© Acta hydrotechnica 22/36 (2004), Ljubljana
ISSN 1581-0267
57
UDK/UDC: 519.61/.64:556.53:627.8 Prejeto/Received: 13. 2. 2004
Kratki znanstveni prispevek – Short Scientific Paper Sprejeto/Accepted: 9. 9. 2005
TOPLOTNA OBREMENITEV SA VE PO IZGRADNJI
SPODNJESA VSKIH STOPENJ
THERMAL LOAD OF THE SA V A RIVER AFTER CONSTRUCTION
OF THE LOWER SA V A RIVER CASCADE
Andrej ŠIRCA
Uvodni del članka predstavlja zgoš čen pregled dela na podro čju matemati čnega modeliranja
termike reke Save v obdobju 1997–2003. V nadaljevanju so opisane zna čilnosti uporabljenih
matemati čnih modelov ter ra čunskih primerov, katerih namen je prikaz toplotnega stanja reke po
izgradnji prve faze verige HE (2012) in po zaklju čku gradnje (2018) ter primerjava s sedanjim
stanjem. Upoštevani sta dve varianti termoenergetskega objekta v Trbovljah ter sedanje stanje NE
Krško (NEK). Analize so izdelane za topli del leta (april–september) za profila NEK in HE Mokrice.
Srednje mese čne re čne temperature se bodo po izgradnji verige HE pri NEK pove čale do +0,4 °C,
pri HE Mokrice pa do +1,6 °C. V razmerah s povratno dobo 4 leta bo povišanje pri NEK znašalo
+1,3 °C, pri HE Mokrice pa do +2,1 °C. Pri povratni dobi 40 let bosta ustrezni povišanji do 2,0 °C
pri NEK in do 2,2 °C pri HE Mokrice. Vpliv TET na obratovanje NEK je manjši, kot je bil ocenjen v
študiji iz leta 1998.
Klju čne besede: toplotna obremenitev, preto čne hidoelektrarne, veriga hidroelektrarn,
matemati čni modeli, reka Sava.
The introductory part of the paper brings a survey of the work performed in the sphere of
mathematical modelling of the Sava river thermal load in the period 1997–2003. In the
continuation, characteristics of the applied mathematical models as well as simulation cases are
given, the purpose of which is to show a thermal condition of the river after construction of the first
phase of the HPP chain (2012) and after its completion (2018) as well as comparison with the
present state. Two alternatives of the thermal power unit in Trbovlje and the present state of the
NPP Krško (NEK) have been considered. Analyses were done for the NEK and HPP Mokrice cross-
sections for the warm part of the year (April–September). After the HPP chain construction, the
average monthly river temperatures at NEK shall increase by up to +0.4 °C and at HPP Mokrice by
up to +1.6 °C. In the 4-year return period conditions the increase at the NEK shall reach +1.3 °C
while at HPP Mokrice it shall reach up to +2.1 °C. Considering the 40-year return period the
relevant increases shall be up to 2.0 °C at the NEK and up to 2.2 °C at the HPP Mokrice. The TPP
Trbovlje impact on the NEK operation is lower than estimated by the previous study from 1998.
Key words: thermal load, run-of-river hydro powerplants, chain of HPPs, mathematical models,
the Sava River.
1. UVOD
Na podlagi uvodnih eksperimentalnih
(VGI-VGL, 1977; 1978; 1979; 1980; 1981) in
teoreti čnih analiz (VGI-VGL, 1989; 1991;
1993; 1995) toplotne obremenitve Save so se v
letu 1997 za čele izvajati podrobnejše
raziskave, ki so vklju čevale terenske meritve
in matemati čno modeliranje. Eksperimentalne
1. INTRODUCTION
Based on introductory experimental (VGI-
VGL, 1977; 1978; 1979; 1980; 1981) and
theoretic analyses (VGI-VGL, 1989; 1991;
1993; 1995) of thermal loads of the Sava river
more detailed research started in 1997 which
included field measurements and mathematical
modelling. Experimental and theoretical basic
research was upgraded in 1998 by an applied

Širca, A.: Toplotna obremenitev Save po izgradnji spodnjesavskih stopenj – Thermal load of the Sava river after
construction of the lower Sava river cascade
© Acta hydrotechnica 22/36 (2004), 57–73, Ljubljana
58
in teoreti čne osnovne raziskave so bile v letu
1998 nadgrajene z uporabno raziskavo
toplotnega vpliva trboveljske termoelektrarne
(TET) na Savo do državne meje, v letu 2003
pa s podrobnejšo študijo termi čnih vplivov
bodoče verige HE na Savi in NE Krško
(NEK). Zadnja študija je vklju čevala tudi
ekonomsko vrednotenje medsebojnih vplivov
energetskih objektov. Eksperimentalni del
raziskav je v bazenu Vrhovo izvajal Inštitut za
hidravli čne raziskave iz Ljubljane (IHR),
matemati čno modeliranje pa Hidrotehni čna
smer FGG (HS-FGG), IBE, d.d. in IHR.
Vodilna ideja raziskav je bila razvoj 1D-
modela za celotno Savo, obravnava
posameznih bazenov in detajlov s 3D-
modelom ter verifikacija modelov s terenskimi
meritvami. Integralnemu poro čilu o vplivu
TET v sedanjih in bodo čih pogojih
obratovanja ob grobih predpostavkah t. i.
kriti čnih in ekstremnih razmer (HS-FGG,
1998) so sledili podrobnejši opis toplotnega
modula v okviru 3D-modela PCFLOW3D in
njegove verifikacije z meritvami iz leta 1995
(Rajar in Širca, 1998), opis v vseh 1D- in 3D-
ra čunih uporabljenega modela izmenjave
toplote na vodni gladini HEATFLOW in
modela HOTLAKE za vrednotenje termike v
bazenih preto čnih HE (Širca in Rajar, 1999),
analiza ustreznosti podatkov iz monitoringa
re čnih temperatur HMZ (Širca in Gutierez,
1999) ter zgoš čen pregled rezultatov (Širca,
2000). V nadaljevanju smo na podlagi
rezultatov obsežnih meritev v letu 1998
podrobno analizirali termiko bazena Vrhovo,
dodatno verificirali 3D-model in potrdili
upravi čenost uporabe 1D-modela (Širca et al.,
2000). Sledili so verifikacija modela
neoviranega re čnega toka HOTRIVER in prve
to čnejše ocene vpliva izgradnje verige HE
(Širca, 2001) ter kon čno izra čun termičnih
vplivov razli čnih kombinacij objektov ob
statisti čno utemeljenih predpostavkah srednjih
(povpre čnih) in izrednih (kriti čnih in
ekstremnih) razmer, nadgradnja modela enega
bazena v model verige HOTCHAIN ter
ekonomsko vrednotenje ugotovljenih
sprememb termike (IBE, 2003a; Širca, 2003).
V nadaljevanju so prikazani kon čni rezultati
izra čunov termike za razli čne kombinacije
objektov in hidrometeoroloških pogojev.
study of the thermal impact of the TPP
Trbovlje (TET) on the Sava river downstream
to the state border, and in 2003 by a detailed
study of thermal impact of the future HPPs
chain on the Sava river and of the NPP Krško
(NEK). The latter study also included
economic evaluation of interrelating impacts
of power plants. The experimental part of
research in the Vrhovo basin was performed
by the Institute of Hydraulic Research (IHR),
while mathematical modelling was performed
by the Hydraulic department of the Faculty of
Civil and Geodetic Engineering (HS-FGG),
IBE, Consulting Engineers and IHR.
The leading idea of investigations was to
develop a 1D model for the complete Sava
river, handling of individual basins and details
with a 3D model and verification of these
models by field measurements. The integral
report on the TET impacts in present and
future operating conditions by assuming the
so-called critical and extreme conditions (HS-
FGG, 1998) was followed by a more detailed
description of a thermal model in the
framework of the 3D PCFLOW3D model and
its verification by measurements performed in
1995 (Rajar and Širca, 1998), description of a
HEATFLOW model of heat exchange on the
water surface, applied in all 1D and 3D
calculations, and the HOTLAKE model of
thermal loads evaluation in the run-of-river
reservoirs (Širca and Rajar, 1999), analysis of
HMZ river temperature monitoring data (Širca
and Gutierez, 1999) and a condensed survey of
results (Širca, 2000). Based on results of
extensive measurements performed in 1998, a
detailed analysis of thermal conditions in the
Vrhovo basin and an additional verification of
the 3D model were performed, and the 1D
model application justified (Širca et al., 2000).
