe applica ions: Kesseli e al. calcula ed he pe o mance o a mic o u -
bine engine composed by s ock u bocha ge componen s in [25] while Dickey
p esen ed he expe imen al pe o mance o a Caps one mic o u bine in e-
g a ed wi h a ield o helios a s in [26]. Mo e ecen ly, LeRoux and Meye
4
made use o a lumped- olume app oach o simula e he pe o mance o a
small-scale dish-mTG sys em using da a om s anda d o - he-shel Ga e
u bocha ge echnology and a model o open-ca i y ubula ecei e s [27].
Semp ini e al. also employed models o sola -only and hyb id mGT sys ems
based on lumped olumes and u bomachine y pe o mance maps aken om
li e a u e [28].
In con as o hese pas wo ks, which ely on gene alized pe o mance
maps o u bomachine y o on exis ing comp esso s/ u bines (engines de-
i ed om u bocha ge s), he cu en pape p esen s a wo-s ep in eg a ed
p ocedu e i) o design sola mGT sys ems by de e mining op imum u boma-
chine y geome ies and pe o mance maps, and ii) o simula e he o -design
beha io in o de o e alua e he highes annual p oduc ion o elec ici y o
a speci ic loca ion.
This in eg a ed app oach o he design and o -design analyses o sola
mGTs allows o he gene a ion o "ad hoc" designs o a speci ic loca ion and
o he calcula ion o mo e eliable pe o mance alues along a ypical yea o
ope a ion as compa ed o hose calcula ed wi h he " adi ional" app oach.
2. Dish-mGT in eg a ed sola sys ems
Powe gene a o s based on in eg a ed dish-mGT sys ems a e mos ly based
on he simple ecupe a ed Joule-B ay on cycle, Fig. 1, e en i o he con igu-
a ions including in e cooling and ehea ha e been p oposed in he li e a u e
[10, 13, 29].
The pa abolic dish is esponsible o he hea supply and is a well es ab-
lished echnology wi h many di e en designs ha ing been es ed in he pas .
Mos o his expe imen al ac i i y aimed a he in eg a ion in dish-S i ling
sys ems [30–32] bu he e a e also p o o ypes wi h mic o u bines. A com-
ple e dish-mGT assembly based on an engine de i ed om a u bocha ge
was s udied in he mid 1980s by NASA (Na ional Ae onau ics and Space
Adminis a ion) in he B ay on Powe Sys em and Sola Ad anced Gas Tu -
bine Engine p ojec s [33, 34]. Amsbeck e al. epo ed he es ing o a
sola -hyb id mGT a he Pla a o ma Sola de Alme ia [35] and Dickey e al.
published es esul s o an adap ed Caps one mGT ope a ed on sola ene gy
a he Weizmann Ins i u e [36]. Finally, Kesseli e al. epo ed es s ca ied
ou by B ay on Ene gy wi h a sys em including dish collec o s, mic o gas
u bines and a comp essed ai s o age sys em [37]. Mos o hese uni s make
use o sola olume ic ecei e s because o he highe e iciency as compa ed
5

Figu e 1: Single-sha ecupe a i e mic o u bine wi h in eg a ed sola ecei e : comp esso
(C), ecupe a o (R), sola ecei e (S), u bine (T) and gene a o (G).
o ca i y ecei e s in ei he ubula o impingemen con igu a ion [38, 39].
The knowledge gained om hese expe imen al ac i i ies is complemen ed by
he ho ough heo e ical analysis explo ing he ad an ages and disad an ages
o using adap ed u bocha ge s o small gas u bines designed om sc a ch
[40–45].
In he ecupe a ed B ay on-Joule cycle shown in Fig. 1, he a ailable hea
ca ied by he gases lea ing he expande is used o p ehea he ai deli e ed
by he comp esso be o e his en e s he combus o , wi h he aim o inc ease
he he mal e iciency o he engine. This layou is bes exploi ed when
associa ed wi h low p essu e a ios which enable he u iliza ion o single-
s age adial u bomachine y coupled o a sola ecei e as a me e subs i u e
o he combus o o a con en ional mGT [16]. The low diag am is as ollows.
