applied
sciences

Article
Improved Solar Operation Control for a Solar Cooling
System of an IT Center
Jan Albers
Institut für Energietechnik, T echnische Universität Berlin, Marchstraße 18, 10587 Berl in, Germany;
[email protected] ; T el.: + 49-30-314-25-314
Received: 7 April 2020; Accepted: 10 May 2020; Published: 12 May 2020
       
  

Abstract:
In this contribution, a model pr edictive contr ol algorithm is developed, which allows
an incr ease of the solar operating hours of a solar cooling system without a negative impact on
the auxiliary electricity demand, e.g., for heat r ejection in a dry cooler . An impr oved method of
the characteristic equations for single-e ff ect
H 2 O / LiBr
absorption chillers is used in combination
with a simple dry-cooler model to describe the part load behavior of both components. The aim of
the contr ol strategy is to find a cut-in and a cut-o ff condition for the solar heat operation (SHO) of
an absorption chiller cooling assembly (i.e., including all the supply pumps and the dry cooler) under
the constraint that the specific electricity demand during SHO is lower than the electricity demand
of a r efer ence cooling technology (e.g., a compression chiller cooling assembly). Especially for the
cut-in condition, the model predictive contr ol algorithm calculates a minimum driving temperature,
which has to be r eached by the solar collector and storage in order to cover the cooling load with
a low cooling water temperatur e but restricted auxiliary electricity demand. Measurements at a solar
cooling system for an IT center wer e used for the testing and a first evaluation of the control algorithm.
Keywords:
solar fraction; minimum driving temperatur e; model predictive contr ol; absorption
chiller; dry cooler; characteristic equation method
1. Introduction
W orldwide, an increase of the cooling demand is expected. In the building sector , the cooling
demand is the most rapidly increasing e ff ective ener gy demand [
1
]. Usually , the cold generation is
r ealized by electrically driven compr ession chillers. Hence, the expected development in e ff ective
ener gy demand will lead to an increased power r equirement as well. Acting on the assumptions
of the W orld Energy Outlook [
2
], the global power r equir ements will incr ease by 60% between
2016 and 2040. Approximately 15% to 20% of this elevation will be caused by the cooling demand.
Consequently , solar -assisted cooling systems (SAC systems) have a large potential to r educe the fossil
fuel consumption r elated to non-regenerative power generation.
On the other hand, it has been shown (e.g., in [
3
]) that a minimum solar fraction is necessary
for SAC systems in or der to achieve a lower primary energy consumption than a conventional
system using an electrically driven compr ession chiller . Henning et al. [
3
] illustrated that the system
performance with r egard to primary ener gy savings is improved when the COP of the thermally driven
chiller incr eases, the solar fraction increases, and the specific electricity consumption of the auxiliary
components like supply pumps and cooling tower etc. decr eases.
For SAC systems with parallel backup heating, the achievable solar fraction is a question of the
possible operating time with solar heat fr om the collector . Solar heat operation (SHO) can start earliest
when the collector temperatur e is higher than a minimum driving temperature
t min
Di
and has to end
latest when the collector temperatur e dr ops below . Of course, additional temperatur e di ff erences
have to be taken into account (e.g., for a heat exchanger between the collector and storage, heat losses
Appl. Sci. 2020 , 10 , 3354; doi:10.3390 / app10103354 www .mdpi.com / journal / applsci

Appl. Sci. 2020 , 10 , 3354 2 of 17
etc.). The minimum driving temperatur e
t min
Di
depends on the cooling load as well as the capacity and
part load behaviour of the chiller . Moreover , it depends on the possible cooling water temperatur e,
which is limited by the dry or wet bulb temperature. Generally speaking,
t min
Di
depends on the load
and meteor ological conditions as well as the technology used for the chiller and the reject heat device
but not on the collector technology . Nevertheless, the collector technology (including storages and
the connection to parallel or serial backup heating systems) has a large influence on the necessary
pr eheating time (i.e., the period from sunrise until
t min
Di
is r eached and solar heat operation can start)
and ther eby influences the overall system performance [ 4 ].
T aking the heat capacity e ff ects of the collector and installation, as well as heat losses to the
surr ounding into account, Izquier do [
5
] determined a solar radiation threshold
I min
as an equivalent
measur e to the minimum driving temperature. For a small SAC system in Madrid, two di ff erent heat
r ejection technologies were compar ed for the same meteorological conditions. In comparison to a wet
cooling tower , a dry cooler r evealed approximately 12 K higher cooling water temperatur es. This led
to about 20 K higher driving temperatur es in the collector circuit and r educed the possible operating
time of the SAC system fr om 9 to 3 h. The preheating time incr eased from appr oximately 3 to 6 h.
The influence of heat capacity e ff ects on the preheating time was investigated by Li [
6
] and
Kohlenbach [
7
] as well. While Li used a separated smaller part of a partitioned hot water storage tank
to r educe the preheating time, Kohlenbach applied di ff er ent temperature nodes of the storage tank for
the contr ol of the chiller before, during, and after solar heat operation. In both refer ences, a constant
(i.e., load and weather independent) start-up temperatur e of t min
Di = 75 and 60 ◦ C was used.
In or der to shorten the preheating time, which is necessary to achieve a desired solar collector outlet
temperatur e and thereby enable a longer solar operation of a single-e ff ect
H 2 O / LiBr
absorption chiller ,
Shirazi et al. [
8
] r ecommend a variable speed pump for the solar collector loop. A comparison of the
simulation r esults to a constant flow strategy showed that the solar fraction can be increased by about
11% by the temperatur e contr ol strategy . Shirazi et al. [
8
] concluded that the longer solar operating time
of the chiller (which r esults fr om the higher collector temperatur e) is more important for achieving
a high solar fraction than the r educed collector e ffi ciency due to a higher collector temperature.
Comparably , Qu et al. [
9
] investigated a constant flow rate versus constant outlet temperatur e
contr ol by transient simulations of an SAC system with parabolic trough collectors and a double-e ff ect
H 2 O / LiBr
absorption chiller . They also indicated that the constant temperature contr ol reduces the
pr eheating time in the morning by appr oximately one hour and extends the operating time of the
chiller driven by solar ener gy by approximately half an hour in the afternoon.
T o make low collector temperatures applicable, Clauß et al. [
10
] described a contr ol strategy
similar to the one mentioned in [
11
] but without the constraint of an overflowing evaporator . Clauß et
al. [
10
] used a contr ol strategy based on the characteristic equation method that determines the requir ed
cooling water temperatur e for a pr edetermined driving temperatur e (e.g., from the solar collector
field) in or der to match a certain cooling load and to maintain the chilled water set value. In addition,
using the cooling water temperatur e as the manipulated variable o ff ers the possibility to save electric
power and also water —if a wet cooling tower is used—provided the available driving temperatur e
fr om the collector is higher than necessary to cover the load. In this case, a higher cooling water
temperatur e can be used, which reduces the electricity demand of the r eject heat device.
Unfortunately , the characteristic equation applied by Clauß et al. [
10
] is valid only for the 10-kW
absorption chiller under investigation (i.e., type sun inverse ). Furthermore, the external supply flow rates
in hot, cooling, and chilled water circuit must agr ee with the nominal flow rates, because otherwise the
slope and loss parameter in the characteristic equation would change. Mor eover , Clauß et al. [
10
] did
not r eport on the reverse applicability of the characteristic equation method, i.e., calculating a necessary
driving temperatur e from a given cooling water temperatur e in order to keep the pr eheating time short.
In this contribution, a model predictive contr ol algorithm is developed, which allows an incr ease of
the solar operating hours of an SAC system by calculating the minimum possible driving temperatur e
under the constraint of a maximum allowed auxiliary electricity demand to ensure a short pr eheating