They were followed by a verification of the
HOTRIVER model of unobstructed river flow
and the first more accurate assessment of the
HPP chain construction impacts (Širca, 2001).
Finally, a calculation of thermal impacts of
different structures combination was made
with statistically justified assumptions of
middle (average) and exceptional (critical and
extreme) conditions, upgrading of a single
basin model into a HOTCHAIN model of the
chain as well as an economical assessment of
modified thermal conditions established (IBE,
2003a; Širca, 2003). In the continuation, the
final results of thermal simulations made for
different structures combination in different
hydrometeorological conditions are given.

Širca, A.: Toplotna obremenitev Save po izgradnji spodnjesavskih stopenj – Thermal load of the Sava river after
construction of the lower Sava river cascade
© Acta hydrotechnica 22/36 (2004), 57–73, Ljubljana
59
2. UPORABLJENI MATEMATI ČNI
MODELI
HOTRIVER je 1D nestacionarni model za
simulacijo širjenja toplote v nezajezenih
rekah. Temelji na poenostavitvi, da
nestacionarne in kontinuirane izvire polutantov
lahko obravnavamo kot vsoto trenutnih
to čkovnih izvirov (Širca in Rajar, 1997; Širca,
2001).
HOTLAKE je osnovni 1D-model za
vrednotenje temperaturnih stanj v bazenih
re čnih (preto čnih) elektrarn. Zgrajen je na
predpostavki, da dolge, ozke bazene lahko
obravnavamo na enak na čin kot nezajezene
vodotoke, to je, s popolno vertikalno in
horizontalno premešanostjo polutantov v
prečnih profilih. Upravi čenost predpostavke je
potrjena z verifikacijo na bazenu Vrhovo in z
rezultati 3D-modela (Širca et al., 2000).
HOTCHAIN je nadgradnja modela
HOTLAKE za ve č zaporednih bazenov.
Osnovna predpostavka je, da se na iztoku iz
gorvodne HE za čne koren bazena dolvodne
HE, pri čemer se temperatura ob gorvodni
pregradi uporabi kot vstopna temperatura za
dolvodni bazen. Predpostavljeno je čisto
preto čno obratovanje HE, kar pri pretokih nad
100 m
3
/s lahko povzro či nekaj lokalne napake,
pri manjših pa ne, ker HE v takšnih razmerah
praviloma obratujejo po pretoku. Tudi pri
ve čjih pretokih (nad 100 m
3
/s) se lokalna
napaka na celotnem ra čunskem odseku
izravna, saj čas potovanja vodnega elementa in
s tem njegov čas izpostavljenosti atmosferskim
vplivom ostaneta enaka.
Zelo pomemben korak razvoja modela
HOTCHAIN je bil dodatno umerjanje člena, ki
nadzoruje evaporacijo (IBE, 2003a). V vseh
primerih verifikacij, ko so nastopale obi čajne
meteorološke razmere, smo namre č upoštevali
le 10 % srednje vrednosti evaporacije,
dobljene iz empiri čnih izrazov 9 avtorjev. V
primerih ekstremnih razmer smo s takšnim
modelom dobili zelo visoke vrednosti re čnih
temperatur, zato smo na podlagi ra čuna
ravnovesnih temperatur v model vgradili
korekcijo, ki pri naraš čanju re čne temperature
od 23 do 28 °C člen evaporacije linerano
pove ča od 10 na 100 %. Merodajni vrednosti
2. MATHEMATICAL MODELS
APPLIED
HOTRIVER is a 1D unsteady-state
simulation model of heat transfer in
undammed rivers. It is based on a simplifi-
cation that unstationary and continuous
pollutant sources can be treated as a sum of
instantaneous point sources (Širca and Rajar,
1997; Širca, 2001).
HOTLAKE is a basic 1D model for
assessment of temperature conditions in
reservoirs of run-of-river power plants. It is
built on a presumption that long, narrow
reservoirs can be treated in the same way as
undammed rivercourses, i.e. with complete
vertical and horizontal pollutants mixing in
cross sections. This presumption has been
justified by a verification performed in the
Vrhovo reservoir and by results of a 3D model
(Širca et al., 2000).
HOTCHAIN is an upgrade of the
HOTLAKE model for more successive
reservoirs. The basic presumption to be met is
that at the upstream HPP outflow the
downstream HPP reservoir begins and that the
water temperature by the upstream dam is used
as the input temperature for the downstream
reservoir. A pure run-of-river HPP operation
mode is foreseen which may cause some local
error with flows above 100 m
3
/s. With lower
flows this should not be the case because in
such conditions the HPPs normally operate in
the run-of-river regime. Even with higher
flows this local error shall be balanced along
the complete calculation section since the
travel time of the water element and
consequently the time of its exposition to
atmospheric impacts remain the same.
An important step of the HOTCHAIN
model development was an additional
calibration of the element controlling
evaporation (IBE, 2003a). Namely, in all
verification cases with usual meteorological
conditions only 10% of mean evaporation
calculated from empirical expressions of 9
authors were considered. In cases with
extreme conditions extremely high values of
river water temperatures were obtained with
such a model. This is why a correction based
on calculation of equilibrium temperature (ET)
was introduced to the model which increased
the evaporation value linearly from 10% to

Širca, A.: Toplotna obremenitev Save po izgradnji spodnjesavskih stopenj – Thermal load of the Sava river after
construction of the lower Sava river cascade
© Acta hydrotechnica 22/36 (2004), 57–73, Ljubljana
60
ravnovesne temperature pri privzeti zra čni
vlagi 65 % sta znašali 26,9 °C (pri temperaturi
zraka 30 °C) in 30,7 °C (pri temperaturi zraka
35 °C).
100% at river water temperature increase from
23°C to 28°C. The decisive values of the ET at
given air humidity of 65% so attained were
26.9 °C (at air temperature of 30 °C) and 30.7
°C (at air temperature of 35 °C).
3. OPIS RA ČUNSKIH PRIMEROV
Obdelanih kon čnih 60 ra čunskih primerov
(preglednica 1) lahko delimo in medsebojno
primerjamo po treh klju čih:
1. glede na število obratujo čih elektro-
energetskih objektov (primeri A, B in
C),
2. glede na naravne pogoje (povpre čne
razmere ter izredni dogodki) ter
3. glede na toplotno mo č objekta v
Trbovljah (brez objekta, 120 MW in
200 MW).
Za vse primere velja, da so nezajezeni re čni
odseki modelirani s programom HOTRIVER
(HR), akumulacije pa z modeli tipa
HOTCHAIN, ki vsebujejo razli čno število
bazenov (HC2, HC6 in HC7). Na lokaciji
NEK se v skladu z na činom obratovanja, ki je
v danih hidrometeoroloških razmerah možen, z
modelom hlajenja NEK (IBE, 2003) dolo či
prirastek re čne temperature in izra čuna
temperatura Save po popolnem premešanju.
3.1 KOMBINACIJE OBJEKTOV
Primer A potrjuje in dolo ča sedanje stanje
toplotne obremenitve Save, ko so zgrajene TE
Trbovlje, HE Vrhovo in NE Krško. Simulacije
so namenjene kontroli modelov ter prikazu
ni čelnih razmer pred za četkom gradnje verige
HE (razen že zgrajene HE Vrhovo) ter prikazu
vpliva obratovanja razli čno mo čnih objektov v
Trbovljah.
Primer B napoveduje spremembe po
izgradnji zgornjega dela verige do Krškega, ki
bo zaklju čena do leta 2012. Poleg objektov
primera A vklju čuje še HE Boštanj, HE Blanca
in HE Krško. Simulacije so namenjene
predvsem oceni vpliva verige HE na NEK, saj
nadaljnja gradnja verige dolvodno od NEK s
termi čnega vidika ne bo imela vpliva
gorvodno. Izjemoma se lahko ta pojavi lokalno
v določenih hidroloških pogojih (nevarnost
recirkulacije hladilne vode), vendar reševanje
3. SIMULATION CASES
The treated 60 calculation examples (Table
1) can be divided and mutually compared
according to the following three keys:
1. regarding the number of operating
electric power units (cases A, B and
C),
2. regarding natural conditions (average
conditions and extreme events) and
3. regarding thermal power of the
Trbovlje unit (without the unit itself,
120 MW and 200 MW).
It is characteristic for all examples that
undammed river sections have been modelled
by the HOTRIVER (HR) model, while the
reservoirs have been modelled by the
HOTCHAIN model taking into account a
different number of reservoirs (HC2, HC6 and
HC7). At NEK location, in accordance with
the operation mode possible in certain
hydrometeorlogical conditions, the NEK
cooling model (IBE, 2003) enables
determination of the river water temperature
increase and calculation of the Sava river
water temperature after complete mixing.
