© Acta hydrotechnica 18/28 (2000), Ljubljana
ISSN 1581-0267
61
UDK: 627.84 UDC: 627.84
Strokovni prispevek Professional paper
HIDRA VLIČ NA PRESOJA VODOSTANA HE PLA VE II
HYDRAULIC EV ALUATION OF THE HPP PLA VE II SURGE TANK
Primož RODIČ Prispevek prinaša opis in rezultate hidravlič ne presoje vodostana elektrarne HE Plave II na reki
Soč i, zaradi spremenjenih geometrijskih in hidravlič nih lastnosti sistema glede na predhodno
študijo. Opisane so različ ne možnosti obratovanja turbine: na konstantni pretok, na konstantno moč in na konstantno odprtje. Na podlagi študije so bile, ob upoštevanju dovoljenega najnižjega in
najvišjega nivoja gladine v vodostanu, z matematič nim modelom določ ene nove, več je vrednosti
koeficientov upora dušilke.
Ključ ne besede: HE Plave, vodostan, dušilka, robni pogoji, masne oscilacije
This paper describes and brings the results of the hydraulic evaluation of the HPP Plave II surge
tank on the Soč a River owing to the hydraulic and geometric characteristics changeover with
regard to the preliminary study. Three different turbine operation possibilities are described:
constant discharge operation; constant power operation and constant wicket gates opening
operation. On the basis of this study considering the maximum and minimum permissible water
levels in the surge tank with the mathematical model, the new, highest values of the throttle
damping characteristics were evaluated.
Key words: HPP Plave, surge tank, throttle, boundary conditions, mass oscillations
1. UVOD
Na reki Soč i obratujejo tri več je elektrarne:
HE Plave I, HE Doblar I in HE Solkan.
Vzporedno s starima elektrarnama HE Plave I
in HE Doblar I gradijo novi tlač no-derivacijski
elektrarni HE Plave II in HE Doblar II, ki
bosta izkoristili zajem vode v obstoječ ih
akumulacijah, vendar z lastnim zajetjem, s
cevovodom, z vodostanom in s strojnico.
V prejšnjih študijah so bili določ eni
temeljni geometrijski parametri obeh
vodostanov in vrednosti uporov dušilk. Ker je
prišlo v obdobju projektiranja vodostana HE
Plave II do nekaterih geometrijskih sprememb
in ker se je pri graditvi dovodnega tunela
pokazala verjetnost večje hrapavosti od
predvidene, posledič no, med drugim, več jega
padca gladine v vodostanu pri zagonu turbine,
je bila upravič ena potreba po novi hidravlič ni
presoji.
1. INTRODUCTION
Three large hydro power plants are already
in operation on the Soč a River: HPP Plave I;
HPP Doblar I and HPP Solkan. Parallel with
the old ones, HPP Plave I and HPP Doblar I,
the new pressure-diversion hydro power plants
HPP Plave II and HPP Doblar II, with water
supplies in the existing storage reservoirs, but
with their own intakes, tunnels, surge tanks
and power stations, are under construction.
In the preliminary studies, the basic surge
tank geometry parameters and throttles
damping characteristics were defined. During
the project time of the HPP Plave II surge
tank, some geometric modifications were
established, while during the pressure tunnel
construction, a likelihood of increased
roughness was proved, which means a greater
water level fall in the surge tank. For these
reasons, a new hydraulic evaluation was
justified.

Rodič , P.: Hidravlič na presoja vodostana HE Plave II - Hydraulic Evaluation of the HPP Plave II Surge Tank
© Acta hydrotechnica 18/28 (2000), 61-73, Ljubljana
62
2. OPIS STARE IN NOVE
ELEKTRARNE HE PLA VE I IN HE
PLA VE II
Zajetje HE Plave I je postavljeno na
desnem bregu reke Soč e tik ob pregradi Ajba.
V dovodnem tunelu, dolžine 6 km, teč e voda s
prosto gladino. Na zač etku in na koncu je
opremljen z boč nima prelivoma in šele tik
pred strojnico preide v tlačni cevovod.
Vodostana torej ni, saj se v primeru zapiranja
turbine oblikuje povratni val, ki potuje nazaj
po dovodnem tunelu oz. se voda preliva preko
spodnjega boč nega preliva. V strojnici je
vgrajena Kaplanova turbina z instaliranim
pretokom 75 m
3
/s in generator z instalirano
moč jo 1 5 MW.
V nasprotju s staro elektrarno teč e voda v
dovodnem tunelu HE Plave II (slika 1), ki ima
premer 6.4 m in je dolg 5990 m, pod tlakom.
Novo zajetje je postavljeno tik ob obstoječ em.