Appl. Sci. 2020 , 10 , 3354 3 of 17
time. This new strategy utilizes an improved and mor e precise method of characteristic equations [
12
].
The computer code of the method is available in [
13
]. The same characteristic equation method is used
to contr ol the absorption chiller itself, irrespective of whether it is operated in a solar or conventional
cooling system [
14
]. Since the chiller contr ol is based on characteristic equations, it is called a CE
contr oller . Nevertheless, the focus of this contribution is not on the absorption chiller control (which
is done by the CE controller and is described, e.g., in [
14
,
15
]), but on the control of the switchover
between solar and backup heat operation of the chiller in a solar cooling system. Hence, following
a short description of the SAC system at the Federal Envir onment Agency in Dessau, Germany (which
was used to test the switchover strategy), the impr oved characteristic equation method is explained
only briefly . Afterwards, the model pr edictive control algorithm for the switchover strategy is derived.
It combines the absorption chiller model with a simple dry-cooler model. Finally , the measur ed results
of the strategy ar e shown and discussed.
2. Materials and Methods
2.1. Solar Assisted Cooling System
In Figur e 1 , a simplified pr ocess and instrumentation diagram of the SAC system at the Federal
Envir onment Agency (UBA) in Dessau, Germany with five heating circuits and four cooling cir cuits,
each combined into one symbol, is depicted. The cold demand is dominated by the cooling circuit
of the IT center with an average cooling load of approximately 20–25 kW ar ound the clock. During
summertime, the absorption chiller is power ed either by district heat from a central CHP plant or by
solar heat fr om a field of vacuum heat pipe collectors (216 m
2
absorber ar ea, 3
×
7.5 m
3
storage volume).
The idea of the r elatively lar ge storage volume and collector field with respect to the cooling load is to
accumulate solar heat during daytime in or der to cover the cooling load by solar heat operation of the
absorption chiller during nighttime as well. The design values of the absorption chiller ar e provided in
T able 1 .
Appl. Sci. 2020 , 10 , x FO R P EER R E VIEW 3 of 17
tempera t ure under the constra i nt of a ma ximum a l l o wed a u xi li a r y elect r icit y demand t o e n sure a
short preheati ng ti me. T h i s new strategy util iz es an improve d and more precise met h od of
char act e rist ic e q u a t i ons [ 1 2 ] . The com p ut er code o f t h e m e t h od i s av ai lab l e in [1 3] . The s a m e
cha r a c teri st i c eq ua ti on met h od i s used to control th e absorption ch iller itself, irr e spective of whether
it i s oper at ed in a so l a r o r convent i on al cool ing sy st em [ 1 4]. Sinc e t h e ch il ler cont rol is bas e d on
char act e rist ic equ a t i on s, it i s cal l ed a CE cont roller . Ne vert heless , t h e focus o f t h is cont ribut i on is not
on t h e ab sorp t i on chi lle r co nt rol (wh i ch i s done by t h e CE cont roll er and is desc rib e d, e . g. , in [1 4 , 1 5 ] ) ,
but on the co ntrol of the switchover between so lar an d back up he a t operat ion of t h e chi lle r in a so l a r
cooling syste m . Hence, following a shor t descriptio n of the SAC sy stem at the Federal Envir o nment
Agency in Dess au, G e rm any (wh i ch was u s ed t o test the switchover strategy), the im proved
char act e rist ic eq uat i on me t h od is exp l a i ned only brie fly . A f t e rwa r ds, t h e mod e l pred ict i ve c o nt rol
a l gori thm f o r the swi t chover stra tegy is deri ved. It combi n es the a b sorpti on chi l l er model wi th a
simple dry-cooler model. Finally, the me as ured res u lt s of the str a tegy are shown and discus se d.
2. Ma t e ri als a nd M e th ods
2.1. Solar Assi sted Cooling Syste m
In Figu re 1, a simplified pr ocess and in strument ation diagr a m of th e SAC system at the Feder a l
Envi ronment A g ency (U BA) i n Des s au , Germa n y wi th f i v e heat ing cir c u i t s and f o ur c ool ing ci rcuit s ,
each combine d into one sy mbol, is depi cted. The col d dem a nd i s dominated b y the cool ing circu i t o f
t h e IT cent er wit h an av e r age coo ling load o f ap p r oxim at el y 2 0 – 2 5 kW arou nd t h e c l ock . Dur i ng
summert ime, t h e absorpt i o n chil ler is po wered e i t h er b y dist r i ct he at from a cent ral C H P p l ant or b y
sol a r he at fro m a fi eld o f v a cu um heat p i p e collect ors ( 2 1 6 m 2 a b sorb er are a , 3 × 7. 5 m 3 stora g e
volume) . The ide a o f t h e rel a t i vel y la rge s t orage volum e an d co llect o r f i el d w i t h re spect t o t h e c oolin g
load is t o acc u mul a t e so la r heat dur i ng dayt ime in order t o cover t h e cooling load by so l a r heat
opera t i o n of the a b sorpti on chi l l er during ni ghtti me a s well . The desi gn v a lues of the a b sorpti on
chil ler are pr ovided in T a ble 1 .

Figure 1. S i m p lified proces s and instru m e ntation diag ram of the SA C sy stem at t h e F e deral
Environm ental Ag ency ( U BA) in D e ssau , G e r m any . On l y t h e tempe r at ure probes and flow mete rs t h a t
are used in the result se ction a r e label l ed .

Figure 1.
Simplified process and instr umentation diagram of the SAC system at the Federal
Environmental Agency (UBA) in Dessau, Germany . Only the temperature pr obes and flow meters that
are used in the r esult section are labelled.

Appl. Sci. 2020 , 10 , 3354 4 of 17
T able 1.
Design values of the absorption chiller type FM050V0.3 at the Federal Environment Agency
(UBA) in Dessau, Germany .
V ariable Description Unit FM050V0.3
t Di Hot water inlet temperature ◦ C 75
V D Hot water volume flow rate m 3 / h 6.0
Q D Driving heat flow kW 44
t Ai Cooling water inlet temperature ◦ C 28
V H Cooling water volume flow rate m 3 / h 18.0
Q H Reject heat flow kW 78
t Eo Chilled water outlet temperature ◦ C 9
V E Chilled water volume flow rate m 3 / h 5.9
Q E Cooling capacity kW 34
COP Coe ffi cient of performance - 0.77
A compr ession-type chiller is used for the peak load and as redundancy for the IT center . During
wintertime, solar heat is used for space heating and the reject heat device (RHD) is used dir ectly for the
cold supply . In this case, neither the compr ession-type chiller nor the absorption chiller is running.
Nominal values of the reject heat device in dry-cooler mode ar e provided in T able 2 . A more detailed
description of the seasonal solar cooling concept can be found in [ 16 ].
T able 2.
Nominal values of the reject heat device in dry-cooler mode at the Federal Envir onment
Agency (UBA) in Dessau, Germany .
V ariable Description Unit Dry-Cooler
t Ki,0 Fluid inlet temperature ◦ C 32
t Ko,0 Fluid outlet temperature ◦ C 29
V K,0 Fluid volume flow rate m 3 / h 45.5
x Mass fraction ethylene-glycol kg / kg 0
t Li,0 Air inlet temperature ◦ C 21
V L,0 Air volume flow rate m 3 / h 45,940
Q L,0 Reject heat flow kW 158
P el,DC,0 Electrical power kW el 13.7
2.2. Operating Period with High Solar Fraction
During summertime, two operating modes ar e possible for the absorption chiller:
• Solar heat operation (SHO); and
• Backup heat operation (BHO).
Independent of BHO or SHO, the thermally driven absorption chiller (TDC) is contr olled by
a model pr edictive contr oller based on an impr oved method of characteristic equations (the so-called
CE contr oller). The CE controller calculates simultaneously the set values in hot and cooling water
(i.e.,
t set
Di
and
t set
Ai
), which ar e necessary to cover the cooling load
Q set
E = V E · ρ E · c p,E ·  t Ei − t set
Eo 
. The CE
contr oller is explained in more detail in [ 15 ] and in the next section.
In summer 2017, several tests were executed in or der to extend the duration of SHO and thereby
incr ease the solar fraction and primary ener gy saving of the SAC system. One of these test periods is
depicted in Figur e 2 , where the cut-in condition for SHO was left unchanged but the cut-o ff condition
was blocked manually in or der to maximize the solar fraction.

Appl. Sci. 2020 , 10 , 3354 5 of 17
Appl. Sci. 2020 , 10 , x FO R P EER R E VIEW 5 of 17

Figure 2. Continuous solar heat operation extending over more than three days during a test period
(i.e ., w i thout the improved control strategy): ( a ) global horizont al irradiation, q  , temperatures in
the hot water circuit, an d control signals fro m RHD; ( b ) flo w rates and co oling capac i ty ; ( c ) ambient
air tem p eratu r e and tem p eratu r es in the ch ille d and co oli n g water circu i t; ( d ) specifi c electri c ity
dem a nd.
SHO started on the f i rst da y when t  > t 
 an d the differe n ce Δt 
,    = t  
 –t   wa s
sm al ler t h an 3 K for at le as t 5 m i n , whic h was t r ue at ap p r oxim at el y 1 0 : 3 0 (c f. Fi gure 1 for t h e senso r
position and Fig u re 3 for t h eir chrono lo gic a l pro g ressi on). At f i rst g l ance , t h is co ndit ion looks st range
be c a us e the stor a g e te mpe r a t u r e wa s l o we r tha n the necessary dri v i n g tempera t ure t 
 =t 
 to
cover t h e coo ling lo ad ( i .e ., t h e st or age was st il l not hot enough) . However, the tempera t ure t   ≈
t  available for the chiller is a mixtur e o f t  and t   (c f. Figure 1). Hen c e, the exist i ng cut-in
condition for SHO mentio ned above (i.e., witho u t th e switchover strategy explaine d later o n ) is a
compromise of t  >t 
 , wh ich wa s t r u e at 1 0 : 0 0 a.m . , and t   >t 
 , w h ich w a s t r u e at 11 :5 0 a.m . .
When the cut- i n condi t i o n beca me true, the f l a p ne ar the solar heat stor age s was opened by the
control sign al C  an d t h e f l ap s ne ar t o t h e d i st r i ct heat ing he at exch anger C  were clo s ed.
Afterw ards , t h e discharge pump P 3 5 was sw itched on and the me asured discharg e flow r a te V 󰇗  >0
was used t o supply t h e a b sorpt i on chi ller w i t h sol a r heat . The o t her curves i n Fig u re 3 w ill be
explained later.
0
2 0
4 0
6 0
8 0
100
C / % ; t / °C
q / ( 10· W / m
2
)
C
DC
C
Hu
t
PS 1 1
q
gh
t
Ho
t
Di
t
S HO, o n
0
10
20
30
V / ( m³/ h )
Q / kW
V
D
Q
E
V
PS
V
H
5
15
25
35
t / ° C
t
am b
t
1A i
t
0Eo
t
set
0Eo
t
set
1A i
00: 00 00: 00 00: 00 00: 00 00: 0 0 00: 00
0. 0
0. 5
1. 0
T i me o f d ay s t arti ng at M ay 31, 2017
w / ( kW
el
/k W
0
)
w
ACCA
w
CCCA
≈
0, 24 kW
el
/kW
0
.
.
.
.
.
.
.
. .
( a )
( b )
( c )
( d )