3.1 STRUCTURES COMBINATIONS
Case A proves and determines the present
state of thermal load of the Sava River with
operating TPP Trbovlje, HPP Vrhovo and NPP
Krško. Simulations are needed for models
control and for description of initial state prior
to the HPPs chain construction (with the
exception of existing HPP Vrhovo) as well as
to show the impact of operation of the
Trbovlje units with different power output.
Case B anticipates changes after
construction of the HPPs chain upper part
down to Krško, which shall be terminated by
2012. Besides structures of Case A it includes
Boštanj, Blanca and Krško HPPs. Simulations
shall provide an assessment of the HPPs chain
impact on the NPP Krško, since further
construction of the chain downstream from
NEK shall have no thermal impact on the
upstream conditions. Exceptionally it may
appear locally and in certain hydrological
conditions (e.g. cooling water re-circulation)

Širca, A.: Toplotna obremenitev Save po izgradnji spodnjesavskih stopenj – Thermal load of the Sava river after
construction of the lower Sava river cascade
© Acta hydrotechnica 22/36 (2004), 57–73, Ljubljana
61
tega problema v tej fazi raziskav še ni bilo
predvideno.
Primer C napoveduje spremembe po
izgradnji celotne verige HE do Mokric, ko sta
poleg objektov, naštetih v Primeru B, zgrajeni
še HE Brežice in HE Mokrice. HE Mokrice
kot zadnja stopnja verige predstavlja hkrati
stanje v mejnem profilu s Hrvaško.
3.2 NARAVNI POGOJI
Navedene kombinacije objektov obravna-
vamo v treh hidrometeoroloških stanjih:
V povprečnih mese čnih razmerah (oznaka
–sred), za katere privzemamo srednje mese čne
pretoke v ustreznih pre čnih profilih Save,
srednje mese čne re čne temperature na
ustreznih lokacijah ter srednje urne vrednosti
meteoroloških parametrov.
V kriti čnih poletnih razmerah (oznaka –
krit), ki so definirane z nizkimi pretoki, ki
trajajo 20 dni in imajo povratno dobo 2 leti,
srednjo mese čno re čno temperaturo za avgust
na vrhu obravnavanega odseka in srednjimi
urnimi vrednostmi meteoroloških parametrov
v dneh, ko najvišja dnevna temperatura
preseže 27 ºC.
V ekstremnih poletnih razmerah (oznaka –
ekst), ki so dolo čene z nizkimi pretoki, ki
trajajo 20 dni in imajo povratno dobo 25 let,
srednjo mese čno re čno temperaturo za avgust
na vrhu obravnavanega odseka, srednjimi
urnimi vrednostmi meteoroloških parametrov
v dneh, ko najvišja dnevna temperatura
preseže 27 ºC.
Za hidrometeorološke podatke uporabljamo
vhodne podatke iz obdobja 1980–2000 ali čim
bližje aproksimacije. To manj ugodno
predpostavko upravi čujemo z izkazanim
trendom večanja števila vro čih poletnih dni, z
izkazanimi spremembami re čnih režimov
(nižje in dolgotrajnejše nizke vode v zadnjih
dekadah) ter z ve čjim faktorjem varnosti pri
napovedih. Nepri čakovano potrditev
pravilnosti te odlo čitve predstavlja nastop
obdobja ekstremnega zna čaja v juniju 2003.
Verjetnosti kriti čnega (25 %) in ekstremnega
dogodka (2,5 %) sta dolo čeni kot produkt
verjetnosti nastopa 20-dnevnih nizkih pretokov
ter so časnega 20-dnevnega obdobja toplih dni
(prag 27 ºC), saj smo predpostavili, da sta
dogodka neodvisna.
but solving of this problem has not yet been
foreseen in this phase of research.
Case C anticipates changes to appear after
construction of the whole HPPs chain down to
Mokrice when besides the units given in the
Example B, also Brežice and Mokrice HPPs
will be built. HPP Mokrice as the last unit of
the chain represents at the same time the
border cross-section with Croatia.
3.2 NATURAL CONDITIONS
The given units combinations are treated in
three hydrometeorological states:
In average monthly conditions (mark
sred), where average monthly flows in
relevant cross sections of the Sava River,
together with average monthly river water
temperatures at suitable locations as well as
average hourly values of meteorological
parameters are taken into account.
In critical summer conditions (mark –
krit) defined by low flows lasting for 20 days
and having a 2-year return period, average
monthly river water temperature for August on
the top of the section treated and average
hourly values of meteorological parameters on
days when the highest daily temperature
exceeds 27 ºC.
Extreme summer conditions (mark –
ekst), defined by low flows lasting for 20 days
and having a 25 year return period, average
monthly river water temperature for August on
the top of the section treated and average
hourly values of meteorological parameters on
days when the highest daily temperature
exceeds 27 ºC.
Input data from the period 1980–2000 or
the closest approximations serve for
hydrometeorological data. This less favourable
presumption is justified by the trend of
increasing number of hot days, by proved
changes in river water regimes (lower and
longer lasting low flows in the last decades)
and by a higher safety factor in forecasting. An
unexpected confirmation of such decision
correctness came in June 2003 in form of a
period of extreme character. Probabilities of
critical (25%) and extreme events (2.5%) have
been defined as a product of probabilities of a
20-day low flow event and a simultaneous 20-
day period of warm days (threshold at 27 ºC),
since it has been presumed that these two
events are independent of one another.

Širca, A.: Toplotna obremenitev Save po izgradnji spodnjesavskih stopenj – Thermal load of the Sava river after
construction of the lower Sava river cascade
© Acta hydrotechnica 22/36 (2004), 57–73, Ljubljana
62
3.3 OBJEKT V TRBOVLJAH
V vseh kombinacijah objektov (A, B in C)
in naravnih pogojev (–sred, –krit in –ekst) je
objekt v Trbovljah obravnavan z mo čjo 120
MW in mo čjo 0, ki pomeni, da TET ne
obratuje. Ustrezni oznaki primerov sta TETja
in TETne. Dodatno je samo za kriti čne in
ekstremne razmere ob vseh konfiguracijah
objektov (A, B in C) upoštevana pove čana
mo č TET 200 MW (primer TETja+), pri čemer
so upoštevani takšni projektni podatki
morebitnega novega objekta, kot so veljali za
opuš čeno TET3.
Vstopna re čna temperatura na zgornjem
koncu ra čunskega odseka je za primere TETja
enaka srednji re čni temperaturi v Rade čah za
obdobje 1980–1997. Za primer TETne je z
upoštevanjem dotoka Savinje zmanjšana za
obremenitev, ki jo v reko vnaša TET, za
primer TETja+ pa na enak na čin ustrezno
pove čana.
3.4 POSEBNI PRIMERI
Pri ra čunih kriti čnih in ekstremnih situacij
nastopa še primer C1, ki je enak primeru C, le
da je bazen Brežice upoštevan v zmanjšanem
obsegu, v okviru zgolj nadvišanih poplavnih
nasipov. Ta varianta akumulacije bo izvedljiva
v primeru soglasja Hrvaške k enotnemu
obratovanju verige HE na obeh straneh meje,
ko bi v Sloveniji odpadla potreba po dnevni
kompenzaciji.
Izven obsega 60 rednih simulacij sta bili
izvedeni še simulacija srednjih razmer julija
1998 kot osnovni verifikacijski primer ter
teoreti čna prognosti čna simulacija stanja, kot
bi nastopilo po izgradnji celotne verige HE
(2018), če bi se ponovile hidrološke in
meteorološke razmere iz julija 1998. Na
podlagi neverificiranega modela za zimsko
stanje je bila narejene tudi groba ocena
hladilnega u činka bodo čih akumulacij
dolvodno od NEK.
3.3 TRBOVLJE UNIT
In all combinations of cases (A, B and C)
and natural conditions (–sred, –krit in –ekst)
the unit in Trbovlje has been treated as a unit
of 120 MW power or 0 MW power which
means that TET is out of operation. Relevant
cases designations are TETja and TETne.