Ambien ai en e s he comp esso (C) whe e i is p essu ized (1-2). This ai
s eam hen lows in o he cold side o he coun e - low compac ecupe a o
(R) whe e i is hea ed by he ho exhaus ai lowing ou om he u bine
(2a-3a). Once p ehea ed, he ai en e s he sola ecei e (S) whe e i is
hea ed up u he by he sola ene gy collec ed by he pa abolic dish and
concen a ed on o he ocal poin whe e he sola ecei e is moun ed. This
componen is a olume ic, p essu ized ecei e wi h a SiC oam abso be
and a qua z glass window ha le s sola ene gy in whils educing bo h
p essu e and con ec i e hea losses. The concen a ed sola beams en e ing
he ecei e hea he oam abso be which, in u n, aises he empe a u e
6
o ai lowing h ough i (ai ac s as a coolan o he abso be ). The ai
exi ing he ecei e lows in o he u bine (T) whe e i is expanded (4-5) and
hen sen o he ho end o he ecupe a o whe e i is cooled down by he
comp esso deli e y ai be o e being eleased o he a mosphe e (5a-6). When
he a ailable sola adia ion exceeds a maximum alue (uppe h eshold), a
ac ion o he o al mass low h ough he engine bypasses bo h sides o he
ecupe a o , hus educing he inle empe a u e o he sola ecei e (3) and
a oiding o e hea ing o he sys em. The elec ic gene a o (G) is moun ed
on he same sha as he u bine and comp esso , hence o a ing a a e y
high, a iable speed (in he ange 100-150 k pm). This means ha powe
elec onics a e equi ed o ensu e ha ol age and equency o he elec ic
ou pu a e s able and in compliance wi h he equi emen s o he g id.
Two echnology le els o he mGT a e conside ed he e, co esponding
o di e en alues o u bine inle empe a u e (TIT) and ecupe a o e ec-
i eness (ε ec,DP ): base-case (800°C-85%) and ad anced sys em (900°C-90%).
This choice is based on echno-economic conside a ions. Tempe a u es lowe
han 800°C would b ing abou a d as ic e iciency d op whe eas empe a u es
abo e 900°C would imply using mo e expensi e ce amic ma e ials in he u -
bine [16, 46]. Recupe a o e ec i eness lowe han 85% would b ing a oo
low in e nal hea ecupe a ion whe eas a alue highe han 90% would imply
a e y hea y and expensi e componen [16, 47].
Figu e 2 shows he he modynamic cycles o bo h he base-case and ad-
anced sys ems. The di e ences lay on he posi ion o s a ion 4 (TIT e ec )
and in he ela i e posi ion o s a ion 5 wi h espec o s a ion 3 (e ec o
ε ec,DP ). The main deign speci ica ions o he sys em a e summa ized in Ta-
ble 1, whe e he ange o DNI (DNIDP ) and p essu e a io ( c,DP ) conside ed
in he sensi i i y analysis a e also gi en.
Main sys em speci ica ions
DNIDP 800 W/m2(sensi i i y 400 W/m2-1000 W/m2)
c,DP 3 (sensi i i y 2.5-4)
˙mai ,DP 0.1 kg/s
TITDP 800 °C(base) 900 °C(ad .)ε ec,DP 85 %(base) 90 %(ad .)
Tamb,DP 25 °C pamb,DP 101325 Pa
p, ec,c,DP 97.0 % p, ec,h,DP 98.5 %
p, c ,DP 96.0 % p,in/ou ,DP 99.5 %
ηmech,DP 99.0 %ηel,DP 90.0 %
∆T u b,DP 5°C ns, ,DP 0.55
Table 1: Independen a iable se (inpu pa ame e s).
7
Figu e 2: Tempe a u e-en opy (le ) and p essu e-en halpy ( igh ) diag ams o he base-
case and ad anced sys ems.
3. Me hodology
The me hodology used o ind he op imum design and pe o mance o
he sola -mGT sys em is based on an in eg a ed p ocedu e which combines
he design and o -design pe o mances o he sys em. Bo h models a e sol ed
wi h a modula -sequen ial app oach which elies on he conse a ion o mass,
momen um and ene gy and on es ablished co ela ions o cha ac e ize com-
ponen s pe o mance and e iciency. The wo king luid is ai which is con-
side ed o be d y eal gas wi h he he modynamic p ope ies p o ided by
Coolp op®[48]. The comple e model is implemen ed in Ma lab®on he
assump ion ha all p ocesses ake place in equilib ium [49].
The i s s age o he design model consis s in calcula ing he wo king
cycle and he cha ac e is ics o he main sys em componen s. To his end,
bo h one dimensional (1-D) and ze o dimensional (0-D) app oaches a e used:
adial u bomachine y (1-D), sola ecei e (0-D), ecupe a o (0-D) and sola
dish (0-D). The design space is limi ed by a su icien ly la ge ange o p essu e
a ios (2.5-4, see Sec ion 5.1) whe ein po en ial designs a e explo ed in o de
o a ain he highes sola - o-elec ic e iciency a he design poin . The basic
geome y o he u bomachines, which includes he me idional low pa h
and blades, is hen used o p oduce he co esponding pe o mance maps
ha will la e be used by he o -design model (see Fig. 4) o e alua e he
beha io o he sys em when subjec ed o bounda y condi ions di e en om
he design ones. This o -design model elies on a sui able con ol s a egy
which ensu es he sa e ope a ion o he sys em wi hin a ce ain ange o
8
bounda y condi ions.