Figure 2.
Continuous solar heat operation extending over more than thr ee days during a test period
(i.e., without the improved control strategy): (
a
) global horizontal irradiation,
q gh
, temperatures in the
hot water circuit, and contr ol signals from RHD; (
b
) flow rates and cooling capacity; (
c
) ambient air
temperature and temperatur es in the chilled and cooling water circuit; (
d
) specific electricity demand.
SHO started on the first day when
t Ho > t set
Di
and the di ff er ence
∆ t on,SHO
S = t set
2Di − t PS11
was smaller
than 3 K for at least 5 min, which was true at appr oximately 10:30 (cf. Figure 1 for the sensor position
and Figur e 3 for their chr onological progr ession). At first glance, this condition looks strange because
the storage temperatur e was lower than the necessary driving temperatur e
t min
Di = t set
Di
to cover the
cooling load (i.e., the storage was still not hot enough). However , the temperature
t PSo ≈ t Di
available
for the chiller is a mixture of
t Ho
and
t PS11
(cf. Figure 1 ). Hence, the existing cut-in condition for SHO
mentioned above (i.e., without the switchover strategy explained later on) is a compromise of
t Ho > t set
Di
,
which was true at 10:00 a.m., and
t PS11 > t set
Di
, which was true at 11:50 a.m. When the cut-in condition
became true, the flap near the solar heat storages was opened by the contr ol signal
C PS
and the flaps
near to the district heating heat exchanger
C DH
wer e closed. Afterwar ds, the discharge pump P35 was
switched on and the measur ed dischar ge flow rate
V PS >
0 was used to supply the absorption chiller
with solar heat. The other curves in Figure 3 will be explained later .

Appl. Sci. 2020 , 10 , 3354 6 of 17
Appl. Sci. 2020 , 10 , x FO R P EER R E VIEW 6 of 17

Figure 3. Start- up period of so lar heat operati o n (SHO) w i th out the improv ed control strategy.
The examine d solar he at operation per i od wa s ongo ing over mor e than three day s (c f. V 󰇗  in
Fig u re 2b). D e spit e t h e vol a t ile so lar irr a di at io n and t h e resu lt ing volat i le dr ivi n g t e mperat u r e t 
for t h e ch il ler , it w a s poss i b le t o co ntrol the evapor at or outlet temperature t  wit h a deviation to
the set val u e t 
 of le ss t h an ±0 .5 K (cf. F i g u re 2c) b y m e ans o f t h e C E cont roller .
Al though the fl ow ra tes of the a b sorption chil l e r were not automa ti ca ll y controlled , the y w e re
not constant (cf. Figure 2b ). The variation of V 󰇗  is an un wanted effect of hydr aulic interdepende ncies
between the di scha rge pump, hea t i n g ci rcui ts, a n d a b sorption ch iller. There f o r e, flow r a tes higher
tha n the design va lue occurred. In contra st, the cooli n g wa ter fl ow ra te V 󰇗  was adju sted man u ally
( o n the thi r d day i n order to a v oi d the hum i di f i er a c t i va ti on, whi c h wa s not successf u l , a n d
aft e rw ard s t o cov e r t h e loa d and keep t h e sol a r heat o p erat ion on g o ing) .
During no rmal operation (i.e., o u tside th e test peri od for the high so lar fraction), SHO is stopped
when t  <t 
 and the difference Δt 
 ,   =t  
 –t   > 0 K becomes true. Since thi s cut-off
condi t i o n was dea c ti va ted duri ng the test peri od, the desorber i n l e t tempera t ure t  var i ed bet w een
ap p r oxim at el y 8 5 and 50 ° C and t h e coo ling wat e r inl e t t e m p erat ur e t o t h e ab sor b er t  between 36
and 18 °C, r e spectively. To achieve these low cooling wa ter tempera t ures i n the reject hea t dev i ce, the
t e chnica l pos s ibi lit y t o pr e-cool t h e in coming am bient a i r by spra yi ng wa ter i n to the a i r f l ow
(ad i ab at ic ev ap orat iv e p r e - cool ing) w a s al lowed, a l t h ough t h is ope r at ion mode i s norma lly b l ocked
due t o hi gh op erat ing cos t s an d h ygi e n ic asp e ct s . By means of t w o short operating period s o f the
humid i fier o n the th ird d a y (c f. control sign al C  of the hum i d i fier in F i gure 2a), a term inat ion of
SHO co uld b e avo i ded.
However, in dependent of t h e ad iab a t i c pre-cool ing possibi lit y , hi gh a i r flow ra t e s in t h e r e je ct
heat device w e re nece ssary when the stor age temper at ures were st il l low (e.g ., in t h e morning ) a n d/ or
am b i ent air t e m p erat ure was h i gh (c f. cont rol s i gn al C  for the ven t ilators in F i g u re 2a). Thus, the
specif ic elect r icit y dem a n d 𝑤 󰇗 of t h e sol a r t h erm a l l y driven absor p t i on chil ler cooling asse mbly
(ACCA) inc l udin g t h e e l e c t ricit y d e ma nd of t h e t h e rmal l y drive n chil ler (TD C ), t h e suppl y pumps
(Pu ) and rejec t heat dev i ce (R HD):
𝑤 󰇗  = P ,  
Q 󰇗  = P , +P , +P , +P , 

Q 󰇗  (1 )
became high e r than the specific electr icit y demand 𝑤 󰇗  o f an e l ectric ally driven com p ression
chiller cooling assembly (CCCA) also including the chiller itself , supply pump s, a n d the reject hea t
device. In this case , no primary ener gy savin g wa s p o ssib l e an ym ore and t h e s o lar he at op e r at ion
should have been stopped. In Fig u re 2d , the instantan e ous me as ure d values o f 𝑤 󰇗  duri ng the test
p e riod ar e c o m p ared t o an av er age d m e as ured v a lue 𝑤 󰇗  of the air-coo l ed co mpression -ty p e
chil ler (which was not in operat ion dur i n g t h e t e st period) . Duri ng t h e fi rst two nights, the continuous
sol a r heat o p erat ion wit h low dr ivi n g t e mper at ures and co nseq uent ly l o w cool ing wat e r
temperatures led to v a lue s o f 𝑤 󰇗   t h at ar e lower t h an 𝑤 󰇗  . Due t o an i n creas i ng am b i ent a i r
tempera t ure, thi s does not a ppl y f o r the whol e t h ir d day . Conse q uent ly, t o av oid va lu es 𝑤 󰇗  >
09: 00 10 : 00 11 : 00 12 : 00 13: 00 14: 00
45
50
55
60
65
70
75
80
85
T i m e of day on Ma y 31, 2017
V / (m³/h) ; t / °C
t
PS11
t
Ho
t
Di
t
set
Di
t
on , SH O
t
PSo
V
PS
+4 5
SHO
on
·1 +4 5
t
mi n, S HO
Di
. .

Figure 3. Start-up period of solar heat operation (SHO) without the improved contr ol strategy .
The examined solar heat operation period was ongoing over mor e than thr ee days (cf.
V PS
in
Figur e 2 b). Despite the volatile solar irradiation and the resulting volatile driving temperatur e
t Di
for
the chiller , it was possible to contr ol the evaporator outlet temperature
t Eo
with a deviation to the set
value t set
Eo of less than ± 0.5 K (cf. Figure 2 c) by means of the CE contr oller .
Although the flow rates of the absorption chiller were not automatically contr olled, they wer e not
constant (cf. Figure 2 b). The variation of
V D
is an unwanted e ff ect of hydraulic inter dependencies
between the dischar ge pump, heating circuits, and absorption chiller . Ther efore, flow rates higher
than the design value occurr ed. In contrast, the cooling water flow rate
V H
was adjusted manually (on
the thir d day in order to avoid the humidifier activation, which was not successful, and afterwar ds to
cover the load and keep the solar heat operation ongoing).
During normal operation (i.e., outside the test period for the high solar fraction), SHO is stopped
when
t Ho < t set
Di
and the di ff er ence
∆ t o ff ,SHO
S = t set
2Di − t PS11 >
0 K becomes true. Since this cut-o ff
condition was deactivated during the test period, the desorber inlet temperatur e
t Di
varied between
appr oximately 85 and 50
◦
C and the cooling water inlet temperatur e to the absorber
t Ai
between 36
and 18
◦
C, r espectively . T o achieve these low cooling water temperatures in the r eject heat device,
the technical possibility to pr e-cool the incoming ambient air by spraying water into the air flow
(adiabatic evaporative pr e-cooling) was allowed, although this operation mode is normally blocked
due to high operating costs and hygienic aspects. By means of two short operating periods of the
humidifier on the thir d day (cf. control signal
C Hu
of the humidifier in Figur e 2 a), a termination of
SHO could be avoided.
However , independent of the adiabatic pre-cooling possibility , high air flow rates in the reject
heat device wer e necessary when the storage temperatur es wer e still low (e.g., in the morning) and / or
ambient air temperatur e was high (cf. contr ol signal
C DC
for the ventilators in Figur e 2 a). Thus,
the specific electricity demand
w
of the solar thermally driven absorption chiller cooling assembly
(ACCA) including the electricity demand of the thermally driven chiller (TDC), the supply pumps (Pu)
and r eject heat device (RHD):
w ACCA = P el,ACCA
Q E
= P el,TDC + P el,Pu + P el,RHD + P aux
el,RHD
Q E
(1)
became higher than the specific electricity demand
w CCCA
of an electrically driven compr ession chiller
cooling assembly (CCCA) also including the chiller itself, supply pumps, and the reject heat device.
In this case, no primary ener gy saving was possible anymore and the solar heat operation should have
been stopped. In Figure 2 d, the instantaneous measur ed values of
w ACCA
during the test period ar e
compar ed to an averaged measured value
w CCCA
of the air -cooled compr ession-type chiller (which
was not in operation during the test period). During the first two nights, the continuous solar heat
operation with low driving temperatur es and consequently low cooling water temperatures led to