Additionally, for all cases (A, B and C) but
only for critical and extreme conditions, an
increased power of TET of 200 MW has been
considered (case of TETja+), where the same
design data of eventual new unit have been
considered as in case of the abandoned TET3.
The input river water temperature at the
upper end of the calculation section, for TETja
cases, is equal to the average river water
temperature at Rade če for the period of 1980–
1997. For cases of TETne, taking into
consideration the Savinja inflow, it has been
decreased for the load brought into the river by
TET and for the case of TETja+, it has been
relevantly increased in the same way.
3.4 SPECIAL CASES
Case C1 is introduced aditionally for
critical and extreme situation calculations
which is the same as case C with the exception
of decreased Brežice reservoir which appears
only in the frame of enheightened flood
embankments. This alternative of reservoir
will be realistic in case of Croatia consensus
regarding unified HPPs chain operation on
both sides of the border, when in Slovenia no
need of daily compensation would exist.
Apart from 60 regular simulations two other
simulations have been performed, i.e.
simulation of average conditions in July 1998
as a basic verification case and theoretic
prognostic simulation of the state that would
emerge after construction of the complete
HPPs chain (2018) if hydrological and
meteorological conditions of July 1998
occurred again. Based on an unverified model
for winter state a rough estimation of a
cooling effect of future reservoirs downstream
NEK has been done as well.

Širca, A.: Toplotna obremenitev Save po izgradnji spodnjesavskih stopenj – Thermal load of the Sava river after
construction of the lower Sava river cascade
© Acta hydrotechnica 22/36 (2004), 57–73, Ljubljana
63
Preglednica 1. Rezultati modeliranja – srednje re čne temperature v obravnavanih prerezih.
Table 1. Results of modelling – average river temperatures in the considered cross-sections.
naravni pogoji obrat. objekti obratov. TET hidrometeorol.
natural conds. operating units TET operation hydrometeorol. SUH VRH BOS BLA KRS NEKin NEKout BRE MOK
 - sred Primer/Case A TETja April 9,7 9,85 10,37 11,66 11,83
Maj/May 12,7 12,96 13,79 15,20 15,48
Junij/June 14,9 15,21 16,17 17,68 18,01
Julij/July 17,6 18,01 19,23 21,20 21,62
Avgust/August 18,1 18,56 19,87 22,54 22,95
September 15,2 15,38 15,96 17,94 18,12
TETne April 9,54 9,69 10,22 11,51 11,68
Maj/May 12,53 12,79 13,62 15,03 15,31
Junij/June 14,71 15,02 15,98 17,49 17,82
Julij/July 17,35 17,77 19,00 20,97 21,39
Avgust/August 17,77 18,23 19,56 22,23 22,65
September 14,96 15,14 15,73 17,71 17,89
Primer/Case B TETja April 9,7 9,85 10,01 10,22 10,36 10,44 11,73 11,90
Maj/May 12,7 12,96 13,23 13,61 13,85 13,98 15,39 15,67
Junij/June 14,9 15,21 15,54 15,98 16,27 16,43 17,94 18,26
Julij/July 17,6 18,01 18,44 19,02 19,41 19,60 21,57 21,98
Avgust/August 18,1 18,56 19,04 19,67 20,09 20,31 22,98 23,37
September 15,2 15,38 15,58 15,83 16 16,10 18,08 18,26
TETne April 9,54 9,69 9,85 10,07 10,21 10,29 11,58 11,75
Maj/May 12,53 12,79 13,07 13,44 13,68 13,82 15,23 15,51
Junij/June 14,71 15,02 15,35 15,8 16,09 16,25 17,76 18,09
Julij/July 17,35 17,77 18,2 18,78 19,17 19,37 21,34 21,75
Avgust/August 17,77 18,23 18,72 19,36 19,78 20,00 22,67 23,07
September 14,96 15,14 15,34 15,6 15,77 15,87 17,85 18,03
Primer/Case C TETja April 9,7 9,85 10,01 10,22 10,36 10,44 11,73 12,17 12,35
Maj/May 12,7 12,96 13,23 13,61 13,85 13,98 15,39 16,17 16,49
Junij/June 14,9 15,21 15,54 15,98 16,27 16,43 17,94 18,87 19,24
Julij/July 17,6 18,01 18,44 19,02 19,41 19,60 21,57 22,75 23,23
Avgust/August 18,1 18,56 19,04 19,67 20,09 20,31 22,98 24,07 24,45
September 15,2 15,38 15,58 15,83 16 16,10 18,08 18,57 18,77
TETne April 9,54 9,69 9,85 10,07 10,21 10,29 11,58 12,03 12,21
Maj/May 12,53 12,79 13,07 13,44 13,68 13,82 15,23 16,02 16,34
Junij/June 14,71 15,02 15,35 15,8 16,09 16,25 17,76 18,7 19,09
Julij/July 17,35 17,77 18,2 18,78 19,17 19,37 21,34 22,54 23,03
Avgust/August 17,77 18,23 18,72 19,36 19,78 20,00 22,67 23,83 24,24
September 14,96 15,14 15,34 15,6 15,77 15,87 17,85 18,35 18,56
 - krit Primer/Case A TETja 25% verj/prob 18,1 19,1 21,60 24,60 25,10
TETja+ 25% verj/prob 18,35 19,34 21,81 24,81 25,28
TETne 25% verj/prob 17,59 18,6 21,17 24,17 24,74
Primer/Case B TETja 25% verj/prob 18,1 19,1 20,13 21,47 22,36 22,83 25,83 26,15
TETja+ 25% verj/prob 18,35 19,34 20,36 21,7 22,58 23,04 26,04 26,33
TETne 25% verj/prob 17,59 18,6 19,64 21,01 21,9 22,38 25,38 25,77
Primer/Case C TETja 25% verj/prob 18,1 19,1 20,13 21,47 22,36 22,83 25,83 26,75 27,00
TETja+ 25% verj/prob 18,35 19,34 20,36 21,7 22,58 23,04 26,04 26,87 27,09
TETne 25% verj/prob 17,59 18,6 19,64 21,01 21,9 22,38 25,38 26,5 26,80
Primer/Case C1 TETja 25% verj/prob 18,1 19,1 20,13 21,47 22,36 22,83 25,83 26,41 26,73
TETja+ 25% verj/prob 18,35 19,34 20,36 21,7 22,58 23,04 26,04 26,56 26,85
TETne 25% verj/prob 17,59 18,6 19,64 21,01 21,9 22,38 25,38 26,08 26,47
 - ekst Primer/Case A TETja 2.5% verj/prob 18,1 19,59 22,75 25,75 26,18
TETja+ 2.5% verj/prob 18,48 19,95 23,01 26,01 26,39
TETne 2.5% verj/prob 17,28 18,8 22,15 25,15 25,69
Primer/Case B TETja 2.5% verj/prob 18,1 19,59 21,1 23,04 24,12 24,61 27,61 27,78
TETja+ 2.5% verj/prob 18,48 19,95 21,45 23,35 24,7 24,82 27,82 27,97
TETne 2.5% verj/prob 17,28 18,8 20,34 22,33 23,55 24,12 27,12 27,34
Primer/Case C TETja 2.5% verj/prob 18,1 19,59 21,1 23,04 24,12 24,61 27,61 28,03 28,19
TETja+ 2.5% verj/prob 18,48 19,95 21,45 23,35 24,7 24,82 27,82 28,21 28,36
TETne 2.5% verj/prob 17,28 18,8 20,34 22,33 23,55 24,12 27,12 27,66 27,84
Primer/Case C1 TETja 2.5% verj/prob 18,1 19,59 21,1 23,04 24,12 24,61 27,61 27,85 28,03
TETja+ 2.5% verj/prob 18,48 19,95 21,45 23,35 24,7 24,82 27,82 27,89 28,21
TETne 2.5% verj/prob 17,28 18,8 20,34 22,33 23,55 24,12 27,12 27,45 27,66
 - jul98 Primer/Case A TETja Julij/July 1998 19,6 20,94 23,03
 - jul18 Primer/Case C TETja Julij/July 1998 19.12 19,6 20,09 20,75 21,17 21,42 23,51 24,56 24,98
Zna čaj vrednosti iz preglednice (barvna legenda) Character of tabulated values (color legend)
podana vrednost za 1D model =  = 1D model input value
 rezultat 1D modela =  = 1D model result
rezultat modela hlajenja NEK =  = NEK cooling system model result
izra čun ni potreben ali ni možen =  = calculation not required or not possible

Širca, A.: Toplotna obremenitev Save po izgradnji spodnjesavskih stopenj – Thermal load of the Sava river after
construction of the lower Sava river cascade
© Acta hydrotechnica 22/36 (2004), 57–73, Ljubljana
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4. REZULTATI
Rezultati vseh ra čunskih primerov so za
profile HE Vrhovo (VRH), HE Boštanj (BOS),
HE Blanca (BLA), HE Krsko (KRS), vtoka v
NEK (NEKin), iztoka iz NEK (NEKout), HE
Brežice (BRE) in HE Mokrice (MOK) zbrani
v Preglednici 1.