3.1. Design model
The s uc u e o he design model shown in he lowcha in Fig. 3 is
common o he base-case and ad anced sys ems (Sec ion 2) and he inpu
da a o he model a e lis ed in Table 1. Upon calcula ion o he wo king
cycle wi h he inpu da a in Table 1, he "The modynamic cycle 1" module
calcula es he inle condi ions (p essu e and empe a u e) o each u boma-
chine y along wi h he co esponding u bine expansion a io ( e,DP =p4/p5)
o a gi en p essu e a io o he comp esso ( c,DP =p2/p1). P essu e losses
ac oss he sola ecei e , ecupe a o and inle /ou le duc s a e aken in o
accoun by means o he p essu e loss ac o s ( p=pou /pin) in Table 1.
Wi h his in o ma ion, he u bomachine y 1-D design modules ("Tu bine"
and "Comp esso ") calcula e he d a geome ies o u bine and comp es-
so , also p o iding hei isen opic e iciencies and o a ional speed. These
da a a e hen used o comple e he simula ion o he he modynamic cycle by
calcula ing he ou le s a es o each u bomachine y and he comple e hea
balance o he ecupe a o . Wi h he he modynamic cycle calcula ed ully,
he ecupe a o is designed using he ε−NTU app oach o calcula e he
Numbe o T ans e Uni s (NTU). This p o ides he o al hea ans e a ea
o he selec ed coun e - low con igu a ion ha yields he a ge e ec i eness
speci ied o iginally.
The ools o design he sola subsys em include he pa abolic dish and
ecei e modules. The ape u e (dish) and window ( ecei e ) a ea o hese
elemen s a e op imized o he nominal condi ions ob ained in he design
model o he mGT by minimizing o hea losses. Inpu s o he pa abolic dish
model a e he design DNI and he hea inpu o he ecei e wi h which he
ecei e model calcula es he ai ou le empe a u e (TIT). Two i e a i e
loops a e inally used o op imize he ape u e a ea o collec o and ecei e :
1. The inne loop sea ches o he op imum size o he ecei e . This
s ems om a balance be ween hea inpu om he collec o and hea
losses o he en i onmen .
2. The ou e loop co ec s he dish ape u e a ea un il he ecei e ou le
empe a u e is equal o he speci ied TIT a he a ed condi ions.
A de ailed desc ip ion and he equa ions o he design models o he mGT
componen s a e gi en in Appendix A.
9
indi idual models o he cons i uen s we e p e iously alida ed agains he-
o e ical o expe imen al da a and hence he model o he comple e sys em is
expec ed o p o ide us ul esul s. In pa icula :
•The pe o mance models o he comp esso and u bine a e well known
and ha e been alida ed by Aungie agains a la ge se o expe imen-
al da a aken om eal applica ions [52, 53]. Mo eo e , he speci ic
models o he comp esso de eloped o he sola applica ion ha e been
alida ed in a p e ious wo k o ai and sCO2[54]. Fo he u bine, a
speci ic alida ion agains expe imen al da a was done by NASA, as a
unc ion o he ela i e size o he clea ance gap. The o al- o- o al and
o al- o-s a ic e iciencies a he design poin ob ained expe imen ally
[55], he esul s o he model and he co esponding e o s a e shown
in Table 2.
δcl, el Re [55] Model E o
To al- o- o al e iciency
0.25% 89.2% 90.2% 1.05%
3% 84.7% 86.0% 1.62%
7% 79.3% 82.3% 3.64%
To al- o-s a ic e iciency
0.25% 87.0% 84.1% 3.51%
3% 82.8% 80.5% 2.88%
7% 77.7% 77.0% 0.87%
Table 2: Valida ion o u bomachine y design models.
•The design and o -design models o he sola componen s (pa abolic
dish and olume ic ecei e ) ha e bo h been alida ed agains da a ob-
ained a he es ig a he Royal Ins i u e o Technology in S ockholm
(KTH) [18, 19].
•The o -design model o he elec ic gene a o is de i ed om expe i-
men al da a ob ained by ENEA di ec ly [8].
•The p ope ies o d y ai wi h eal gas beha io a e compu ed wi h
Coolp op®whose accu acy is widely acknowledged wi hin he indus-
ial and scien i ic communi ies [48].