Appl. Sci. 2020 , 10 , 3354 7 of 17
values of
w ACCA
that ar e lower than
w CCCA
. Due to an increasing ambient air temperatur e, this does
not apply for the whole thir d day . Consequently , to avoid values
w ACCA > w CCCA
, an improved
cut-o ff condition for SHO must take the specific electricity demand of the conventional or refer ence
cooling assembly into account (in addition to the available solar driving temperatur e in the storage
t PS11
and the minimum driving temperatur e
t min
Di = t set
Di
, which is necessary to cover the load under
given weather conditions).
The ongoing of SHO on the fourth day , with low solar irradiation but relatively high ambient
air temperatur e, was used to define the boundary . During the whole day , the storage temperature
did not incr ease above 50
◦
C. Ther efore, a tr emendous e ff ort of electricity and water was necessary to
r each cooling water temperatur es lower than 20
◦
C in or der to cover the load. However , for all this,
the possible cooling capacity was lower than the demand. Thus, in the evening, the evaporator outlet
temperatur e did not match the set value anymore (cf. Figure 2 c). At midnight of the fifth day , the solar
heat operation (SHO) was stopped manually and the chiller was operated by district heating (BHO).
2.3. CE Method and CE Controller
The contr ol strategy described in Section 3.2 to start the solar heat operation (SHO) of an SAC
system as early as possible and to operate it in SHO mode as long as possible under the constraint of
a maximum electricity demand
w ACCA < w CCCA
necessitates a calculation pr ocedure for the part load
behavior of an absorption chiller . For this purpose, the characteristic equation method was applied.
In contrast to the characteristic equation method used by Clauß et al. [
10
], the method in this
contribution is general for
H 2 O / LiBr
single-e ff ect chillers [
12
]. By means of a r evised heat transfer
calculation in the absorber and desorber as compared to the established method (cf. [
17
]), the variation
of thermodynamic losses under part load conditions can be accounted for in an explicit calculation
pr ocedure. Accor ding to the improved method, the cooling capacity
Q E
of an absorption chiller is
a linear function of a characteristic temperatur e di ff erence ∆ ∆ t ∗
i :
∆ ∆ t ∗
i = t Di · ( 1 − K 1 ) − t Ai · ( 1 − K 2 ) + t Ei · ( 1 − K 3 ) , (2)
Q E = K 4 · ∆ ∆ t ∗
i , (3)
Q D = K 5 · ∆ ∆ t ∗
i + K 6 · ∆ ∆ t ∗
min,i , (4)
∆ ∆ t ∗
min,i = K 1 · t Di − K 2 · t Ai + t Ei · ( K 3 − 1 ) . (5)
The characteristic temperatur e di ff erence
∆ ∆ t ∗
i
combines the inlet temperatur es
t Xi
(wher e
X = D
,
E
,
C
,
A
holds for the main heat exchangers, desorber , evaporator , condenser , and absorber).
The coe ffi cients
K 1
to
K 3
in Equation (2) account for the phase equilibrium data of the respective
working pair (i.e.,
H 2 O / LiBr
) in combination with the external and internal heat capacity flow rates
W X
and heat transfer capabilities
Y X = U X · A X
. Hence, the characteristic temperature di ff er ence
∆ ∆ t ∗
i
also includes all the information of the load-dependent and load-independent losses. The capacity of
the chiller (i.e., its ‘thermal size’) is described by slope parameters
K 4
and
K 5
, r espectively . Finally ,
the coe ffi cient
K 6
scales the minimum driving heat
Q D,min = K 6 · ∆ ∆ t ∗
min,i
, which results mainly fr om
the limited internal heat r ecovery in the solution heat exchanger . The minimum driving heat
Q D,min
is
also not constant. It can be calculated with a second characteristic temperature di ff er ence
∆ ∆ t ∗
min,i
,
which is also a function of the independent external inlet temperatur es
t Xi
and coe ffi cients
K 1
to
K 3
[
12
].
The determining equations for all coe ffi cients
K N
with
N =
1
. . .
6 can be found in [
13
] or [
18
]. For the
absorption chiller at UBA, the values are depicted in T able 3 at the design conditions specified in
T able 1 .

Appl. Sci. 2020 , 10 , 3354 8 of 17
T able 3.
Characteristic coe ffi cients of the absorption chiller at the Federal Envir onment Agency (UBA)
in Dessau, Germany .
E ff ective Coe ffi cients (Dimensionless) Slope Parameters (in kW / K) Conversion Factor
K 1 K 2 K 3 K 4 K 5 K 6 K Eo
0.07 − 1.02 − 0.09 1.20 1.45 0.15 1.23
Mor eover , for control purposes, the external evaporator outlet temperature
t Eo
is of inter est
rather than
t Ei
. Instead of
∆ ∆ t ∗
i
, a modified characteristic temperatur e di ff erence
∆ ∆ t ∗
can be derived
analytically , which combines the hot and cooling water inlet temperature and chilled water outlet
temperatur e:
∆ ∆ t ∗ = t Di · ( 1 − K 1 ) − t Ai · ( 1 − K 2 ) + t Eo · ( 1 − K 3 ) . (6)
Since the same coe ffi cients
K 1
to
K 3
(with their r espective physical meaning) are applied,
a well-defined conversion factor
K Eo =  1 − ( K 1 − K 2 ) · K 4 / W E  − 1
is available to transform Equations
(3) and (4) into Equations (7) and (8) for use with
∆ ∆ t ∗
instead of
∆ ∆ t ∗
i
. W ith the modified slope
parameters K ∗
4 = K Eo · K 4 and K ∗
5 = ( K Eo · ( K 5 − K 6 ) + K 6 ) , the characteristic equations conform to:
Q E = K ∗
4 · ∆ ∆ t ∗ , (7)
Q D = K ∗
5 · ∆ ∆ t ∗ + K 6 · ∆ ∆ t ∗
min . (8)
In addition, for serial cooling water flow from the absorber to the condenser , the two characteristic
temperatur e di ff erences ∆ ∆ t ∗ and ∆ ∆ t ∗
min ar e linked by the external thrust ∆ t T i = t Di − t Ai [ 12 ]:
∆ ∆ t ∗
min = ( t Di − t Ai ) − ∆ ∆ t ∗ . (9)
Thus, with
K ∗∗
5 = K Eo · ( K 5 − K 6 )
, the characteristic equation for the driving heat can be rewritten as:
Q D = K ∗∗
5 · ∆ ∆ t ∗ + K 6 · ∆ t T i . (10)
A comparison of the measur ed and calculated values for the cooling capacity (i.e.,
Q E
and
Q C
E
)
and driving heat (i.e.,
Q D
and
Q C
D
) is depicted in Figure 4 a for the operating period discussed in
Section 2.2 . The same values are plotted as a function of
∆ ∆ t ∗
in Figur e 4 b. Due to the variations in
the hot and cooling water flow rate (cf.
V D
and
V H
in Figur e 2 b), the slope parameters
K ∗
4
and
K ∗∗
5
ar e
not constant. Thus, neither the calculated values nor the measured values of the cooling capacity ar e
displayed as a straight line. For the driving heat, a straight line was not to be expected at all (even at
constant flow rates), because the temperature thr ust
∆ t T i = t Di − t Ai
will cause a scatter ar ound the
straight line given by
K ∗∗
5
and
∆ ∆ t ∗
. An additional reason for the di ff er ences and scatter results fr om the
dynamic operating conditions of the measur ements in contrast to the calculated values, which assume
steady state conditions by definition in the method. Nevertheless, the agreement of the measur ed and
calculated values seems to be satisfying.