Na koncu dovodnega tunela je predviden spoj
s spodnjo vodostansko komoro. Ta je
podkvastega prereza, širok in visok v osi 5.0
m; na oddaljenosti 102 m od spoja se razcepi
na dva kraka, dolga 20 m, do dveh vertikalnih
cilindrič nih jaškov s premerom 26.22 m in
višine od dna komore ob jašku do pete kalote
20.04 m. Dovod se proti strojnici nadaljuje kot
tlač ni cevovod dolžine 1 83 m, od tega 92 m s
premerom 6.4 m in 81 m s premerom 5.5 m.
Tudi v novi strojnici je predvidena Kaplanova
turbina. Instalirani pretok nove elektrarne HE
Plave II je 105 m
3
/s, bruto padec 26.92 m in
največ ja moč agregata 20.5 MW.
3. VLOGA VODOSTANA V
SISTEMU DERIV ACIJSKE
ELEKTRARNE
Vodostan je postavljen na mestu med
obič ajno le rahlo nagnjenim daljšim dovodnim
tunelom pod tlakom in strmo padajoč im
tlač nim cevovodom. Gre za objekt, ki lahko
sprejme in odda relativno velike količ ine vode.
Odvisno od parametrov, lastnih vsakemu
sistemu posebej, obstajajo različ ne oblike
vodostanov: od najbolj preprostih, cilindrič nih,
do zahtevnejših, s komorami, prelivi in z
dušilkami.
2. HPP PLA VE I AND HPP PLA VE
II DESCRIPTION
The HPP Plave I intake is located on the
right bank of the Soč a River, close to the Ajba
Dam. The free surface water diversion tunnel
is of 6 km length, with side weirs at the
beginning and at the ending, and only close to
the power station does it convert into penstock.
There is no surge tank, because in case of the
turbine closing, the return positive wave forms
and water spills over the lower side of the
weir. In the power station, a vertical Kaplan
turbine with a rated discharge of 75 m
3
/s and a
generator with a rated power of 15 MW are
built in.
Unlike HPP Plave I, HPP Plave II (Figure 1)
has a low pressure diversion tunnel of 5990 m
length and 6.4 m diameter. The new intake is
located close to the old one. At the end of the
pressure tunnel, a connection with the lower
expansion chamber is foreseen. It is horseshoe
shaped, with a width and height of 5.0 m; 102
m from the connection point it divides into two
legs of 20 m length, to the surge shafts with a
26.22 m diameter and a 20.04 m height. The
diversion tunnel continues to the power station
as a penstock with a 183 m length, and a 92 m
by 6.4 m and 81 m by 5.5 m diameter. In the
power station, a vertical Kaplan turbine is also
foreseen. The rated discharge of the new HPP
Plave II is 105 m
3
/s, the gross head, 26.92 m
and the maximum power, 20.5 MW.
3. SURGE TANK ROLE IN THE
SYSTEM OF A DIVERSION TYPE
HYDRO POWERPLANT
The surge tank is located between the
slightly inclined pressure conduit and the
steeply sloping penstock. It can intercept or
give away a relatively large amount of water.
Dependant on the system parameters, the surge
tank could be very simple, cylindrical, or more
complicated, with expansion chambers, weirs
and restricted orifices, i.e., throttles.

Rodič , P.: Hidravlič na presoja vodostana HE Plave II - Hydraulic Evaluation of the HPP Plave II Surge Tank
© Acta hydrotechnica 18/28 (2000), 61-73, Ljubljana
63
Slika 1 . Situacija in vzdolžni prerez od vodostana do strojnice HE Plave II.
Figure 1. Ground plan and cross section from surge tank to HPP Plave II Power Station.
V sistemu derivacijske elektrarne je vloga
vodostana naslednja:
− pred vodnim udarom šč iti dovodni tunel in
tlač ni cevovod (zmanjšanje amplitud tlač nih
valov v tlač nem cevovodu ugodno vpliva na
stabilnost regulacije vodilnika in kontrolo
hitrosti gonilnika),
− v primeru zapiranja turbine sprejme razliko
dotoka vode iz dovodnega tunela in odtoka
skozi tlač ni cevovod,
− v primeru odpiranja hitro zagotavlja
potrebo po več jem pretoku.
Vodostan mora biti projektiran tako, da  so
oscilacije nivoja gladine oz. piezometrič nega
tlaka pod dušilko tudi v primeru obratovanja
na konstantno moč (pogl. 4.3.1 ) dušene (to je
t.i. hidravlič na stabilnost vodostana) in da so
amplitude znotraj predpisanih meja.