5. Resul s
This las Sec ion p esen s h ee di e en se s o esul s:
16

1. The esul s ob ained by unning he design model o he base-case
(TIT = 800°Cand ε eg,DP = 0.85) and ad anced (TIT = 900°Cand
ε eg,DP = 0.90) sys ems o a design DNI o 800 W/m2and an ai low
a e o 0.1 kg/s (see Table 1). In his analysis, he sensi i i y o he
a ed p essu e a io is also assessed.
2. The o -design pe o mance maps and he esul s o he annual simula-
ion o he wo sys ems men ioned in he p e ious bulle poin .
3. The esul s o a sensi i i y analysis wi h espec o he design DNI o
h ee di e en loca ions (Beijing, Se ille and San Diego).
5.1. Resul s a he design poin
The ollowing pe o mance me ics a e used o cha ac e ize he a o eci ed
sys ems:
•The global (sola - o-elec ic) e iciency (ηglobal) is de ined as he a-
io om ne elec ic ou pu (Pel) o o al hea inpu o he sys em
(DNI ·Adish), Eq. (1). I can be applied o ei he design o o -design
condi ions.
•The speci ic ou pu can be e e ed o he ai mass low a e ( ˆ
Pel, Eq.
(2)) o o he ape u e a ea o he pa abolic dish ( ˆ
Psola ,DP , Eq. (3)).
I can also be applied o ei he design o o -design condi ions.
•The e iciencies o he pa abolic dish collec o (ηdish,DP ), sola ecei e
(η c ,DP ) and mGT (ηmGT,DP ), de ined by Eqs. (4-6).
ηglobal =Pel
DNI ·Adish
(1)
ˆ
Pel =Pel
˙m1
(2)
ˆ
Psola =Pel
Adish
(3)
ηdish =˙
Qin ,DP
DNIDP ·Aa,dish
(4)
η c ,DP =˙
Qmg ,DP
˙
Qin ,DP
(5)
17
ηmGT,DP =Pel,DP
˙
Qmg ,DP
(6)
A comple e sensi i i y analysis o sys em and componen pe o mance
agains p essu e a io ( c,DP ) is shown in Fig. 9 o he base-case and ad-
anced sys ems (g een and blue lines espec i ely). Fi s ly, i is wo h no ing
ha bo h sys ems achie e maximum ηglobal o a p essu e a io o abou 3.2,
e en i a highe p essu e a io would ha e been expec ed o he ad anced
case. This is mos ly because o he highe ecupe a o e ec i eness o he ad-
anced case which p omo es a lowe p essu e a io o exploi he ecupe a i e
po en ial ully, Table 1. The e iciency o he pa abolic dish is independen
om c,DP as shown in Sec ion Appendix A.5, whe eas he e iciency o he
ecei e inc eases sligh ly wi h p essu e a io because o he highe densi y
o ai . Sha speed also inc eases because mo e comp ession wo k is needed
whe eas he ape u e a eas o dish and ecei e inc ease wi h c,DP due o
he highe hea inpu ha comes abou because o he dec easing inle em-
pe a u e o he ecei e (lowe u bine exhaus empe a u e).
In he ligh o he in o ma ion in Fig. 9 and in o de o main ain a
easible sha speed o some 130 k pm, a lowe p essu e a io equal o 3 is
inally selec ed, e en i he a ed e iciency shown is sligh ly lowe han he
op imum alue.
Table 3 summa izes he dependen a iables calcula ed in he design p o-
cess. The base-case sys em p oduces mo e han 7 kWewi h an ape u e a ea
o 50 m2while he ad anced sys em gene a es almos 9 kWe(abou 25%
mo e) wi h a 3% la ge ape u e a ea only. This powe gain is mainly due
o he highe TIT and  eg,DP which aise he mean empe a u e o hea
addi ion o he wo king cycle, ans o ma ions 30
−40and 300
−400 in Fig. 2.
18
Figu e 9: Global (sola - o-elec ic) e iciency s. p essu e a io and speci ic powe (abo e),
u bomachine y o al- o- o al e iciencies s. p essu e a io (cen e ) and sha speed and
dish/ ecei e ape u e a eas s. p essu e a io (below). Base-case and ad anced sys ems
shown in g een and blue espec i ely.