Appl. Sci. 2020 , 10 , 3354 9 of 17
Appl. Sci. 2020 , 10 , x FO R P EER R E VIEW 9 of 17

( a ) ( b )
Figure 4. Comparison of the measured and calculate d valu es for the absor p tion chill er and dry-cooler
model as a fun c tion of time ( a ) and for the absorption chiller as a functio n of the inlet characteristic
temperature difference ( b ).
3. R e su lts — M od el Pre d ic tiv e Co ntr o l
The model pr edictive control str a tegy fo r an extende d so lar he at o p eration of the SAC syste m
combines t h e absorpt i on ch ill er model (i. e ., t h e impr oved cha r a c teri sti c eq ua ti on method) wi th a p a rt
load mode l f o r t h e r e ject heat dev i ce. Since t h e co mbinat ion of absorpt i on ch ill ers wit h dr y cool ers
ha s become increa singly more common a n d the humi difier at th e Feder a l En vironment A g ency in
Dess au is nor m al ly b l ocke d, a dr y-coo l e r model i s s u f f ic ient . A f t e r t h e descr i pt io n of t h e dry - c ooler
model, t h e co nt rol st r a t e gy is der i ved.
3. 1. Dr y-C ool e r Mo del
In Fig u re 5, t h e nomenclature for the dr y-cooler mod e l is dep i cted. A control sig n al C  is used
to a d just the a i r fl ow ra te V 󰇗  by cha n gi ng the rota ti ona l speed of t h e ventilators or their motors,
respectively. The necessar y e l ectric al p o wer o f the d r y-coo l er P , fo r a ce rt ain air f l ow rat e V 󰇗  is
proporti ona l to the pressure drop a n d tota l eff i ci ency η ,  , incl ud ing al l mechanic al a n d elect r ic a l
losse s o f the motor-ventilator as sembly . In a ddit i on, a con s t a nt au xili ar y p o wer consum p t ion P ,

can be consid ered (e .g., for a control un it). Assum i ng a q u a d ra ti c devel o pment of the a i r- side pressure
drop Δp  wi th respect to the pressure drop under nom i nal condition s (i.e., Δp  =Δ p , ⋅ V 󰇗  V 󰇗 ,

 ),
thi s lea d s to: P , =   ⋅ 󰇗 
 , +P ,
 =  ,
 , ⋅   󰇗 ,   ⋅ V 󰇗    +P ,
 =

f

 ⋅ V 󰇗    +P ,
 . (1 1)

Figure 5. Nom enclatu re for d r y - cooler m o de l.
00:00 00:00 00:0 0 00:00 00:00 00:00
0
10
20
30
40
50
T ime o f da y starting at May 31, 2017
P
el, DC
; Q
X
/ kW
Q
E
Q
C
E
Q
D
Q
C
D

P
'
el, D C
P
el, D C
.
.
.
.
.
0 10 20 30 40 50
0
10
20
30
40
50
ΔΔ t *

i

/ K
Q X / kW
Q E
Q C
E
Q D
Q C
D

.
.
.
.
.

Figure 4.
Comparison of the measur ed and calculated values for the absorption chiller and dry-cooler
model as a function of time (
a
) and for the absorption chiller as a function of the inlet characteristic
temperature di ff er ence ( b ).
3. Results—Model Predictive Control
The model pr edictive contr ol strategy for an extended solar heat operation of the SAC system
combines the absorption chiller model (i.e., the impr oved characteristic equation method) with a part
load model for the r eject heat device. Since the combination of absorption chillers with dry coolers has
become incr easingly more common and the humidifier at the Federal Envir onment Agency in Dessau
is normally blocked, a dry-cooler model is su ffi cient. After the description of the dry-cooler model,
the contr ol strategy is derived.
3.1. Dry-Cooler Model
In Figur e 5 , the nomenclature for the dry-cooler model is depicted. A control signal C DC is used
to adjust the air flow rate
V L
by changing the r otational speed of the ventilators or their motors,
r espectively . The necessary electrical power of the dry-cooler
P el,DC
for a certain air flow rate
V L
is
pr oportional to the pressur e drop and total e ffi ciency
η DC,tot
, including all mechanical and electrical
losses of the motor -ventilator assembly . In addition, a constant auxiliary power consumption
P aux
el,DC
can be consider ed (e.g., for a control unit). Assuming a quadratic development of the air-side pr essure
dr op
∆ p L
with r espect to the pr essure dr op under nominal conditions (i.e.,
∆ p L = ∆ p L,0 ·  V L / V L,0  2
),
this leads to:
P el,DC =
∆ p L · V L
η DC,tot
+ P aux
el,DC =
∆ p L,0
η DC,tot ·  V L,0  2 ·  V L  3 + P aux
el,DC = f fric ·  V L  3 + P aux
el,DC . (11)
which can be r ewritten by expanding the fraction with V L,0 as:
P el,DC =
∆ p 0 · V L,0
η DC,tot ·  V L,0  2 · V L,0
·  V L  3 + P aux
el,DC = P el,DC,0 · ( C DC ) 3 + P aux
el,DC , (12)
wher e
C DC = V L / V L,0
is the normalised flow rate or the contr ol signal of the dry cooler , respectively ,
and P el,DC,0 is the electrical power under nominal conditions.

Appl. Sci. 2020 , 10 , 3354 10 of 17
Appl. Sci. 2020 , 10 , x FO R P EER R E VIEW 9 of 17

( a ) ( b )
Figure 4. Comparison of the measured and calculate d valu es for the absor p tion chill er and dry-cooler
model as a fun c tion of time ( a ) and for the absorption chiller as a functio n of the inlet characteristic
temperature difference ( b ).
3. R e su lts — M od el Pre d ic tiv e Co ntr o l
The model pr edictive control str a tegy fo r an extende d so lar he at o p eration of the SAC syste m
combines t h e absorpt i on ch ill er model (i. e ., t h e impr oved cha r a c teri sti c eq ua ti on method) wi th a p a rt
load mode l f o r t h e r e ject heat dev i ce. Since t h e co mbinat ion of absorpt i on ch ill ers wit h dr y cool ers
ha s become increa singly more common a n d the humi difier at th e Feder a l En vironment A g ency in
Dess au is nor m al ly b l ocke d, a dr y-coo l e r model i s s u f f ic ient . A f t e r t h e descr i pt io n of t h e dry - c ooler
model, t h e co nt rol st r a t e gy is der i ved.
3. 1. Dr y-C ool e r Mo del
In Fig u re 5, t h e nomenclature for the dr y-cooler mod e l is dep i cted. A control sig n al C  is used
to a d just the a i r fl ow ra te V 󰇗  by cha n gi ng the rota ti ona l speed of t h e ventilators or their motors,
respectively. The necessar y e l ectric al p o wer o f the d r y-coo l er P , fo r a ce rt ain air f l ow rat e V 󰇗  is
proporti ona l to the pressure drop a n d tota l eff i ci ency η ,  , incl ud ing al l mechanic al a n d elect r ic a l
losse s o f the motor-ventilator as sembly . In a ddit i on, a con s t a nt au xili ar y p o wer consum p t ion P ,

can be consid ered (e .g., for a control un it). Assum i ng a q u a d ra ti c devel o pment of the a i r- side pressure
drop Δp  wi th respect to the pressure drop under nom i nal condition s (i.e., Δp  =Δ p , ⋅ V 󰇗  V 󰇗 ,

 ),
thi s lea d s to: P , =   ⋅ 󰇗 
 , +P ,
 =  ,
 , ⋅   󰇗 ,   ⋅ V 󰇗    +P ,
 =

f

 ⋅ V 󰇗    +P ,
 . (1 1)

Figure 5. Nom enclatu re for d r y - cooler m o de l.
00 :0 0 00 :00 00 :0 0 00: 00 00 :0 0 00 :0 0
0
10
20
30
40
50
T i me o f d a y s t ar t i ng a t M a y 3 1 , 2 017
P
el , D C
; Q
X
/ kW
Q
E
Q
C
E
Q
D
Q
C
D

P
'
el , D C
P
el , D C
.
.
.
.
.
0 10 20 30 40 50
0
10
20
30
40
50
ΔΔ t *

i

/ K
Q X / kW
Q E
Q C
E
Q D
Q C
D

.
.
.
.
.

Figure 5. Nomenclature for dry-cooler model.
The unknown air flow rate
V L
, which causes the electrical power ,
P el,DC
for a certain load
condition, r esults from the r eject heat flow of the absorption chiller from the absorber and condenser ,
Q L = Q A + Q C . It is equivalent to the negative sum of the evaporator and desorber heat flow:
Q L =  Q A + Q C  = −  Q E + Q D  = V L · ρ L · c p,L · ( t Li − t Lo ) . (13)
T o determine
V L
(and ther eby
P el,DC
), the r equired air outlet temperatur e
t Lo
in Equation (13) can
be calculated fr om the dimensionless temperature glide,
P L
of the air str eam, assuming a counter flow
heat exchanger (i.e., neglecting all cr oss-counter flow e ff ects):
P L = t Lo − t Li
t Ki − t Li
= 1 − exp ( ( R L − 1 ) · NTU L )
1 − R L · exp ( ( R L − 1 ) · NTU L ) . (14)
The r equired cooling water inlet temperatur e of the dry-cooler
t Ki
on the left-hand side of Equation
(14) is equal to the condenser outlet temperatur e,
t Co
of the absorption chiller . It follows fr om the inlet
temperatur e
t Ai
plus the temperatur e increase in the cooling water flow of the absorption chiller due to
the total r eject heat flow
Q E + Q D = −  Q A + Q C 
. Since the cooling water valve is used only for safety
r easons, it is normally fully open. Consequently , for serial cooling water flow , the flow rates in the
absorber and condenser and in the dry-cooler ar e the same, i.e., W A = W C = W K = V K · ρ K · c p,K :
t Ki = t Co = t Ai + Q E + Q D
W A
. (15)
Combining Equations (14) and (15) r esults in:
t Lo = P L · ( t Co − t Li ) + t Li = P L ·       t Ai + Q E + Q D
W A
− t Li       + t Li . (16)
and subsequently inserting Equation (16) into Equation (13) with the ambient air temperatur e as the
air inlet temperatur e t Li = t amb leads to:
V L = W A
ρ L · c p,L · P L
· Q E + Q D
Q E + Q D + W A · ( t Ai − t amb ) . (17)
However , Equation (17) determines
V L
only implicitly , because
P L
is a function of
V L
since the
dimensionless heat transfer capability
NTU L
and heat capacity flow rate ratio
R L
in Equation (14)
depend on V L :
NTU L = Y L
W L
= U L · A L
ρ L · c p,L · V L
R L = W L
W A
= ρ L · c p,L · V L
W A
. (18)