The surge tank role in the system of the
diversion type hydro power plant is:
− it protects the pressure tunnel and the
penstock from pressure surges due to water
hammering (the pressure surge reduction
has a good influence on the wicket gate
regulation stability and the turbine speed
control),
− in the case of turbine closing, it intercepts
the difference between the inflow through
the pressure tunnel and the outflow through
the penstock,
− in the case of turbine opening, it assures the
need of a larger discharge.
The oscillations of water level and
piezometric pressure under the throttle,
respectively, are damped in the properly
projected surge tank, even in he case of
constant power operation (sect. 4.3.1) (this is
so-called hydraulic stability) with amplitudes
within the regulation area.

Rodič , P.: Hidravlič na presoja vodostana HE Plave II - Hydraulic Evaluation of the HPP Plave II Surge Tank
© Acta hydrotechnica 18/28 (2000), 61-73, Ljubljana
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Da bi bile oscilacije zagotovo dušene, je
potrebno izpolniti dva kriterija:
− Thomov kriterij, ki določa najmanjši
potrebni horizontalni presek vodostana, ki
se nato zaradi varnosti navadno poveč a za
50 do 80 odstotkov:
In order that the oscillations should be
damped, two conditions must be carry out:
− Thoma’s criterion, which defines the least
necessary surge tank horizontal cross
section (which could be enlarged by 50 –
80% for safety’s sake):
1 1 2
1 1 2
2 R H A g
Q L
A
neto
⋅ ⋅ ⋅
⋅
> (1)
− kriterij hidravlič nih izgub: − hydraulic losses criterion:
3
1 br
H
R < (2)
pri č emer pomeni:
A
2
horizontalni presek vodostana, [m
2
]
A
1
presek dovodnega tunela, [m
2
]
L
1
dolžina dovodnega tunela, [m]
Q
1
pretok v dovodnem tunelu, [m
3
/s]
g zemeljski pospešek, [s/m
2
]
H
br
bruto padec, [m]
R
1
vsota hidravlič nih izgub v dovodnem
tunelu, [m]
H
neto
neto padec (= H
br
 – R
1
), [m].
4. OSNOVNE ENAČ BE IN ROBNI
POGOJI ZA RAČ UN MASNIH
OSCILACIJ V VODOSTANU
4.1 DINAMIČ NA ENAČ BA
Dinamič na enač ba opisuje tok vode v
dovodnem tunelu, pri č emer se vztrajnost
vodne mase v vodostanu zaradi relativno
majhnih hitrosti zanemari. Enač ba, zapisana v
obliki za numerič no reševanje, je naslednja:
where it means:
A
2
horizontal cross section, [m
2
]
A
1
pressure tunnel cross section, [m
2
]
L
1
pressure tunnel length, [m]
Q
1
pressure tunnel discharge, [m
3
/s]
g gravitational acceleration, [s/m
2
]
H
br
gross head, [m]
R
1
pressure tunnel hydraulic losses sum,
[m]
H
neto
net head (= H
br
 – R
1
), [m].
4. BASIC EQUATIONS AND
BOUNDARY CONDITIONS FOR
THE CALCULATION OF MASS
OSCILLATIONS IN THE SURGE
TANKS
4.1 DYNAMIC EQUATION
The dynamic equation describes the water
flow in the pressure tunnel, where the water
mass persistence in the surge tank is neglected
due to relatively small velocities. The
equation, arranged for numerical calculation,
is:
t H
L
A g
Q
a
∆ ⋅ ⋅
⋅
− = ∆ 1 1 1 (3)
2 2 2 1 1 1 Q Q r Q Q r z H
a
− + = (4)

Rodič , P.: Hidravlič na presoja vodostana HE Plave II - Hydraulic Evaluation of the HPP Plave II Surge Tank
© Acta hydrotechnica 18/28 (2000), 61-73, Ljubljana
65
pri čemer, poleg že zgoraj opisanih
parametrov, pomeni še:
Δ Q
1
sprememba pretoka v dovodnem tunelu,
[m
3
/s]
H
a
pospešna (akceleracijska) višina, ki je
razlika med trenutnim nivojem gladine
oz. piezometrič neim tlakom pod dušilko
in tistim nivojem gladine, ki bi se
vzpostavil v vodostanu, če bi v
dovodnem tunelu ves č as tekel trenutni
pretok Q
1
, [m]
z odmik nivoja gladine v vodostanu od
nivoja zgornje vode, [m]
r
1
koeficient hidravličnega upora v
dovodnem tunelu, [s
2
/m
5
]
r
2
koeficient upora dušilke, [s
2
/m
5
]
Q
2
pretok v vodostanu, [m
3
/s]
Δ t č asovni korak, [s].