4. RESULTS
Model results of all simulation cases are
given in Table 1 for cross-sections of HPP
Vrhovo (VRH), HPP Boštanj (BOS), HPP
Blanca (BLA), HPP Krško (KRS), NEK
inflow (NEKin), NEK discharge (NEKout),
HPP Brežice (BRE) and HPP Mokrice
(MOK).
Slika 1. Konfiguracija obstoje čih objektov na in ob Savi (primer A).
Figure 1. Configuration of the existing units on and along the Sava River (Case A).
4.1 PRIMER A: OBSTOJE ČE STANJE
Ker so bile verifikacije modelov že ve čkrat
opisane, sami opisi sedanjega stanja pa so
razmeroma nezanimivi, podajamo za primer A
(slika 1) le komentar vrednotenja vplivov
obratovanja TE Trbovlje na dolvodne
toplotne razmere v Savi. Iz rezultatov v
Preglednici 1 je razvidno, da znaša vpliv TE
Trbovlje pri polni sedanji mo či (leto 2003) in
povpre čnih razmerah pri NEK +0,31 °C v
avgustu in +0,15 °C v aprilu. V kriti čnih
razmerah in sedanji mo či bi bil vpliv TET na
temperaturo pri NEK +0,43 °C, v ekstremnih
razmerah pa +0,6 °C. Do zadnjega
obravnavanega profila, HE Mokrice, bi se
vpliv TET v ekstremnih razmerah zmanjšal na
+0,49 °C. V primeru pove čane mo či TET
(TET+) bi vpliv TET+ pri NEK v kriti čnih
4.1 CASE A: EXISTING STATE (2003)
Since case verifications have been
described already and the descriptions of the
present state are uninteresting, we shall give
here, for case A (Figure 1), only a comment on
the evaluation of the TPP Trbovlje operation
impacts on the downstream thermal
conditions in the Sava River. It is evident from
the Table 1 that the TPP Trbovlje impact at
full present power (year 2003) and average
conditions at NEK is +0.31 °C in August and
+0.15 °C in April. In critical conditions and
present power the TET impact on the
temperature by NEK shall reach +0.43 °C,
while in extreme conditions it shall reach +0.6
°C. At the last treated profile at HPP Mokrice,
the impact of TET in extreme conditions
would decrease to +0.49 °C. At increased
power of TET (TET+) the impact of TET+ at

Širca, A.: Toplotna obremenitev Save po izgradnji spodnjesavskih stopenj – Thermal load of the Sava river after
construction of the lower Sava river cascade
© Acta hydrotechnica 22/36 (2004), 57–73, Ljubljana
65
razmerah znašal +0,64 °C, v ekstremnih pa
+0,86 °C glede na ni čelno stanje brez objekta
TET.
Razlike med TET in TET+ (oziroma TET2
in TET3) so torej precej manjše, kot so bile
ocenjene v letu 1998 v študiji TOPOS-TET3
(FGG, 1998). Razlogi za razliko so
upoštevanje novejših in to čnejših podatkov za
pretoke in temperature Save in Savinje na
soto čju, blažje, vendar z verjetnostnim
ra čunom utemeljene definicije kriti čnih in
ekstremnih razmer v tej študiji ter popravki
modelov termike v definicijskem podro čju,
kjer re čna temperatura preseže 23 °C.
NEK would reach +0.64 °C in critical
conditions and +0.86 °C in extreme
conditions, both compared with the state
without TET.
Differences between TET and TET+ (i.e.
between TET2 and TET3) are considerably
smaller than those evaluated in 1998 (FGG,
1998). The reasons for this difference lie in
new and more accurate flow and temperature
data for the Sava and Savinja rivers at the
confluence, in more moderate but statistically
supported definitions of critical and extreme
events as well as in thermal models corrections
for cases when river water temperature
exceeds 23 °C.
Slika 2. Konfiguracija predvidenih objektov na in ob Savi za primer B (2012).
Figure 2. Configuration of anticipated units on and along the Sava River for Case B (2012).
4.2 PRIMER B: STANJE PO IZGRADNJI
HE KRŠKO (2012)
Spremembe re čne termike zaradi
gradnje verige HE vrednotimo na podlagi
primerjave rezultatov primerov A (slika 1) in
B (slika 2) v profilih NEK in HE Mokrice
(preglednica 1). Srednje re čne temperature na
zajetju NEK se bodo zaradi izgradnje verige
HE in ob hkrati obratujo či TET razmeroma
malo spremenile: v aprilu bo sprememba
manjša od 0,1 °C, v avgustu pa bo dosegla
0,44 °C. Ve čje spremembe bodo pri NEK
4.2 CASE B: STATE AFTER HPP KRŠKO
CONSTRUCTION (2012)
Changes in river water thermal load due
to HPPs construction have been evaluated by
comparison of results of cases A (Figure 1)
and B (Figure 2) in NEK and HPP Mokrice
profiles (Table 1). Average river water
temperatures at NEK intake shall face
relatively small changes due to HPPs chain
construction and due to simultaneous
operation of TET: in April, this change will be
smaller than 0.1 °C while in August it will
reach 0.44 °C. At NEK, greater changes will

Širca, A.: Toplotna obremenitev Save po izgradnji spodnjesavskih stopenj – Thermal load of the Sava river after
construction of the lower Sava river cascade
© Acta hydrotechnica 22/36 (2004), 57–73, Ljubljana
66
opazne v kriti čnih razmerah (+1,23 °C) in še
ve čje v ekstremnih (+1,86 °C). V profilu HE
Mokrice bodo srednje mese čne re čne
temperature po izgradnji zgornjega dela verige
HE višje za 0,07 °C v aprilu in za 0,42 °C v
avgustu. V kriti čnih razmerah bo povišanje
glede na sedanje stanje +1,05 °C, v ekstremnih
razmerah pa +1,6 °C. Pri HE Mokrice se bo
srednja mese čna aprilska temperatura zaradi
izgradnje zgornjega dela verige HE dvignila v
aprilu z 11,83 na 11,9 °C, v avgustu z 22,95 na
23,37 °C, v kriti čnih razmerah s 25,1 na 26,15
°C in v ekstremnih s 26,18 na 27,78 °C.
Razlike med primeri z in brez
obratovanja TET se po izgradnji zgornjega
dela verige HE ne bodo bistveno spremenile:
Pri NEK bo razlika med stanjem brez in z
obratovanjem TET v aprilu +0,15 °C, v
avgustu +0,31 °C, v kriti čnih razmerah +0,45
°C in v ekstremnih razmerah +0,49 °C.
Morebitna TET+ bo re čno temperaturo v
kriti čnih razmerah dvigovala za +0,66 °C v
ekstremnih pa za +0,7 °C, oboje v primerjavi z
ni čelnim stanjem brez objekta v Trbovljah.
Obratovanje TET bo v primeru B v profilu HE
Mokrice povzro čalo podobne prirastke re čne
temperature kot pri NEK. Tudi vpliv
morebitne TET+ bo zelo podoben kot pri
NEK, in sicer v kriti čnih razmerah +0,56 °C in
v ekstremnih razmerah +0,63 °C glede na
ni čelno stanje brez TET. Pri analizah vpliva
TET na NEK je zanimivo, da bodo prirastki
re čne temperature ob višjih obremenitvah
nekoliko manjši, ker se zelo ogreta voda manj
segreva od tiste pri obi čajnih temperaturah
oziroma so procesi izmenjave z okolico
intenzivnejši.