Appl. Sci. 2020 , 10 , 3354 11 of 17
In or der to solve Equation (17) explicitly for
V L
, an approximation
P 0
L
for the dimensionless
temperatur e glide, P L is used from [ 12 ], appendix O:
P L ≈ P 0
L =       1 + W L
W L,0
· 1
P L,0
− 1 !      
− 1
. (19)
In this equation,
W L,0 = ρ L · c p,L · V L,0
holds for the air side capacity flow rate at the nominal
condition (Index 0) and
P L,0
is calculated with
W L,0
(i.e., also at the nominal condition). Thus, at the
normalized flow velocity
C DC = W L / W L,0 =
1, the approximation
P 0
L
equals
P L,0
(i.e., the exact value).
For
C DC =
0, Equation (19) conver ges to the same limit value
P 0
L =
1 as
P L
in Equation (14). Between
C DC = 0 and C DC = 1, the exponential dependency is consider ed by a recipr ocal approach.
Inserting appr oximation Equation (19) into Equation (17) leads to an approximated but explicit
equation for the air volume flow rate
V 0
L ≈ V L
or the normalized flow velocity
C 0
DC = V 0
L / V L,0
when
constant pr operty data can be assumed:
C 0
DC =  Q E + Q D  · P L,0
b L,0 ·  Q E + Q D  + a L,0 · ( t Ai − t amb ) . (20)
W ith
P L,0
determined, e.g., from manufactur ers’ data under nominal conditions or from
measur ements at a single refer ence point, and the coe ffi cients:
a L,0 = V L,0 · P L,0 · ρ L · c p,L , (21)
b L,0 = a L,0 / W A + P L,0 − 1 (22)
the appr oximated electrical power P 0
el,DC ≈ P el,DC under the part load condition can be calculated:
P 0
el,DC = P el,DC,0 ·  C 0
DC  3 + P el,DC,aux . (23)
A comparison between the measur ed and appr oximated values for the electrical power (i.e.,
P el,DC
and
P 0
el,DC
) is depicted in Figur e 4 a for the operating period discussed in Section 2.2 . without
the humidification of ambient air .
3.2. Switchover Control Strategy
The aim of the following contr ol strategy is to find a cut-in and a cut-o ff condition for the solar
heat operation (SHO) of an absorption chiller cooling assembly (ACCA) under the constraint that the
specific electricity demand during SHO is lower than the electricity demand of a refer ence cooling
technology (e.g., a compr ession chiller cooling assembly , CCCA).
The specific electricity demand of the ACCA is dominated by the electricity demand of the dry
cooler . Thus, a simplified cut-in condition for SHO is to allow a maximum control signal
C on,SHO
DC
,
which r esults in an approximated specific electricity demand
w ACCA
lower or equal than the specific
electricity demand of the compr ession chiller cooling assembly , i.e.:
w ACCA ≈
P el,DC,0 ·  C on,SHO
DC  3 + P el,DC,aux
Q set
E
≤ w CCCA . (24)

Appl. Sci. 2020 , 10 , 3354 12 of 17
Solving for the maximum allowed C on,SHO
DC leads to the boundary value:
C on,SHO
DC = 3
v
t w CCCA · Q set
E − P el,DC,aux
P el,DC,0
. (25)
This depends on the r eference cooling technology (
w CCCA
), load condition (
Q set
E
), and electrical
values of the r eject heat technology of the SAC system (
P el,DC,0
,
P el,DC,aux
). In addition, the control
signal of the air flow rate
C 0
DC = C on,SHO
DC
for the same cooling load
Q E = Q set
E
and the necessary
driving heat flow accor ding to the characteristic Equation (8) is determined by Equation (20), hence:
C on,SHO
DC =  Q set
E + K Eo · ( K 5 − K 6 ) · ∆ ∆ t ∗ + K 6 · ( t Di − t Ai )  · P L,0
b L,0 ·  Q set
E + K Eo · ( K 5 − K 6 ) · ∆ ∆ t ∗ + K 6 · ( t Di − t Ai )  + a L,0 · ( t Ai − t amb )
. (26)
In this equation, only the supply temperatur es
t Di
and
t Ai
ar e unknown, because
C on,SHO
DC
is fixed
by the load and technology parameters accor ding to Equation (25). On the right-hand side,
t Eo = t set
Eo
in
∆ ∆ t ∗
and
t amb
ar e fixed by the load and weather condition and the coe ffi cients
a L,0
,
b L,0
, and
K N
describe the thermal part load behaviour of the dry-cooler and absorption chiller .
The cooling water inlet temperatur e
t Ai
in Equation (26) can be eliminated by the r earranged
characteristic Equation (7) in combination with the characteristic temperatur e in Equation (6), i.e.:
t Ai = 1
1 − K 2
·       
( 1 − K 1 ) · t Di + ( 1 − K 3 ) · t set
Eo − Q set
E
K ∗
4       
. (27)
After inserting Equation (27) into Equation (26), it can be solved for the driving temperature
t Di = t on,SHO
Di
, which is necessary for a cooling load
Q set
E
at a chilled water temperatur e of
t set
Eo
and
a maximum allowed contr ol signal for the dry cooler
C on,SHO
DC
in or der to keep the specific electricity
demand w ACCA below W max = w CCCA when the absorption chiller is operated with solar heat:
t on,SHO
Di = 1
K SHO
c
·   K SHO
b −  K ∗∗
5 + K ∗
4  · K SHO
a  · Q set
E / K ∗
4 − K SHO
b · ( 1 − K 3 ) · t set
Eo +  C on,SHO
DC · a L,0  · t amb  , (28)
wher e:
K SHO
a = C on,SHO
DC · b L,0 − P L,0 , (29)
K SHO
b =  C on,SHO
DC · a L,0 − K 6 · K SHO
a  / ( 1 − K 2 ) , (30)
K SHO
c = ( 1 − K 1 ) / ( 1 − K 2 ) ·  C on,SHO
DC · a L,0 − K 6 · K SHO
a  + K 6 · K SHO
a . (31)
Finally , the operating limits of the absorption chiller have to be considered. For example, to avoid
crystallization of the
H 2 O / LiBr
solution, a minimum cooling water temperature
t min
Ai
is allowed. Hence,
fr om the r earranged characteristic Equation (7) follows a minimum driving temperature for the load
case Q E = Q set
E ; t Eo = t set
Eo :
t min,SHO
Di = 1
1 − K 1
·       
( 1 − K 2 ) · t min
Ai − ( 1 − K 3 ) · t set
Eo + Q set
E
K ∗
4       
. (32)
Consequently , the necessary driving temperature to start the solar heat operation is the maximum
of the afor ementioned temperatures:
t on,SHO = max  t min,SHO
Di , t on,SHO
Di  . (33)

Appl. Sci. 2020 , 10 , 3354 13 of 17
The cut-in condition for solar heat operation (i.e.,
SHO on
) becomes true when the highest storage
temperatur e
t PS11
and the outlet temperatur e of the solar heat exchanger
t Ho
ar e both higher than the
necessary cut-in temperatur e for solar operation t on,SHO :
SHO on = ( t PS11 > t on,SHO and t Ho > t on,SHO ) . (34)
The cut-o ff condition for SHO consists of thr ee aspects: Solar heat operation should be stopped
when the highest temperatur e in the solar heat storage
t PS11
has decr eased below the necessary
driving temperatur e
t set
Di
to cover the load or the necessary driving temperatur e
t on,SHO
for SHO,
and simultaneously , the electricity demand becomes too high or the load cannot be matched anymore.
Thus, the cut-o ff condition r eads:
SHO o ff =  max  t set
Di , t on,SHO  − t PS11 > ∆ t o ff ,SHO
2 
and  C DC > C o ff ,SHO
DC or t Eo − t set
Eo > ∆ t o ff ,SHO
0  . (35)
T ypical values for the thresholds ∆ t o ff ,SHO
2 and ∆ t o ff ,SHO
0 ar e 2 and 0.2 K, respectively .
4. Discussion
The model pr edictive switchover strategy for extended solar heat operation (SHO) with improved
cut-in and cut-o ff conditions has been implemented into the industrial programmable logic contr oller
(PLC) of the single-stage
H 2 O / LiBr
-absorption chiller of type FM050v0.3 operated at the Federal
Envir onment Agency (UBA) since 2011. Nowadays, this chiller is marketed as type “Bee” [
19
].
V ia a Profi-Bus-connection, the information for the contr ol signals of the flaps
C PS
and
C DH
is sent
to the building management system, where it is put into execution. The switchover fr om BHO to
SHO without a model-based cut-in condition is described in Figur e 2 . Now , the impr oved switchover
strategy including a model-based cut-in / o ff condition is described. The measur ements and overall
r esults of the strategy are depicted in Figur e 6 for an operating period of 2 days in September 2019.
In Figur es 7 and 8 , the cut-in and cut-o ff time periods are shown separately . On the first day , solar heat
operation of the absorption chiller started at 11:00 a.m. and ended on the next day at approximately
08:00 a.m. Thus, the duration of the solar heat operation period is 21 h in comparison to 13 h of
sunshine duration, i.e., fr om 06:30 a.m. until 07:30 p.m.
The driving temperatur e
t Di
used in SHO started with appr oximately 67
◦
C, incr eased up to
78
◦
C in the afternoon of the first day , and decreased down to 49
◦
C in the morning of the next day .
The corr esponding cooling water temperatur es
t Ai
of 25, 29, and 19
◦
C, which ar e necessary to cover
the nearly constant cooling load of 23–29 kW
0
, wer e supplied by the heat rejection device in dry-cooler
mode with a control signal
C DC
of less the 60%. Accordingly , the mean specific electricity demand
during the whole SHO period
w ACCA ≈
0.18 kW
el
/ kW
0
is appr oximately 25% below the average specific
electricity demand of the r eference cooling technology w CCCA = 0.24 kW el / kW 0 (cf. Figure 6 d).
Inserting the electrical values
P el,DC,0
= 13.5 kW
el
and
P el,DC,aux
= 1.7 kW
el
of the r eject heat device
at UBA into Equation (25) together with
w CCCA
= 0.24 kW
el
/ kW
0
and the measur ed cooling load of
about 23 to 29 kW
0
leads to a maximum allowed contr ol signal for the dry cooler
C on,SHO
DC
of 0.66 to 0.73.
Instead of this variable value, a constant value
C on,SHO
DC
= 0.6 was used for test purposes. The resulting
necessary driving temperatur e to start the solar heat operation
t on,SHO
of about 60 to 64
◦
C during the
pr eheating time is plotted in Figure 7 . At 10:50 a.m., the cut-in condition became true (cf. Equation
(34) and
SHO on
in Figur e 7 ) and a delay timer of 10 min was started. Since
SHO on =
1 was true over
the full delay period, the information for the contr ol signal
C PS
of the flap to be opened and
C DH
of
the flaps to be closed was sent to the building management system via Pr ofi-Bus. Thus, at 11:00 a.m.,
solar operation started with a lower desorber inlet temperatur e
t Di ≈
67
◦
C as befor e (i.e.,
t Di ≈
74
◦
C
during BHO with district heating, cf. Figure 7 ). If the cut-in condition became false (i.e.,
SHO on =
0)