4.2 KONTINUITETNA ENAČ BA
Kontinuitetna enač ba opisuje dejstvo, da je
algebraič na vsota vseh pretokov na spoju
dovodnega tunela, vodostana in tlač nega
cevovoda enaka 0:
where it means:
Δ Q
1
change of discharge in the pressure
tunnel, [m
3
/s]
H
a
accelerating height as the difference
between the momentary water level or
piezometric pressure level under the
throttle and that water level which would
re-establish, if the discharge in the
pressure tunnel would be the momentary
disharge Q
1
 all the time, [m]
z water level deviation in the surge tank
from the headwater level, [m]
r
1
hydraulic resistance coefficient in the
pressure tunnel, [s
2
/m
5
]
r
2
throttle damping coefficient, [s
2
/m
5
]
Q
2
surge tank discharge,  [m
3
/s]
Δ t time step, [s].
4.2 CONTINUITY EQUATION
The continuity equation describes the fact
that the algebraic sum of all discharges at the
junction of the pressure tunnel, surge tank and
penstock are equal to zero:
0
3 2 1 = + + Q Q Q (5)
t
z
A Q
∆ ∆ − =
2 2
(6)
pri č emer pomeni še:
Q
3
pretok v tlač nem cevovodu oz. skozi
turbino, [m
3
/s]
Δ z sprememba gladine v vodostanu, [m].
4.3 ROBNI POGOJI
Levi (zgornji) robni pogoj predstavlja tako
rekoč konstantna kota zajezbe. Desni (spodnji)
robni pogoj pa predstavlja pretok Q
3
 skozi
turbino.
Na sliki 2 je predstavljen diagram, v
katerem so poleg krivulje vseh hidravlič nih
izgub (*) na dovodnem tunelu in tlač nem
cevovodu vrisane tri znač ilne krivulje, ki
predstavljajo tri različ ne možnosti obratovanja
turbine: na konstantno moč (I), na konstantni
pretok (II) in na konstantno odprtje (III).
where also means:
Q
3
penstock (turbine) discharge, [m
3
/s]
Δ z change of water level in the surge tank,
[m]
4.3 BOUNDARY CONDITIONS
The left (upper) boundary condition is the
practically constant headwater level. The right
(lower) boundary condition is the discharge Q
3
through the turbine.
Figure 2 presents the diagram, whereby the
side of the resistance curve (*), three
characteristic curves, which represent three
different possibilities of the turbine operation,
are drawn into: constant power operation (I),
constant discharge operation (II) and constant
wicket gate opening operation (III).

Rodič , P.: Hidravlič na presoja vodostana HE Plave II - Hydraulic Evaluation of the HPP Plave II Surge Tank
© Acta hydrotechnica 18/28 (2000), 61-73, Ljubljana
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Slika 2.
Figure 2.
4.3.1 OBRATOVANJE NA KONSTANTNO
MOČ Prehod obratovanja elektrarne na novo moč ,
ki jo zahteva električ no omrežje, pomeni tudi
prehod iz starega v novo dinamič no
ravnovesje. Zaradi tega se v vodostanu
sprožijo masne oscilacije oz. temu ustrezne
oscilacije tlaka na turbini. Da bi elektrarna že
takoj po začetnem izvedenem manevru
spremembe položaja vodilnika konstantno
obratovala z novo moč jo, mora vodilnik ves
č as poveč evati oz. zmanjševati pretok skozi
turbino po naslednji zakonitosti:
4.3.1 CONSTANT POWER OPERATION:
The transition of the power plant operation
to the new power on the demand of the electric
network, also means the transition from the old
to the new dynamic equilibrium. The
consequences are mass oscillations in the
surge tank and pressure oscillations on the
turbine. In order to operate on the constant
new power immediately after the starting
manoeuvre of changing the wicket gates
position, the wicket gates must constantly
magnify and reduce discharge through the
turbine by the following equation.
H c
N
Q
⋅
=
3
(7)
kjer pomeni:
N zahtevana konstantna moč , [MW]
H tlak na turbini, [m]
c spremenljivka, v kateri je vključ en
koeficient izkoristka agregata (v tej
študiji upoštevan kot konstanten).
where it means:
N demanded constant power, [MW]
H pressure on the turbine, [m]
c parameter with included unit efficiency
(here adopted as constant)
Rr H
Hbr
P1
P1'
P0
P2'
P2
+z
-z
Q
III
II
I
Hbr / 3
*
H c
N
Q
3
⋅
=
. konst Q Q
30 3
= =
H g 2 A Q
vodilnik 3
⋅ =

Rodič , P.: Hidravlič na presoja vodostana HE Plave II - Hydraulic Evaluation of the HPP Plave II Surge Tank
© Acta hydrotechnica 18/28 (2000), 61-73, Ljubljana
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Manjši padec zahteva več ji pretok in
obratno, kot je razvidno iz krivulje moč i (I) na
sliki 2. Ta sicer seka krivuljo hidravlič nih
izgub v dveh toč kah P
1
 in P
2
. Ti predstavljata
mogoč i kombinaciji pretoka in tlaka na turbini,
ob zahtevani moč i v stanju dinamič nega
ravnovesja. S poveč evanjem moč i se toč ki P
1
in P
2
 približujeta (na diagramu P
1
' in P
2
') in se
v skrajnem primeru največ je mogoč e dosežene
moč i sreč ata v toč ki P
0
, v kateri se krivulji
hidravlič nih izgub in moč i le še dotakneta. V
tem primeru je vsota hidravlič nih izgub enaka
eni tretjini bruto padca.