19
Base-case sys em
Pel,DP 7.19 kWeηs, ,DP 82.44 %
Adish (ddish) 50.0 m2(8.0 m) ηs,c,DP 76.52 %
A c (d c ) 167 cm2(14.6 cm) ηdish,DP 90.35 %
HT A ec 5570 m2η ec,DP 82.79 %
NT U ec,DP 5.45 ηmGT,DP 24.03 %
NDP 129690 pm ηglobal,DP 17.97 %
ˆ
Psol,DP 0.144 kWe/m2ˆ
Pel,DP 71.9 kWe/(kg·s)
Ad anced sys em
Pel,DP 8.96 kWeηs, ,DP 81.64 %
Adish (ddish) 51.5 m2(8.1 m) ηs,c,DP 76.97 %
A c (d c ) 171 cm2(14.8 cm) ηdish,DP 90.34 %
HT A ec 8757 m2η ec,DP 82.04 %
NT U ec,DP 8.58 ηmGT,DP 29.34 %
NDP 132540 pm ηglobal,DP 21.74 %
ˆ
Psol,DP 0.174 kWe/m2ˆ
Pel,DP 89.6 kWe/(kg·s)
Table 3: Main design speci ica ions o he base-case and ad anced sys ems o 800 W/m2
and he op imum c,DP .
5.2. Resul s o he annual simula ions
The o -design model shown in Sec ion 3.2 is used he e o calcula e he
sola -mGT pe o mance maps linking powe ou pu and e iciency o he
DNI a gi en ambien empe a u es. These maps a e hen u ilized o e al-
ua e he annual yield (p oduc ion o ene gy) o gi en annual dis ibu ions
o DNI and ambien empe a u e in a speci ied loca ion.
In o de o analyze he esul s o he o -design model, he ollowing h ee
addi ional pe o mance me ics a e in oduced:
•The mean annual con e sion e iciency (¯ηglobal, Eq. (7)) is he a io
om he ne annual elec ici y (Eel,ne ) o he a ailable sola ene gy
inpu (Esol) o e he yea . I mus be no ed ha he la e may di e
om he sola ene gy ac ually ha es ed by he sys em (Qsol) due o
pe iods when he sys em is no in ope a ion because o he e y high
o e y low DNI:DNI < DNIcu −in o DNI > DNIcu −o , Fig. 6.
•The capaci y ac o o he sys em ( capaci y, Eq. (8)) is he a io om
he annual yield (Eel,ne ) o he elec ic ene gy ha would be p oduced
i he sys em wo ked a he nominal ou pu (Pel,DP ) h oughou he
yea (8760 hou s).
•The dumped sola ene gy ac o dumped, Eq. (9), is he a io om he
sola ene gy ha is a ailable bu no ha es ed by he sys em (Esol −
Qsol) o he a ailable sola ene gy inpu (Esol). This me ic is used o
20
quan i y he ac ion o a ailable sola ene gy ha canno be ha es ed
because he sys em is al eady unning a ull o minimum capaci y.
¯ηglobal =Eel,ne
Qsol
(7)
capaci y =Eel,ne
Pel,DP ·8760 (8)
dumped = 1 −
Esol −Qsol
Esol
(9)
Figu e 10 shows he pe o mance maps ob ained o he base-case (g een)
and ad anced (blue) sys ems. The inabili y o abso b a e y high adia ion
becomes e iden in he uppe cha s and ansla es in o a d as ic d op in
e iciency (bo om cha s) due o a la ge ac ion o he a ailable sola ene gy
ha is dumped o by he sys em a high DNI.
Annual simula ions a e pe o med o h ee selec ed loca ions -Beijing
(China), Se ille (Spain) and San Diego (USA)- o which hou ly alues
o DNI and ambien empe a u e a e ob ained om he Sys em Ad iso y
Model so wa e [56]. This in o ma ion is shown in Fig. 11, whose le cha
shows he numbe o Sun hou s (ho izon al axis), peak DNI ( e ical axis)
and annual sola ene gy a ailable (a ea sub ended by he cu e). Simila
in o ma ion is shown o ambien empe a u e on he igh hand side o Fig.
11. Acco ding o he esul s shown in Table 4, he highes yield is ob ained
in San Diego whe e he base-case sys em achie es 15.87% annual con e sion
e iciency and 24.77% capaci y ac o , wi h jus 10.69% o he a ailable sola
ene gy being dumped o he sys em. Se ille shows simila pe o mance bu ,
in con as , he e iciency in Beijing is jus 11.13% and he capaci y ac o is
10.51%, mainly due o he high amoun o dumped sola ene gy (mo e han
37%). I mus be no ed ha he high dumped in his loca ion is no due o
equen o e lows o sola ene gy (DNI > DNIcu −o ) bu o long pe iods
o ime wi h DNI lowe han he cu -in alue (DNI < DNIcu −in). Finally,
when he ad anced sys ems a e conside ed, hese yield simila pe o mances
in e ms o dumped sola ene gy and capaci y ac o s whe eas he annual
e iciency is a ound 2.7-3.5 pe cen age poin s highe in all loca ions.