Appl. Sci. 2020 , 10 , 3354 14 of 17
during the delay period, the timer would have been r eset to zero and r estarted when
SHO on =
1 had
become true again. Thereby , a cut-in delay was realized.
Appl. Sci. 2020 , 10 , x FO R P EER R E VIEW 13 of 17

Figure 6. Solar heat operatio n over 21 h with the im prove d c o ntrol strateg y : ( a ) globa l horizontal
irradiation, q  , te mperatures in hot water circui t and control signals from R H D; ( b ) f l ow r a tes an d
cooling capac i t y ; ( c ) am bi ent air tem p eratu r e and tem p era t u r es in the ch ille d and coo l i n g water
circu i t; ( d ) spe c ific ele c tric ity d e m a nd.

Figure 7. Start- u p of solar hea t operation wi t h the im prove d control strate g y .
0
2 0
4 0
6 0
8 0
100
C / % ; t / °C
q / ( 10· W / m
2
)
C
DC
C
Hu
t
PS 1 1
q
gh
t
Ho
t
Di
t
S HO, o n
0
10
20
30
V / ( m³/ h )
Q / kW
V
D
Q
E
V
PS
V
H
5
15
25
35
t / ° C
t
am b
t
1A i
t
0Eo
t
set
0Eo
t
set
1A i
00: 00 08: 00 16: 00 00: 00 08: 00 16: 00 00: 00
0. 0
0. 5
1. 0
T i me o f d ay s tart i ng at S ep 02, 2019
w / ( kW
el
/k W
0
)
w
ACCA
w
CCCA
≈
0 ,2 4 k W
el
/kW
0
.
. .
.
.
.
.
.
.
09: 00 10: 00 11: 00 12: 00 13: 00 14 : 00
45
50
55
60
65
70
75
80
85
T i me o f d a y o n S e p 0 2 , 2 0 1 9
V / ( m ³ / h) ; t / ° C
t
PS 1 1
t
Ho
t
Di
t
se t
Di
t
on , S H O
t
PSo
V
PS
+4 5 SH O
on
·2 + 4 5 SH O
of f
·1 + 4 5
t
mi n, S H O
Di
.
.
( a )
( b )
( c )
( d )

Figure 6.
Solar heat operation over 21 h with the improved contr ol strategy: (
a
) global horizontal
irradiation,
q gh
, temperatures in hot water cir cuit and control signals fr om RHD; (
b
) flow rates and
cooling capacity; (
c
) ambient air temperature and temperatur es in the chilled and cooling water circuit;
( d ) specific electricity demand.
Appl. Sci. 2020 , 10 , x FO R P EER R E VIEW 13 of 17

Figure 6. Solar heat operatio n over 21 h with the im prove d c o ntrol strateg y : ( a ) globa l horizontal
irradiation, q  , te mperatures in hot water circui t and control signals from R H D; ( b ) f l ow r a tes an d
cooling capac i t y ; ( c ) am bi ent air tem p eratu r e and tem p era t u r es in the ch ille d and coo l i n g water
circu i t; ( d ) spe c ific ele c tric ity d e m a nd.

Figure 7. Start- u p of solar hea t operation wi t h the im prove d control strate g y .
0
2 0
4 0
6 0
8 0
100
C / % ; t / ° C
q / ( 1 0· W / m
2
)
C
DC
C
Hu
t
PS 1 1
q
gh
t
Ho
t
Di
t
S HO, o n
0
10
20
30
V / ( m ³/ h )
Q / k W
V
D
Q
E
V
PS
V
H
5
15
25
35
t / ° C
t
am b
t
1A i
t
0E o
t
se t
0E o
t
se t
1A i
00: 00 08 : 0 0 16: 00 00: 00 08: 00 16: 00 00 : 0 0
0. 0
0. 5
1. 0
T i m e o f d a y s t ar t i ng at S ep 02, 2 019
w / ( k W
el
/k W
0
)
w
A CCA
w
C CCA
≈
0 ,2 4 k W
el
/k W
0
.
. .
.
.
.
.
.
.
09: 00 10: 00 11: 00 12: 00 13: 00 14 : 00
45
50
55
60
65
70
75
80
85
Ti me o f d a y o n S e p 0 2 , 2 0 1 9
V / (m ³/h) ; t / ° C
t
PS11
t
Ho
t
Di
t
set
Di
t
on ,SH O
t
PSo
V
PS
+4 5 SHO
on
·2+45 SHO
off
·1+45
t
mi n, S H O
Di
.
.
( a )
( b )
( c )
( d )

Figure 7. Start-up of solar heat operation with the improved contr ol strategy .

Appl. Sci. 2020 , 10 , 3354 15 of 17
Appl. Sci. 2020 , 10 , x FO R P EER R E VIEW 14 of 17

Figure 8. Shu tdown of solar heat operation with the im pro v ed control str a teg y .
The dr iving t e mperat ure t  used in SHO st art e d wit h approx imat e l y 6 7 °C, incr ease d up t o
7 8 °C i n the af ternoon of the f i rst day, a n d decrea sed down to 4 9 °C i n the morni n g of the next da y.
The correspo n ding coo ling water tempe r ature s t  o f 25 , 2 9 , and 1 9 ° C , which are necess ary t o c o v e r
the nearly co nstant coolin g lo ad o f 23–29 kW 0 , were supplied by the hea t rej e c t ion device in dry -
cool er mode wi th a control si gnal C  of less t h e 6 0 %. Accord ing l y, t h e me an sp ecif ic elect r ici t y
demand during the whole SHO period 𝑤 󰇗   ≈ 0. 1 8 kW el /kW 0 is approx imat el y 2 5 % below t h e
aver age specific e l ectricity demand o f th e refe rence c ooling technology 𝑤 󰇗  = 0. 24 kW el /kW 0 (c f .
Fig u re 6d ).
Inserting the electric al values P ,, = 13 .5 kW el and P ,,   = 1.7 kW el o f t h e r e j e c t h e a t d e v i c e
a t UBA i n to Eq ua ti on (25 ) together wi th w 󰇗   = 0.24 kW el /kW 0 an d t h e mea s ur ed c ooling lo ad o f
a b out 23 to 29 kW 0 lea d s t o a maxim u m allow e d co nt rol sign a l f o r t h e dry cooler C 
, of 0.66 to
0. 73 . Inst e a d of t h is v a r i ab le v a lu e, a co nst a nt v a l u e C 
,  = 0.6 w a s used for te st purposes. The
resu lt ing nec e ss ary dr iv in g t e m p erat ur e t o st art t h e sol a r h e at op erat ion t ,  of about 60 to 6 4 °C
duri ng the prehea ti ng ti me i s pl otted i n Fi gure 7 . At 10 :5 0 a.m., the cut- i n condi t ion beca me true ( c f .
Eq ua ti on ( 34) a n d SHO  i n Fi gure 7) a n d a del a y t i mer of 10 mi n wa s st arted. Si nce SHO  =1 was
true over the f u ll del a y peri od, the i n f o rma t i o n f o r the control si gna l C  of the flap to be opened and
C  of the fl a p s to be cl osed wa s sent to t h e bu ild ing management system v i a Pr ofi-Bu s. Thus , at
11 :0 0 a . m . , so l a r op e r at ion s t art e d w i t h a lower desorb er in let t e m p e r at ure t  ≈ 6 7 ° C a s b e f o r e ( i . e . ,
t  ≈ 74 °C dur i n g BHO w i th district heat ing, c f . F i gu re 7) . If the cut- i n conditi o n b e came f a l s e (i .e.,
SHO  =0 ) duri ng the dela y peri od, the ti mer woul d ha v e b e en reset t o ze ro and r e st ar t e d when
SHO  =1 had become true agai n. Thereb y, a c u t - in de la y w a s rea l i z ed.
Due t o t h e lo wer dr ivin g t e mperat ure t  ≈ 67 °C (which i s a m i xed t e m p erat ure o f t  ≈ 70 °C
from t h e sol a r heat exchang e r and t   ≈ 65 °C f r om the stora g e) , the set va lue f o r the cool i n g wa ter
t 
 wa s decre a s e d by t h e CE cont rol l er fo r a wh il e in o r der t o mat c h t h e coo lin g lo ad and chi lled
wa ter set v a lue, t  ≈t 
 . The r ef ore , the c o ntr o lle r of the d r y - cool e r i n c r eas e d the c o ntr o l s i g n a l C 
to a d just t  to t 
 ( c f . Fi gure 6a ). Shortly af t e r 11 a . m., C  also inc r eased above the cut - off value
C 
,   = 0.5 a n d the cut- off condi t i o n SHO   a ccordi n g to Eq uati on ( 35) became true. Thus, f o r a
defin i te re sult, SHO  and SHO  ha ve to be used as set a n d reset in p u t s in a b i s t ab le funct i on b l ock .
Wi th the ri si ng a m bi e n t a i r te mpera t ur e unti l 0 4 : 0 0 p.m., the nec e ssa ry dri v i n g te mpera t ur e
t , =t 
, al so i n crea ses a ccordi n g to Eq ua ti on (28 ) . Si nce the a v ai la bl e tem p era t ure f r om the
solar collecto r and storag e is h i gh eno u gh, SHO is ongoing . At night t i me, t h e ava i l a bl e st orage
temperature t   fa ll s b e l o w t ,  . Nevertheless, the second part of the cut- of f c o nd i t i o n i n
Eq ua ti on (3 5) i s not true. Due to the l o w a m bi ent a i r tempera t ure, a l o w cooling wa ter tem p era t ure
is al so av ai l a b l e t o count e r b al ance t h e lo w driv in g te mperature . T h ereby, the c h illed w a t e r s e t v a l u e
is still ma t c hed wi t h ou t an increase of the speci fic electrici t y dema nd w 󰇗   (cf. F i g u r e 6 d ). F r o m
ap p r oxim at el y 06 :3 0 a.m . o f t h e second day on, t h e c ooling w a t e r t e m p erat ure t  i s lim it ed by t h e
bounda ry v a lue t 
 = 19 °C ( c f . Fi gure 8 ) . Wi th a continuousl y decrea si ng dri v i n g tempera t ure
06: 00 07: 00 08: 00 09: 00 10: 00 11: 00
0
10
20
30
40
50
60
70
80
T i m e of day o n Sep 03, 2 019
V / (m ³ /h) ; C
DC
/ % ; t / °C
C
DC
t
Eo
t
set
Eo
t
set
Di
t
Di
t
on , SH O
t
PS11
V
PS
SHO
on
·2
SHO
off
V
D
t
Ai
t
set
Ai
.
.
.