Č eprav pride v poštev samo dinamič no
ravnovesje, ki ga predstavlja toč ka P
1
, pa v
splošnem vedno obstaja tudi dinamič no
ravnovesje okoli toč ke P
2
. V primeru, da sta si
ti dve toč ki preblizu, lahko ob več jem padcu
gladine v vodostanu vlogo novega
dinamič nega ravnovesja prevzame prav toč ka
P
2
, kar vodi v izpraznitev vodostana oz. v t.i.
hidravlič ni kolaps.
4.3.2 OBRATOVANJE NA KONSTANTNI
PRETOK
A lower head demands a higher discharge,
and the opposite, as seen from the power curve
(I) on Figure 2. It intersects the resistance
curve at the two points P
1
 in P
2
. They represent
possible combinations of discharge and
pressure on the turbine in the state of dynamic
equilibrium. With power magnifying, P
1
 and
P
2
 come near each other (P
1
' in P
2
' on the
diagram) to meet at the point P
0
 in the case of
necessity, when the power takes the peak value
and both curves only touch each other. In that
case, the hydraulic losses sum is equal to one
third of a gross head.
Although only the dynamic equilibrium
which represents the point P
1 
is relevant, in the
general case, there always exists, as well, the
dynamic equilibrium with the point P
2
. In case
P
1
 and P
2
 are too close to each other, and if the
water level in the surge tank drops too much,
the point P
2
 takes over the role of the new
dynamic equilibrium, which can lead to the
emptying of the surge tank, as called hydraulic
collapse.
4.3.2 CONSTANT DISCHARGE
OPERATION
.
30 3
konst Q Q = = (8)
Vzdrževanje konstantnega pretoka vsekakor
zagotavlja stabilno obratovanje, saj premica
(II) seka krivuljo hidravlič nih izgub samo v
eni toč ki P
1
, v kateri se vzpostavi novo
dinamič no ravnotežje. Zaradi oscilacij gladin v
vodostanu oz. piezometričnih tlakov pod
dušilko v prehodnem obdobju oscilira tudi
moč .
V praksi se takšno obratovanje ne izvaja;
uporablja se ga zgolj kot preprostejši robni
pogoj pri računih masnih oscilacij v
vodostanih visokotlač nih hidroelektrarn. Ta
pogoj je bil upoštevan pri določ itvi prvotnih
vrednosti upora dušilke.
4.3.3 OBRATOVANJE NA KONSTANTNO
ODPRTJE
The constan discharge operation, anyway,
assures stabile operation, because the line (II)
intersects the resistance curve only at one
point P
1
, which represents the new dynamic
equilibrium. Owing to water level oscillations
in the surge tank, as well as and piezometric
pressure, oscillations under the throttle
temporarily oscillate the power too.
This way of operation is completely
inconvenient in the praxis. It is usable only as
the simplest boundary condition at mass
oscillations calculation for high head hydro
power plants. In the preliminary study this
condition was considered.
4.3.3 CONSTANT WICKET GATES
OPENING OPERATION
H g A Q
ik vodi
⋅ = 2
ln 3
(9)

Rodič , P.: Hidravlič na presoja vodostana HE Plave II - Hydraulic Evaluation of the HPP Plave II Surge Tank
© Acta hydrotechnica 18/28 (2000), 61-73, Ljubljana
68
kjer pomeni:
A
vodilnik
efektivna velikost odprtja vodilnika
(t.j. ob upoštevanju koeficienta
pretoka, [m
2
].
Obratovanje na konstantno odprtje je prav
tako stabilno obratovanje, saj tudi v tem
primeru krivulja (III) seka krivuljo
hidravlič nih izgub v eni sami toč ki. Znač ilnost
takšnega obratovanja je najhitrejša
vzpostavitev novega dinamič nega ravnovesja,
saj s padcem tlaka pade tudi pretok in obratno.
Obratovanje na konstantno odprtje je
preprosto, saj se že na zač etku nastavi položaj
vodilnika na končno odprtje. Takšno
obratovanje je nemenjeno elektrarnam, ki
imajo manjši delež v sistemu proizvodnje
električ ne energije, saj so oscilacije moč i tu
največ je.