4.3 PRIMER C: STANJE PO IZGRADNJI
CELE VERIGE (2018)
Spremembe re čnih temperatur zaradi
izgradnje celotne verige HE vrednotimo na
podlagi primerjav ra čunov primera A (slika 1)
in C (slika 3). Komentiramo jih le za lokacijo
HE Mokrice, saj pri NE Krško med primeroma
B (opisi v prejšnjem podpoglavju) in C ni
razlike. Ob maksimalno obratujo čih TET in
NEK bodo srednje re čne temperature pri HE
Mokrice po izgradnji verige HE znašale v
aprilu 12,35 °C, v avgustu 24,45 °C, v
be evident in critical conditions (+1.23 °C) and
even greater in extreme conditions (+1.86 °C).
At the HPP Mokrice profile, after construction
of the upper part of the HPPs chain, the
average monthly river water temperatures shall
increase for 0.07 °C in April and for 0.42 °C in
August. In critical conditions, regarding the
present state, this increase shall reach +1.05
°C, and in extreme conditions +1.6 °C. At HPP
Mokrice, due to the upper part of the HPPs
chain construction, the average monthly
temperature shall increase from 11.83 to 11.9
°C in April and from 22.95 to 23.37 °C in
August while in critical conditions the
temperature will increase from 25.1 to 26.15
°C and in extreme conditions from 26.18 to
27.78 °C.
Differences between cases with and
without TET operation after construction of
the upper part of the HPPs chain will not be
great: at NEK the difference occurring in case
TET will operate or not shall reach +0.15 °C in
April and +0.31 °C in August, in critical
conditions +0.45 °C and in extreme conditions
+0.49 °C. Eventual TET+ shall increase the
river water temperature in critical conditions
by +0.66 °C and in extreme conditions by +0.7
°C, both values being compared with the zero
state without a unit in Trbovlje. The TET
operation in Case B shall cause similar
increase of the river water temperature in the
profile of HPP Mokrice and at NEK. The
impact of eventual TET+ will be also very
similar to that occurring at NEK, i.e. in critical
conditions it will reach +0.56 °C and in
extreme conditions +0.63 °C, compared with
the zero state without TET. In analyses of the
TET impact on NEK it is interesting that the
increases of the river water temperature at
greater loads will be somewhat smaller since
hot water heats less than water of normal
temperature.
4.3 CASE C: STATE OF COMPLETED
HPPS CHAIN (2018)
Changes in river water temperatures due to
construction of the complete HPPs chain
have been evaluated by comparison of results
of Cases A (Figure 1) and C (Figure 3). The
comment is given only for location of HPP
Mokrice, since at NPP Krško there is no
difference between Case B (see the previous
subchapter) and Case C. At maximum
operation of TET and NEK the average
monthly river water temperatures at HPP
Mokrice after construction of the HPPs chain

Širca, A.: Toplotna obremenitev Save po izgradnji spodnjesavskih stopenj – Thermal load of the Sava river after
construction of the lower Sava river cascade
© Acta hydrotechnica 22/36 (2004), 57–73, Ljubljana
67
kriti čnih razmerah 27,0 °C in v ekstremnih
28,19 °C. Glede na sedanje stanje (primer A)
znašajo prirastki v aprilu +0,52 °C, v avgustu
+1,5 °C, v kriti čnih razmerah +1,9 °C in v
ekstremnih razmerah +2,01 °C.
will reach 12.35 °C in April, 24.45 °C in
August, 27.0 °C in critical conditions and
28.19 °C in extreme conditions. Regarding
present state (Case A) the increases reach
+0.52 °C in April, +1.5 °C in August, +1.9 °C
in critical and +2.01 °C in extreme conditions.
Slika 3. Konfiguracija predvidenih objektov ob in na Savi, primer C (2018).
Figure 3. Configuration of the anticipated units on and along the Sava River, Case C (2018).
Obratovanje TET bo imelo po zaklju čeni
izgradnji verige nekoliko manjši vpliv na
re čno temperaturo pri HE Mokrice (oz. na
državni meji) kot v profilu NEK (glej tudi
komentar primera B). V primerjavi s stanjem
brez obratovanja TET bo prirastek na ra čun
TET pri HE Mokrice v aprilu znašal +0,14 °C,
v avgustu +0,21 °C, v kriti čnih razmerah +0,2
°C in v ekstremnih +0,35 °C. V primeru
obratovanja nadomestnega objekta TET+ (200
MW
e
) bi prirastki pri HE Mokrice glede na
stanje brez objekta v Trbovljah znašali v
kriti čnih razmerah +0,29 °C (temperatura
27,09 °C) in +0,52 °C v ekstremnih
(temperatura 28,36 °C). Temperatura 28,36 je
najvišja dosežena temperatura v tej študiji in
pomeni precejšnje preseganje najve čje
dovoljene temperature pod NEK, 28 °C, po
popolnem premešanju. Pri tem se pojavlja
vprašanje, ali je temperatura 28 °C dovoljena
na izstopu hladilne vode NEK ali na državni
meji. Če velja drugo (kar smo upoštevali v
After completion of the HPPs chain, the
TET operation will have somewhat smaller
impact on the river water temperature at HPP
Mokrice (on the state border) than at the NEK
profile (see also comment on Case B). In
comparison with the zero state (without TET
operation) the increase accounted to TET at
the HPP Mokrice shall reach +0.14 °C in
April, +0.21 °C in August, +0.2 °C in critical
conditions and +0.35 °C in extreme
conditions. In case of the substitutional unit
TET+ (200 MW
e
) o peration the increases at
HPP Mokrice, in comparison with the zero
state, shall reach +0.29 °C in critical
conditions (temperature 27.09 °C) and +0.52
°C in extreme conditions (temperature 28.36
°C). The temperature of 28.36 °C is the
highest temperature achieved in this Study and
exceeds the highest permitted temperature at
NEK which is 28 °C after complete mixing. A
question arises here whether the temperature
of 28 °C is permitted at the cooling water
outflow at NEK or at the state border. If the
second is right (and what was considered in
our Study as well), it is permissible for the

Širca, A.: Toplotna obremenitev Save po izgradnji spodnjesavskih stopenj – Thermal load of the Sava river after
construction of the lower Sava river cascade
© Acta hydrotechnica 22/36 (2004), 57–73, Ljubljana
68
naši študiji), je dopustno, da na odseku med
NEK in mejo re čna temperatura še naraste, če
pa je pogoj 28 °C postavljen na iztoku NEK, bi
bilo v takšnem primeru že potrebno precejšnje
omejevanje mo či NEK.
4.4 PRIMER C1: MANJŠI BAZEN
BREŽICE
V profilu HE Mokrice ter s polno
obratujo čima TET in NEK bi bila srednja
re čna temperatura v kriti čnih razmerah v
primeru C1 26,73 °C, v primeru C pa 27,0, kar
pomeni razliko 0,27 °C. V ekstremnih
razmerah bi imeli v primeru C1 temperaturo
28,03 °C, v primeru C pa 28,19 °C, kar
pomeni le razliko 0,16 °C. V takšnih razmerah
torej znova velja, da so pri višjih absolutnih
re čnih temperaturah razlike med variantami
manjše. Ista zakonitost velja za vpliv TET+
oziroma pri primerjavi s stanjem brez objekta
v Trbovljah. Razlika med primeroma C in C1
pri HE Mokrice znaša ob obratujo čih TET+ in
NEK v kriti čnih razmerah 0,24 °C, v
ekstremnih pa 0,15 °C. Če TET ne obratuje,
obratuje pa NEK, je razlika med primeroma C
in C1 pri Mokricah 0,33 °C v kriti čnih
razmerah in 0,18 °C v ekstremnih razmerah.
4.5 PRIMER D: ZIMSKO STANJE PO
IZGRADNJI VERIGE
Namen izra čunov primera D je bil ocena
hladilne sposobnosti bodo čih akumulacij v
primeru zimskih nizkovodnih razmer.
Poskusne simulacije modela HOTRIVER s
podatki za 27. in 28. 11. 1995 so pokazale zelo
slabo ujemanje ra čunskih rezultatov in meritev
pri NEK. Iz tega smo sklepali, da model,
umerjen s povpre čnimi temperaturami zraka in
vode med 15–20 ºC (poletje), ne more
zadovoljivo simulirati razmer pri povpre čnih
temperaturah okoli 0–5 ºC (zima). Osnovna
ovira pri simuliranju zimskega termi čnega
stanja reke je bila pomanjkanje meritev re čne
termike za hladno obdobje leta. Za zadovoljivo
umerjanje modela je namre č treba imeti
meritve vstopnih in izstopnih temperatur na
nekem re čnem odseku vsaj za dva zaporedna
dneva oziroma minimalno 24 ur, naš časovni
niz pa je obsegal le nekaj ve č kot 12 ur. Zaradi
river water temperature to rise even more in
the section from NEK to the State border.