Figure 8. Shutdown of solar heat operation with the improved contr ol strategy .
Due to the lower driving temperatur e
t Di ≈
67
◦
C (which is a mixed temperatur e of
t Ho ≈
70
◦
C
fr om the solar heat exchanger and
t PS11 ≈
65
◦
C fr om the storage), the set value for the cooling water
t set
Ai
was decr eased by the CE controller for a while in or der to match the cooling load and chilled water set
value,
t Eo ≈ t set
Eo
. Therefor e, the controller of the dry-cooler incr eased the control signal
C DC
to adjust
t Ko
to
t set
Ai
(cf. Figur e 6 a). Shortly after 11 a.m.,
C DC
also incr eased above the cut-o ff value
C o ff ,SHO
DC
= 0.5
and the cut-o ff condition
SHO o ff
accor ding to Equation (35) became true. Thus, for a definite result,
SHO on and SHO o ff have to be used as set and r eset inputs in a bistable function block.
W ith the rising ambient air temperature until 04:00 p.m., the necessary driving temperature
t on,SHO = t on,SHO
Di
also incr eases accor ding to Equation (28). Since the available temperature fr om
the solar collector and storage is high enough, SHO is ongoing. At nighttime, the available storage
temperatur e
t PS11
falls below
t on,SHO
. Nevertheless, the second part of the cut-o ff condition in Equation
(35) is not true. Due to the low ambient air temperature, a low cooling water temperature is also available
to counterbalance the low driving temperatur e. Thereby , the chilled water set value is still matched
without an incr ease of the specific electricity demand
w ACCA
(cf. Figur e 6 d). Fr om approximately
06:30 a.m. of the second day on, the cooling water temperature
t Ai
is limited by the boundary value
t min
Ai
= 19
◦
C (cf. Figure 8 ). W ith a continuously decreasing driving temperatur e
t Di ≈ t PS11
below 50
◦
C,
the evaporator outlet temperatur e t Eo starts to incr ease and the cooling load is not matched anymor e.
Consequently , SHO has to be stopped approximately at 07:30 a.m.
The rapid incr ease of
t on,SHO = t min,SHO
Di
at appr oximately 7:45 a.m. is an e ff ect of a switching
action in one of the heating cir cuits, which causes a much lower hot water flow rate
V D
for some
minutes. For flow rates close to zer o, the slope coe ffi cients
K ∗
4
and
K ∗∗
5
(i.e., the possible capacity of the
chiller or its ‘thermal size’) become very small and consequently the necessary driving temperatur e
t on,SHO
high. Unfortunately , this interference happened in parallel or at the end of the cut-o ff delay for
SHO. Nevertheless, it did not switch o ff the solar heat operation (although it looks like it) and did
not have any e ff ect on the end of SHO at all. The cut-o ff condition (cf. Equation (35) or
SHO o ff
in
Figur e 8 ) was true since 07:10 a.m. W ith the cut-o ff delay time of 20 min, SHO was stopped at 07:30
a.m. A very few minutes later (i.e., after communication between PLC and the building management
system), the dischar ge pump P35 was switched o ff and the flow rate
V PS
r eached zero. Now , SHO also
stopped hydraulically . Incidentally , at the same moment, V D increased after the short interruption.
The potential of the impr oved control strategy was illustrated by a theor etical application during
the test period in 2017 (cf. Figur e 2 ), when the cooling load was low during the preheating time in the
morning of the first day (cf. Figure 3 ). Under these operating conditions, the cut-in condition
SHO on
would have become true befor e 10:00 a.m. and a necessary solar driving temperatur e below 65
◦
C at
the outlet of the solar heat exchanger t Ho would have been su ffi cient to start SHO.

Appl. Sci. 2020 , 10 , 3354 16 of 17
5. Conclusions
For solar cooling systems with an absorption chiller cooling assembly (i.e., including all the
supply pumps and the heat r ejection device), the possible operating time with solar heat is a key
parameter to achieve high solar fractions and thereby high primary ener gy savings. Hence, for SAC
systems, the solar heat operation (SHO) of the absorption chiller should be started as early as possible
and should be continued as long as possible in or der to reduce the backup heating demand, ther eby
r educing the main source of the primary ener gy demand. On the other hand, when the SHO mode is
activated too early and / or stopped too late, the available driving temperature fr om solar collector is low .
Consequently , a lower cooling water temperature is necessary to cover the cooling load. It depends
on the part load behavior of the chiller and can be calculated by the characteristic equation method.
The lower cooling water temperatur e causes a higher electricity demand in the reject heat device.
These theor etical interdependencies wer e exemplified during a test period with continuous solar heat
operation over mor e than three days at the SAC system of the Federal Envir onment Agency in Dessau,
Germany . It was shown that the resulting electricity demand during solar heat operation might exceed
the demand of the refer ence technology (e.g., a compression chiller cooling assembly) and no primary
ener gy savings are possible anymor e.
In or der to extend the solar heat operation period on the one hand, and to ensure a specific
electricity demand below a boundary value on the other hand, a model pr edictive switchover strategy
was developed. The combination of an impr oved characteristic equation method for the part load
behavior of absorption chillers with a simple dry-cooler model was used to find a suitable cut-in and
cut-o ff condition for the solar heat operation. The two conditions depend on a minimum solar driving
temperatur e, which has to be reached by the solar collector and storage befor e solar heat operation is
enabled. The minimum driving temperatur e depends on technical coe ffi cients describing the part load
characteristics of the dry cooler and absorption chiller , and also on the load and weather conditions.
Measur ements at a solar cooling system for an IT center with a cooling demand of approximately
20–30 kW
0
ar ound the clock showed that solar heat operation could be started with approximately
67
◦
C and was possible down to 49
◦
C. The duration of solar heat operation was 21 h in comparison to
13 h of sunshine duration, and the mean specific electricity demand during the whole SHO period was
appr oximately 25% below the average specific electricity demand of the refer ence cooling technology .
Although the model pr edictive switchover strategy utilizes the same method of characteristic
equations as the contr ol algorithm of the relevant absorption chiller in the investigated SAC system,
it is generally possible to apply the switchover strategy independent of the chiller control. In contrast
to the state of the art, wher e constant (or at least load and weather independent) cut-in temperatures
for solar heat operation ar e used, the new switchover strategy incorporates the actual load and weather
condition as well as the part load capability of the absorption chiller and reject heat device. Thus,
the new switchover strategy pr ovides the cut-in temperature as a quality of the whole absorption
chiller cooling assembly supplied by solar ener gy .
Funding:
This resear ch was funded by the Bundesministerium für W irtschaft und Energie (BMW i), grant numbers
03ET1171A and 03ET1583.
Conflicts of Interest: The author declares no conflict of inter est.
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