5. RAČ UN IN REZULTATI
HIDRA VLIČ NE PRESOJE
VODOSTANA HE PLA VE II
5.1 TEMELJNI PODATKI
instalirani pretok Q
inst
: 105 m
3
/s,
največ ja kota zgornje vode, upoštevana v
hidravlič ni presoji: 1 06.00 m n.m.
najmanjša kota zgornje vode: 104.00 m n.m.,
najmanjša kota spodnje vode: 77.58 m n.m.
nominalni neto padec H
nom
: 18.23 m.
nominalna moč N
nom
: 17.4 MW,
največ ja moč N
max
: 20.5 MW
5.2 MANEVRI IN REGULACIJA
Manever pomeni spremembo odprtja
vodilnika in položaja lopatice gonilnika zaradi
spremembe obremenitve. Na zač etku se izvaja
po predvideni odvisnosti od časa, v
nadaljevanju pa v odvisnosti od trenutnega
padca na turbini oz. pogoja vzdrževanja (nove)
konstantne moč i po enač bi, poenostavljeni z
upoštevanim konstantnim izkoristkom
agregata:
where it means:
A
vodilnik
effective wicket gates opening (with
consideration of discharge
coefficient), [m
2
]
The constant wicket gates opening
operation is a stabile operation because the
curve (III) intersects the resistance curve at
only one point. Its main characteristic is that it
is the fastest way to take up the new dynamic
equilibrium; namely, when the water level
falls, the discharge falls too, and, to the
contrary, they rise together.
The constant wicket gates opening
operation is very simple because, just in the
beginning, the wicket gates are setting up to
the new position. This way of operation is
usable for the power plant with a smaller share
in the electric energy production, because
power oscillations are the highest here.
5. CALCULATION AND RESULTS
OF THE HYDRAULIC
EV ALUATION OF THE HPP
PLA VE II SURGE TANK
5.1 BASIC DATA
rated discharge Q
inst
: 105 m
3
/s,
maximum headwater level, considered in
hydraulic evaluation: 106.00 m n.m.
minimum headwater level: 104.00 m n.m.,
minimum tail water level: 77.58 m n.m.
rated net height H
nom
: 18.23 m.
rated power N
nom
: 17.4 MW,
maximum power N
max
: 20.5 MW
5.2 MANOEUVRE AND REGULATION
Manoeuvre means the wicket gates open
and the runner blade position changes because
of the load change. It is dependant on time, at
the beginning, and then dependant on the
momentary turbine head by the equation with
an adopted constant unit efficiency:
H c
N
Q
⋅
=
3
(10)

Rodič , P.: Hidravlič na presoja vodostana HE Plave II - Hydraulic Evaluation of the HPP Plave II Surge Tank
© Acta hydrotechnica 18/28 (2000), 61-73, Ljubljana
69
Pri tem se upošteva največ ja mogoč a
nastavitev odprtja vodilnika A
100%
:
It  takes into consideration the highest
possibly wicket gate opening A
100%
:
nom
inst
H g
Q
A
⋅
=
2
% 1 00
(11)
V konkretnem izrač unu je sicer za zač etna
manevra odpiranja oz. zapiranja, ki sta odvisna
samo od č asa, upoštevana naslednja dinamika:
− linearno odpiranje vodilnika od 0 do 100
odstotkov v 35s
− zapiranje vodilnika v dveh linearnih
sekvencah od 100 do 30 odstotkov v 10.5s
in od 30 do 0 odstotkov v 14.5s.
5.3 KRITERIJI ZA DOLOČ ITEV
NAJVEČ JE IN NAJMANJŠE GLADINE V
VODOSTANU
Največ ja gladina v vodostanu je določ ena
kot največ ja dosežena gladina za primer
zaporednih manevrov odpiranja in zapiranja
med 0 in 1 00 odstotki največ je moč i N
max
, z
upoštevanjem najmanj 15-minutnega
č akalnega č asa med zapiranjem in zač etkom
vnovič nega odpiranja. Pri tem je upoštevana
kota zgornje vode 106.00 m n.m., kota spodnje
vode 77.58 m n.m. in koeficient hrapavosti
0.012. Kota gladine v vodostanu ne sme
preseč i kote 11 3.0 m n.m., ki predstavlja
najvišjo koto vodostanskega jaška,
piezometrič na kota pod dušilko pa ne sme
preseč i kote 11 8.0 m n.m.