However, if the condition of 28 °C is set on
the NEK outflow, the NEK power output shall
be considerably limited.
4.4 CASE C1: SMALLER BREŽICE
RESERVOIR
With TET and NEK in full operation, in the
HPP Mokrice profile the average river water
temperature will reach in critical conditions
26.73 °C in Case C1, and 27.0 in Case C
which gives a difference of 0.27 °C. In
extreme conditions the temperature shall reach
28.03 °C in Case C1, and 28.19 °C in Case C
which gives the difference of only 0.16 °C. It
is here evident again that at higher absolute
river water temperatures the differences
between alternatives are smaller. The same
rule is valid for the impact of TET+ or in
comparison with the zero state without the
TET unit. The difference between Cases C and
C1 at HPP Mokrice, with TET+ and NEK
operating in critical conditions reach 0.24 °C,
and 0.15 °C in extreme conditions. If TET is
out of operation while NEK is operating, the
difference between Cases C and C1 at Mokrice
reaches 0.33 °C in critical conditions and 0.18
°C in extreme conditions.
4.5 CASE D: WINTER CONDITIONS
AFTER HPPS CHAIN CONSTRUCTION
The purpose of calculating Case D was to
evaluate the cooling capacities of future
reservoirs in case of winter low flows. Trial
simulations of the HOTRIVER model with
data for November 27 and 28, 1995, showed
very weak matching of computational results
and measurements at NEK. A conclusion was
that a model, calibrated by average (summer)
air and water temperatures between 15–20 ºC
cannot simulate the conditions at the average
of 0–5ºC (winter) at a satisfactory level. The
basic obstacle in simulating winter thermal
state of the river was in the lack of river
thermal state measurements during cool period
of the year. To obtain a satisfactory model
calibration, measurements of input and outlet
temperatures at a certain river section for at
least two successive days or 24 hours at a
minimum shall be done, while the time period
used in our case was only somewhat longer
than 12 hours. This is why calculations of the

Širca, A.: Toplotna obremenitev Save po izgradnji spodnjesavskih stopenj – Thermal load of the Sava river after
construction of the lower Sava river cascade
© Acta hydrotechnica 22/36 (2004), 57–73, Ljubljana
69
tega so izra čuni re čne termike v hladnem
obdobju leta omejeni na poskus ocene hladilne
sposobnosti bazenov Brežice in Mokrice, ki
smo ga izvedli z obstoje čimi modeli in
nekaterimi predpostavkami.
V tem primeru za razliko od ostalih na
odseku brežiškega bazena dolvodno od NEK
in v bazenu Mokrice nismo predpostavili
popolnega mešanja, temve č smo upoštevali le
zgornji sloj debeline 2 m. S tem smo skušali
zajeti vpliv stratifikacije (HS-FGG, 1998), ki
bo v zimskih razmerah zanesljivo nastopil. Za
tako definiran površinski sloj smo
predpostavili ra čunski pretok 40 m
3
/s ter
zvišanje srednje februarske temperature 4,7 ºC
zaradi vpliva NEK za 3 ºC (na 7,7 ºC) oziroma
za 5 ºC (na 9,7 ºC). V takšnih razmerah bi na
odseku med NEK in HE Brežice v primeru
∆T = 3 ºC prišlo do ohlajanja sloja za –0,24
ºC, do HE Mokrice pa skupno za –0,30 ºC. V
primeru ∆T = 5 ºC bi ohlajanje do HE Brežice
znašalo –0,51 ºC, do HE Mokrice pa že –0,67
ºC.
V drugi seriji ra čunov smo predpostavili, da
zgornji, ogreti sloj debeline 2 m v bazenu
Brežice sega le do polovice širine, da se torej
po izpustu iz NEK drži levega brega. Temu
ustrezno je bil pretok sloja zmanjšan na 20
m
3
/s. V takšnem primeru bi na odseku med
NEK in HE Brežice pri ∆T = 3 ºC prišlo do
ohlajanja »polovi čnega« sloja za –0,22 ºC, v
primeru ∆T = 5 ºC pa za –0,51 ºC. Nadaljnje
ohlajanje do HE Mokrice v tem primeru ni bilo
ra čunano, saj je manj verjetno, da bi se oblak
tople vode držal levega brega še tudi po
prehodu pregrade HE Brežice. Približno
takšno stanje »polovi čne obremenjenosti« reke
je bilo za poletne razmere že tudi prognozirano
s 3D-modelom v študiji »Vpliv NE Krško na
obratovanje verige HE na spodnji Savi« (IBE,
1998). Hladilna kapaciteta bazena Brežice pri
tem ni bila ra čunana, kot tudi niso bile zaradi
pomanjkanja podatkov ra čunane splošne
razmere v hladnejšem delu leta (pozimi).
Predstavljeni aproksimativni rezultati
kažejo, da je ob ustreznih ukrepih (oblikovanje
objektov) in so časnem upoštevanju okoljske
regulative možno ra čunati na intenzivnejše
naravno hlajenje toplotno obremenjene savske
vode dolvodno od NEK. Podrobnejše in bolj
zanesljive rezultate bo mogo če dobiti po
river thermal state in the cool period of the
year have been limited only to an evaluation of
the cooling capacity of the Brežice and
Mokrice reservoirs which has been performed
with the existing models and some
presumptions.
In this case, and in contrast to the others, at
the Brežice reservoir section downstream NEK
and in the Mokrice reservoir no complete
mixing but only the upper layer of 2 m
thickness has been considered. In this way the
stratification effect (HS-FGG, 1998) which
definitely occurs in winter conditions has been
taken into account. For so defined surface
layer a calculated flow of 40 m
3
/s and an
increase of the average February temperature
of 4.7 ºC by 3 ºC (to 7.7 ºC) or by 5 ºC (to 9.7
ºC) being a consequence of NEK impact has
been presumed. In such circumstances, at a
section between NEK and HPP Brežice, in
case of ∆T = 3 ºC, the surface layer shall be
cooled down by –0.24 ºC, while down to HPP
Mokrice this cooling shall reach –0.30 ºC in
total. In case of ∆T = 5 ºC the cooling down to
HPP Brežice shall reach –0.51 ºC and down to
HPP Mokrice –0.67 ºC.
In the second calculation series it has been
presumed that the upper, warmed layer of 2
m thickness in the Brežice reservoir extends
only to the half of the reservoir width and
that it sticks to the left bank after the outflow
from NEK. Relevantly, the layer flow has been
reduced to 20 m
3
/s. In such case, between
NEK and the HPP Brežice, at ∆T=3 ºC,
cooling of the “half” layer by –0.22 ºC shall
occur and in case of ∆T = 5 ºC the temperature
shall decrease by –0.51 ºC. Further cooling
down to HPP Mokrice has not been calculated
for it is less possible that the warm plume
would stick to the left bank also after passing
through the HPP Brežice dam. A similar state
of »half thermal load« of the river has been
forecasted for summer conditions by using a
3D model in the study »NPP Krško impact on
the HPPs chain operation on the lower Sava
River« (IBE, 1998). The Brežice reservoir
cooling capacity as well as the conditions in
the cooler part of the year (winter), due to lack
of data, have not been calculated therein.
The presented approximative results show
that by suitable measures (design of structures)
and simultaneous consideration of
environmental legislation more intensive
natural cooling of the Sava water downstream
NEK can be expected. More detailed and
reliable results shall be obtained after the

Širca, A.: Toplotna obremenitev Save po izgradnji spodnjesavskih stopenj – Thermal load of the Sava river after
construction of the lower Sava river cascade
© Acta hydrotechnica 22/36 (2004), 57–73, Ljubljana
70
vzpostavitvi ustreznega monitoringa re čne
temperature pri HE Vrhovo in prilagoditvi
modela HOTRIVER / HOTCHAIN tudi za
hladno obdobje leta. Najbolj zanesljivo in
temeljito pa je možno izdelati podrobnejše
prognoze z nadaljnjimi ciljnimi obravnavami s
3D modelom PCFLOW3D, ki predhodno prav
tako zahteva verifikacijske podatke za zimsko
obdobje.
introduction of an adequate river water
temperature monitoring system at HPP Vrhovo
and adaptation of the HOTRIVER /
HOTCHAIN model for the cooler part of the
year as well. However, the most reliable and
thorough prognoses can definitely be done by
further PCFLOW3D 3D model targeted
investigations which nevertheless require
verification data for the winter period.