21

Figu e 10: Pe o mance maps o he base-case (le ) and ad anced ( igh ) sys ems: ne
powe ou pu s. DN I (abo e) and global (sola - o-elec ic) e iciency s. DN I (below)
Figu e 11: Du a ion cu es o hou ly DNI (le ) and ambien empe a u e ( igh ) o he
h ee selec ed loca ions in a Typical Me eo ological Yea (p o ided by SAM [56]).
22
Base-case sys em
Loca ions Beijing Se ille San Diego
DNIDP [W/m2] 800 800 800
Esol [kWh] 59494 88676 98304
Qsol [kWh] 37223 76273 87797
Eel,ne [kWh] 6622 13384 15605
¯ηglobal 11.13% 15.09% 15.87%
dumped 37.43% 13.99% 10.69%
capaci y 10.51% 21.24% 24.77%
Ad anced sys em
Loca ions Beijing Se ille San Diego
DNIDP [W/m2] 800 800 800
Esol [kWh] 61257 91304 101217
Qsol [kWh] 39424 79669 91087
Eel,ne [kWh] 8463 16938 19581
¯ηglobal 13.82% 18.55% 19.35%
dumped 35.64% 12.74% 10.01%
capaci y 10.78% 21.58% 24.95%
Table 4: Pe o mance o he base-case and ad anced sys ems designed o 800 W/m2in a
Typical Me eo ological Yea (TMY).
5.3. Sensi i i y analysis. Impac o design DNI
Sec ions 5.1 and 5.2 ha e shown ha la gely di e en pe o mances can
be ob ained when he same sys em is ope a ed unde dissimila bounda y
condi ions. Fo his eason, a sensi i i y analysis is now pe o med in o de
o assess o wha ex en he loca ion impac s he e e ence alue o DNI
ha is con enien o conside in he design p ocess; i.e., DNIDP ha yields
highes annual e iciency ¯ηglobal, Eq. (7). This me ic depends on he hou ly
dis ibu ion o DNI and on he pe o mance maps o he sys em.
The sensi i i y analysis is pe o med ollowing he p ocedu e shown in
Fig. 12. Mass low a e and u bine inle empe a u e a e se o hei a ed
alues (0.1 kg/s and 800/900 °C o he base-case/ad anced sys ems espec-
i ely) and he alue o DNI a he design poin (ex e nal loop) is changed
in he ange o in e es (400-1000 W/m2). This means ha he mic o u bine
design emains unal e ed wi h espec o he o iginal design o DNIDP =800
W/m2whe eas he sola subsys em (pa abolic dish and olume ic ecei e )
is e-sized acco ding o he new alue o DNIDP .
The calcula ions o each DNIDP a e based on non-dimensional pe o -
mance maps o he sys em, ob ained om hose shown in Sec ion 3.2 o
he e e ence case a 800 W/m2. These maps shown in Fig. 10 a e hen
dimensionalized again by me ely mul iplying he ho izon al scale by he co -
esponding alue o DNIDP . E en i he p ocedu e is no u e ly accu a e,
23
Figu e 12: P ocedu e o sea ch o he op imum DN IDP .
he e o incu ed does no b ing abou signi ican de ia ions in e ms o an-
nual sys em pe o mance inasmuch as he e iciency o he pa abolic dish is
a he independen om i s size wi hin easonable limi s (see Eqs. (A.15) o
(A.16)), while he e iciency o he ecei e is only sligh ly a ec ed by DNI
o gi en TIT and Tamb. Fo he sake o e i ica ion o his s a emen , he
pe o mance maps ob ained wi h he non-dimensional app oach and hose
buil using he comple e o -design p ocedu e in Sec ion 3.2 a e shown in
solid blue and do ed whi e lines in Fig. 13, con i ming ha he e is e y
good ag eemen in all cases.
The non-dimensional pe o mance maps o he base-case and ad anced
sys ems a e shown in Fig. 14 whe e he non-dimensional powe ou pu is
plo ed agains ela i e DNI o a ious ambien empe a u es. The esul -
ing a ia ions o ¯ηglobal, capaci y and dumped o he base case and ad anced
sys ems when hese pe o mance maps a e used a e illus a ed in Fig. 15.
The lowe op imal DNIDP is ound o Beijing (660 W/m2 o he base-case
sys em and 610 W/m2 o he ad anced sys em) whils he highes DNIDP,op
co esponds o San Diego (815 W/m2 o bo h sys ems), wi h Se ille laying
24
Figu e 13: Valida ion o he pe o mance maps used in he sea ch o he op imum DN IDP :
maps calcula ed wi h he comple e o -design p ocedu e (whi e do s) and non-dimensional
maps (blue line).