Najmanjša gladina v vodostanu je določ ena
kot najnižja dosežena gladina za primer
zaporednih manevrov odpiranja in zapiranja
med 0 in 1 00 odstotki največ je moč i N
max
 z
upoštevanjem najmanj 15-minutnega
č akalnega č asa med zapiranjem in zač etkom
vnovič nega odpiranja. Pri tem je upoštevana
kota zgornje vode 104.00 m n.m., kota spodnje
vode 77.58 m n.m. in koeficient hrapavosti
cevovodov 0.016. Kota gladine v vodostanu ne
sme biti nižja od kote 93.1 m n.m.,
piezometrič na kota pod dušilko pa ne sme biti
nižja od kote temena dovodnega tunela na
priključ ku vodostana 87.2 m n.m.
V primeru zaporednih manevrov je za
začetek vsakega naslednjega manevra
odloč ilen tisti trenutek, ki v naslednjem nihaju
daje ekstremne vrednosti nivojev gladin.
In the concrete calculation, the following
starting manoeuvres dynamics were
considered:
− linear wicket gates opening from 0% to
100% in 35s
− wicket gates closing in two linear sequences
from 100% to 30% in 10.5s and 30% to 0%
in 14.5s.
5.3 MAXIMUM AND MINIMUM WATER
LEVEL CRITERIONS IN THE SURGE
TANK
The maximum water level in the surge tank
is defined as the highest level in the case of a
series of openings and closings between 0%
and 100% maximal power N
max
, with at least
15 minutes consideration of waiting time
between the closing and the start of the
renewed opening. The head level water of
106.00 m a.s.l., tail water level water of 77.58
m a.s.l. and Manning’s resistance coefficient
of 0.012 must be considered in its calculation.
The water level must not exceed 113.0 m a.s.l.,
which represents the highest surge tank level,
and the piezometric pressure level under the
throttle must not exceed 118.0 m a.s.l.
The minimum water level in the surge tank
is defined as the lowest level in the case of a
series of openings and closings between 0%
and 100% maximal power N
max,
 with at least
15 minutes consideration of waiting time
between the closing and the start of the
renewed opening. The head level water of
104.00 m a.s.l., tail water level water of 77.58
m a.s.l. and Manning’s resistance coefficient
of 0.016 must be considered in its calculation.
The water level must not be lower than 93.1 m
a.s.l., and the piezometric pressure level under
the throttle must not be lower than  87.2 m
a.s.l., which represents the top of the pressure
tunnel under the throttle.
The starting time for each following
manoeuvre is the moment which gives the
peak value in the next surge.

Rodič , P.: Hidravlič na presoja vodostana HE Plave II - Hydraulic Evaluation of the HPP Plave II Surge Tank
© Acta hydrotechnica 18/28 (2000), 61-73, Ljubljana
70
5.4 REZULTATI
Kljub temu, da naj bi se po vsebini iz toč ke
5.3 upošteval najmanj 1 5-minutni č akalni č as
med zapiranjem in začetkom vnovič nega
odpiranja, je izvedena hidravlič na presoja s
strožjim kriterijem, in sicer kadarkoli se zač ne
vnovič no odpiranje. Gre sicer za ekstremen in
neobič ajen, vendar v praksi izvedljiv primer,
ki ga mora biti elektrarna zaradi varnosti
sposobna prenesti.
Rezultat hidravlične presoje sta novi
vrednosti upora dušilke, ki sta v skladu s
pogoji iz toč ke 5.3. Njuni vrednosti sta:
− pri vtekanju v vodostan r
vtok
: 0.00125 s
2
/m
5
− pri iztekanju iz vodostana r
iztok
:
0.00078 s
2
/m
5
.
Rezultati hidravlič ne presoje so prikazani
tudi v obliki diagramov oscilacij gladin
(poudarjena krivulja) in piezometrič nih tlakov
pod dušilko.
5.4.1 NAJVEČ JI DVIG IN PADEC
GLADINE PRI NEUPOŠTEVANJU
NAJMANJ 1 5-MINUTNEGA Č AKALNEGA
Č ASA
Dvig gladine tako v drugem nihaju kot v
tretjem nihaju znaša 112.98 m n.m.,
piezometrič nega tlaka pa 11 6.22 m n.m. (v
drugem nihaju) (slika 3). Največ ji padec
gladine znaša v obeh nihajih 93.16 m n.m.,
piezometrič nega tlaka pa 92.25 m n.m. (slika
4)
5.4 RESULTS
In spite of the criterion in sect. 5.3,  which
defines 15 minutes waiting time between the
closing and the start of renewed opening, the
hydraulic evaluation was carried out with
rigorous criterion, which permits the starting
time anytime. Actually, this is extreme and
unusual, but within the praxis, a completely
realisable case which the power plant must
stand  for the sake of safety.