5. ZAKLJU ČEK
Srednje mese čne re čne temperature se
bodo na ra čun izgradnje verige HE malo
spremenile. Na zajetju NEK bodo prirastki
re čne T manjši od +0,5 °C (avgusta +0,42 °C).
V mejnem profilu bodo prirastki bolj opazni:
po izgradnji celotne verige HE bodo julija
znašali do +1,64 °C).
V času izrednih dogodkov bodo
spremembe bolj opazne, še zlasti po zaklju čku
gradnje celotne verige HE (primer C). Pri HE
Mokrice bodo prirastki srednje re čne
temperature v kriti čnih razmerah znašali od
+1,1 °C (primer B) do +2,1 °C (primer C), v
ekstremnih razmerah pa od +1,7 °C (primer B)
do +2,2 °C (primer C). Opazna bodo tudi
povišanja na zajetju NEK, in sicer +1,3 °C v
kriti čnih in do +2,0 °C v ekstremnih razmerah.
Pri NEK med primeroma B in C ni razlike v
rezultatih.
Zmanjšanje bazena Brežice v okvir
poplavnih nasipov (primer C1) povzro či
znižanje re čne T pri Mokricah za 0,3 °C v
kriti čnih in za 0,2 °C v ekstremnih razmerah.
Na nivoju srednjih mese čnih vrednosti
varianta C1 zaradi pri čakovanih minimalnih
razlik glede na varianto C ni bila obravnavana.
Vpliv obratovanja TET s sedanjo mo čjo
(stanje 2003) znaša v povpre čnih razmerah pri
NEK najve č +0,3 °C (v avgustu), kar se z
izgradnjo verige ne bo spremenilo. V kriti čnih
razmerah vpliva TET na re čno temperaturo pri
NEK v višini 0,43 °C, kar bo po izgradnji
verige naraslo na +0,45 °C. V ekstremnih
razmerah se bo razlika zaradi TET pri NEK
zmanjšala s sedanjih +0,6 °C na +0,49 °C.
Zmanjševanje razlike je posledica mo čnejše
izmenjave re čne toplote z atmosfero pri višjih
re čnih temperaturah. V profilu HE Mokrice je
5. CONCLUSIONS
As a consequence of the HPPs chain
construction average monthly river water
temperatures shall slightly differ. At the NEK
intake the water temperature increase shall not
exceed +0.5 °C (in August +0.42 °C). At the
state border the increase shall be more evident:
after construction of the complete HPPs chain
it shall reach up to +1.64 °C in July.
During exceptional events changes will be
more evident especially after construction of
the complete HPPs chain (Case C). At HPP
Mokrice the increase of the average water
temperature in critical conditions shall range
from +1.1 °C (Case B) to +2.1 °C (Case C)
while in extreme conditions it shall range from
+1.7 °C (Case B) to +2.2 °C (Case C).
Increase at NEK intake will be evident as well,
i.e. +1.3 °C in critical conditions and up to
+2.0 °C in the extreme ones. At NEK there is
no difference in results as regards Case B and
Case C.
Reduction of the Brežice reservoir within
the frame of flood embankments (Case C1)
shall cause reduction of water temperature at
Mokrice by 0.3 °C in critical conditions and by
0.2 °C in the extreme ones. Due to expected
minimal differences regarding the C
alternative, the C1 alternative has not been
treated on the level of average monthly values.
The TET operation impact at its present
power output (year 2003) and in average
conditions does not exceed +0.3 °C (in
August) at NEK which shall not change with
the HPPs chain construction. In critical
conditions the TET impact on the river water
temperature at NEK reaches 0.43 °C, which
shall increase to +0.45 °C after the HPPs chain
construction. In extreme conditions, the
difference caused by TET shall decrease at
NEK from the present +0.6 °C to +0.49 °C.
The difference decrease is a consequence of
greater river surface heat exchange at higher
river water temperatures. At the site of future
HPP Mokrice the present TET impact on the
average river water temperature does not

Širca, A.: Toplotna obremenitev Save po izgradnji spodnjesavskih stopenj – Thermal load of the Sava river after
construction of the lower Sava river cascade
© Acta hydrotechnica 22/36 (2004), 57–73, Ljubljana
71
sedanji vpliv TET na srednjo re čno
temperaturo najve č +0,30 °C (avgust) in bo po
izgradnji verige ostal nespremenjen. V
kriti čnih razmerah bo sedanji vpliv TET s
+0,36 °C padel na +0,20 °C po izgradnji
celotne verige in v ekstremnih razmerah s
sedanjih +0,49 °C na +0,35 °C po izgradnji
verige.
Razlika med TET+ in TET se pri NEK v
kriti čnih razmerah odraža z razliko srednje
re čne temperature +0,21 °C, v ekstremnih pa
+0,26 °C. Po izgradnji verige gorvodno od
NEK bo razlika v kriti čnih razmerah ostala
+0,21 °C, v ekstremnih pa se bo zmanjšala na
vrednost +0,21 °C. V profilu HE Mokrice je
potencialna sedanja razlika med TET+ in TET
+0,18 °C v kriti čnih in +0,21 °C v ekstremnih
razmerah, kar se bo po izgradnji celotne verige
zmanjšalo na +0,09 °C v kriti čnih in +0,17 °C
v ekstremnih razmerah. Manjša razlika pri
višjih absolutnih temperaturah je posledica
intenzivnejše toplotne izmenjave med reko in
ozra čjem. V primerjavi s predhodno študijo
TOPOS-TET3 (FGG, 1998) so ugotovljene
precej manjše razlike med TET+ in TET.
Razlogi za to so razlika v definicijah kriti čnih
in ekstremnih dogodkov, za zelo visoke re čne
temperature dodatno umerjeni modeli, to čnejše
vrednotenje vpliva NEK ter to čnejši izra čun
mešanja Save in Savinje v novejši študiji.
exceed +0.30 °C (August) and shall remain
unchanged after the chain construction. In
critical conditions after the construction of the
chain the present TET impact shall be cut
down from +0.36 °C to +0.20 °C and in
extreme conditions from the present +0.49 °C
to +0.35 °C.
The difference between TET+ and TET
at NEK is reflected by the difference of the
average river water temperature of +0.21 °C in
critical conditions and of +0.26 °C in the
extreme ones. After construction of the HPPs
chain the difference will remain +0.21 °C in
critical conditions, while in extreme contions it
shall decrease to the value of +0.21 °C. In the
HPP Mokrice profile the potential present
difference between TET+ and TET attains
+0.18 °C in critical conditions and +0.21 °C in
the extreme ones which shall be reduced after
construction of the complete HPPs chain to
+0.09 °C in critical and to +0.17 °C in the
extreme conditions. The smaller difference at
higher absolute temperatures is a consequence
of more intensive thermal exchange between
the river and the air. Compared with the
previous study TOPOS-TET3 (FGG, 1998)
considerably smaller differences between
TET+ and TET have been established. The
reason lies in the difference of critical and
extreme events definitions, additionally
calibrated models for extremely high river
water temperatures, more accurate evaluation
of the NEK impact and more accurate
calculation of the Sava and Savinja Rivers
mixing in the more recent Study.
ZAHV ALA
Članek je povzetek tehničnega dela študije
“Medsebojni vplivi energetskih objektov ob in
na reki Savi z vidika toplotne obremenitve
Save”, katere naro čnik je bilo Ministrstvo za
okolje, prostor in energijo. Zahvaljujemo se za
dovoljenje za objavo.
ACKNOWLEDGEMENTS
This paper is a summary of the technical
part of the study: “Interrelating impacts of
power producers by and on the Sava River
from the viewpoint of the river thermal loads”
which was financed by the Ministry of the
Environment, Spatial Planning and Energy.
Their publication permission is gratefully
acknowledged.
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Naslov avtorja – Author's Address
doc. dr. Andrej ŠIRCA
IBE – Inženirski biro Elektroprojekt – IBE, Consulting Engineers
Hajdrihova 2, SI-1000 Ljubljana, Slovenia
E-mail: andrej.sirca@ibe.si