Figu e 14: Non-dimensional ou pu o he base-case ( op) and ad anced (bo om) sys ems
s. ela i e DN I o di e en ambien empe a u es.
25
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Appendix A. Design models
This Sec ion p esen s he equa ions and sol ing p ocedu es implemen ed
in each design module o he lowcha in Fig. 3.
Appendix A.1. The modynamic cycle
The modules calcula ing he design he modynamic cycle in Fig. 3 (“The -
modynamic cycle 1 and 2’’) a e based on he applica ion o mass and ene gy
conse a ion and componen e iciencies [57]. Thus, he ou le condi ions
om comp esso and expande a e calcula ed om he o al- o- o al p es-
su e a ios and he isen opic e iciencies whils he inle and ou le s a es
o he ecupe a o a e compu ed om a ixed e ec i eness and p essu e loss
ac o (ε eg,DP , p,cold,DP and p,ho ,DP in Table 1). Wi h his in o ma ion,
he model calcula es all he he modynamic s a es in Fig. 1 along wi h he
sha ou pu o a gi en mass low a e a comp esso inle ( ˙m1=0.1 kg/s).
The ne elec ic ou pu is hen calcula ed by me ely applying elec ic and
mechanical e iciencies.
37

Appendix A.2. Tu bomachine y
The design modules o comp esso and u bine p o ide he o al- o- o al
isen opic e iciencies and he o a ional speed o he sized s ages [58], based
on he one-dimensional app oaches p oposed by Aungie in [52] and [53].
In he main, his app oach assumes cons an low ield a iables ( eloci y,
empe a u e and p essu e) a each c oss-sec ion o he low passage (channel).
These a iables a e ob ained om s eady-s a e mass, ene gy and momen um
balance equa ions compu ed along he mean s eam su ace using empi ical
luid dynamics and o al p essu e loss co ela ions. A bounda y laye model
is applied o ake in o accoun he o al p essu e loss due o skin ic ion
be ween he luid and passage walls, wi h he esul ing a ia ion o Reynolds
numbe along he mean s eam su ace being used o e alua e he en opy
ise and, in u n, he isen opic e iciency.
The ma ching o comp esso and u bine is ini ia ed in he u bine as-
suming a e e ence speci ic speed ns, =0.55 on he based on ecommenda ions
by Rodge s [59] and Aungie [53], Eq. (A.1). Based on his alue, i is pos-
sible o calcula e he o a ional speed ha yields highes u bine e iciency
[60, 61]. This is hen used along wi h he spou ing eloci y c0,is ( eloci y
ob ained in a o al- o-s a ic isen opic expansion) o calcula e he angen ial
speed o he blade (u ip, ) and he co esponding o o diame e (d ip, ), Eq.
(A.2) as desc ibed by Aungie [53].
ωDP =ns,
∆h0.75
s,
√˙ ou
(A.1)
ν s, =u ip
c0,is
= 0.737 ·n0.2
s, (A.2)
The o a ional speed o he comp esso is he same as ha o he expande
and i can be used o calcula e he speci ic speed (ns,c) and diame e (ds,c)
o his machine, Eqs. (A.3,A.4). This in o ma ion is ob ained by in e po-
la ing he co esponding ns s. dscha o maximum comp esso e iciency
(Co die line, shown dashed ed in Fig. A.1) in he ange o applica ion
o adial u bomachine y: 50<ns,c<100 [62]. The speci ic diame e (ds,c) so
ob ained is used o calcula e he ip diame e o he impelle (d ip,c).
ns,c =ωDP
√˙ in
∆h0.75
s,c
(A.3)
38
Figu e A.1: Speci ic speed s. speci ic diame e diag am o a comp esso showing he
Co die line o adial s ages in dashed ed. Adap ed om [62].
ds,c = 2.865 ·n−0.946
s,c =d ip
∆h0.25
s,c
√˙ in
(A.4)
The sizing o he u bine is pe o med in he ollowing o de : o o , nozzle,
inle olu e and exhaus di use . Fo hese elemen s, a d a geome y is
p oduced om a se o de aul design speci ica ions in combina ion wi h
empi ical co ela ions based on he e e ence speci ic speed, as sugges ed by
Aungie [53]. These speci ica ions include he spou ing eloci y o he s age,
speci ic diame e o he o o , inle low angle, numbe , cho d and hickness
o he blades and inle - o-ou le adii a io o he nozzle. The main design
s eps applied o hese da a a e summa ized below, as desc ibed in [53] whe e
mo e de ails can be ound:
•The main geome ical pa ame e s o he o o a e calcula ed om ns,
and d ip, unde he assump ion ha inle eloci y is adial ( ela i e
o o inle angle is 90°):
–The me idional plane o he u bine is sized so as o minimize he
a ia ion o a ea be ween he inle and ou le sec ions unde he
cons an mass low a e es ic ion, Fig. A.2.
–The numbe , mean line geome y and hickness dis ibu ion o he
blades is calcula ed wi h empi ical co ela ions.
–The easibili y o he esul ing geome y is e i ied agains he
speci ic guidelines p oposed by Aungie [53].
39
•In o de o size he nozzle, he minimum numbe o blades needed o
yield adial ela i e low a he inle o he wheel and, a he same ime,
a blade loading lowe han 1 is calcula ed.
•An ellip ical con igu a ion is conside ed o he olu e, whe e he a i-
a ion o c oss sec ional a ea comes de e mined by mass conse a ion,
a cons an size pa ame e SP=1 and angula momen um conse a ion
a nozzle inle .
SP =√˙ ou
∆h0.25
s
= 1 (A.5)
•The design o he exhaus di use is ob ained om empi ical co ela-
ions on he assump ions ha he a io be ween ou le and inle a eas
is equal o 1.5 and ha he di e gence angle is 11°.
The a o edesc ibed p ocedu e gene a es a d a geome y o he ac ual
design poin , yielding a ce ain mass low a e and o al- o- o al expansion
a io. These alues a e hen used o co ec he design un il he a ge
alues a e a ained. Once he inal design is ob ained, he co esponding
pe o mance map is p oduced by me ely calcula ing he pe o mance o he
expande o di e en se s o bounda y condi ions, including he speci ic con-
di ions o which sec ions o he machine ge choked.
The comp esso design p ocess does no s a om a se o speci ica ions
bu i is ca ied ou di ec ly by means o he empi ical pe o mance model
p oposed by Aungie [52]. In his, guessed alues o he o al- o- o al isen-
opic e iciency and o al p essu e loss coe icien ( om o o inle o olu e
ou le ) a e ini ially assumed and he geome y o each componen o he
comp esso is e alua ed as ollows:
•The impelle inle sec ion is sized in o de o minimize he ela i e
Mach numbe a he sh oud, whils he ou le diame e is in luenced
by he blade exi angle as a esul o a ade-o be ween s age wo k
and dis o ion, and slip ac o s o each d ip,c; his is shown in Eqs.
(A.3,A.4) and in Fig. A.2. The numbe o blades esul s om he
minimum alue yielding a blade loading lowe han 0.9.
•The di use can be o he aned o aneless ype. In he o me case,
he numbe o anes, he a ea a io and he di e gence angle esul
om an op imiza ion p ocess o yield maximum e iciency wi h a o al
load lowe han 0.3.
40
Figu e A.2: Me idional low passage o he comp esso impelle (le ) and u bine wheel
( igh ) o he base-case (abo e) and ad anced (below) sys ems.
•The ou le adius o he olu e is calcula ed i e a i ely by ixing a
size pa ame e o 1.05. The adius dis ibu ion is hen ob ained om
con inui y by keeping he size pa ame e cons an .
To p ope ly ake in o accoun he s ong in luence o he clea ance gap
be ween o o and sh oud (casing) [63, 64] he ollowing de ini ion is used:
δcl =δcl, e ·bblade
bblade, e 0.6
,(A.6)
whe e he e e ence blade heigh is bblade, e = 5 mm and he e e ence gap
δcl, e is 0.4 mm and 0.3 mm o u bines and comp esso s, espec i ely.
Finally, he e ec o oughness is accoun ed o wi h a simple skin ic ion
model based on bounda y laye analysis in which a peak- o- alley oughness
o 1 µm is assumed [65].
The pe o mance maps o comp esso and u bine o he base-case and
ad anced sys ems a e shown in Fig. A.4. These maps show o al- o- o al
isen opic en halpy change and isen opic e iciency e sus mass low a e o
sha speeds anging om 70% o 115% o he design poin alue.
41
Figu e B.1: Elec ic e iciency o gene a o s. sha wo k and o a ional speed (le ) and
maximum sha powe s. o a ional speed ( igh ). Scales a e non-dimensional.
han ups eam. The a ia ions o he global hea ans e coe icien wi h he
mass low a e a e e alua ed using Eq. (B.7).
U=UDP ·˙m
˙mDP 0.8
(B.7)
The p essu e losses o ecupe a o , sola ecei e and inle /ou le duc s
a e a ied acco ding o Eq. (B.8).
∆p= ∆pDP ·˙m
˙mDP 1.21
·
ρDP
ρ(B.8)
48