The results of the hydraulics evaluation are
new values of the throttle damping
characteristics. These are:
− when water flows into the surge tank r
vtok
:
0.00125 s
2
/m
5
− when water flows out of  the surge tank
r
iztok
: 0.00078 s
2
/m
5
.
The result of the hydraulic evaluation are
also shown in the diagrams of the water level
oscillations bold curve) and the piezometric
pressure oscillations.
5.4.1 MAXIMAL WATER LEVEL RISE
AND FALL WITHOUT 15 MINUTES
WAITING TIME.
The maximal water level rise, equal in the
second and third surge, is 112.98 m a.s.l.; the
piezometric pressure rise is 116.22 m a.s.l. (in
the second surge) (Figure 3). The maximal
water level fall is 93.16 m a.s.l., and the
maximal piezometric pressure fall is 92.25 m
a.s.l. (Figure 4), both in the second and third
surges.
5.4.2 NAJVEČ JI DVIG IN PADEC
GLADINE PRI UPOŠTEVANJU NAJMANJ
1 5 MINUTNEGA Č AKALNEGA Č ASA
Največ ji dvig gladine znaša 11 2.95 m n.m.,
piezometrič nega tlaka pa 11 6.07 m n.m.
(slika 5). Največ ji padec gladine znaša 93.60
m n.m., piezometrič nega tlaka pa 93.50 m n.m.
(slika 6).
5.4.2 MAXIMAL WATER LEVEL RISE
AND FALL WITH 15 MINUTES WAITING
TIME
The maximal water level rise is 112.95 m
a.s.l., and the maximal piezometric pressure
rise is 116.07 m a.s.l. (Figure 5). The maximal
water level fall is 93.60 m n.m., and the
maximal piezometric pressure fall is 93.50 m
a.s.l. (Figure 6).

Rodič , P.: Hidravlič na presoja vodostana HE Plave II - Hydraulic Evaluation of the HPP Plave II Surge Tank
© Acta hydrotechnica 18/28 (2000), 61-73, Ljubljana
71
Slika 3. Maksimalni dvig gladine pri neupoštevanju najmanj 1 5 minutnega č akalnega č asa.
Figure 3. Maximal water level rise without 15 minutes waiting time.
Slika 4. Maksimalni padec gladine pri neupoštevanju najmanj 1 5 minutnega č akalnega č asa.
Figure 4. Maximal water level fall without 15 minutes waiting time.
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
0:00 0:05 0:10 0:15 0:20 0:25 0:30 0:35 0:40 0:45 0:50 0:55 1:00
č as [ura:min] / time [hr:min]
kota [m n.m.] / level [m s.l.]
gladina / w ater level piezometrič ni tlak pod dušilko / piezometric pressure under the throttle
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
0:00 0:05 0:10 0:15 0:20 0:25 0:30 0:35 0:40 0:45 0:50 0:55 1:00
č as [ura:min] / time [hr:min]
kota [m n.m.] / level [m s.l.]
gladina / w ater level piezometrič ni tlak pod dušilko / piezometric pressure under the throttle

Rodič , P.: Hidravlič na presoja vodostana HE Plave II - Hydraulic Evaluation of the HPP Plave II Surge Tank
© Acta hydrotechnica 18/28 (2000), 61-73, Ljubljana
72
Slika 5. Maksimalni dvig gladine pri upoštevanju najmanj 1 5 minutnega č akalnega č asa.
Figure 5. Maximal water level rise with 15 minutes waiting time.
Slika 6. Maksimalni padec gladine pri upoštevanju najmanj 1 5 minutnega č akalnega č asa.
Figure 6. Maximal water level fall with 15 minutes waiting time.
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
0:00 0:05 0:10 0:15 0:20 0:25 0:30 0:35 0:40 0:45 0:50 0:55 1:00
č as [ura:min] / time [hr:min]
kota [m n.m.] / level [m s.l.]
gladina / w ater level piezometrič ni tlak pod dušilko / piezometric pressure under the throttle
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
0:00 0:05 0:10 0:15 0:20 0:25 0:30 0:35 0:40 0:45 0:50 0:55 1:00
č as [ura:min] / time [hr:min]
kota [m n.m.] / level [m s.l.]
gladina / w ater level piezometrič ni tlak pod dušilko / piezometric pressure under the throttle

Rodič , P.: Hidravlič na presoja vodostana HE Plave II - Hydraulic Evaluation of the HPP Plave II Surge Tank
© Acta hydrotechnica 18/28 (2000), 61-73, Ljubljana
73
6. ZAKLJUČ EK
S hidravlič no presojo sta bili določ eni novi
vrednosti upora dušilke vodostana HE Plave
II, ki sta za približno 1 0 odstotkov več ji od
prvotnih. Vzrok temu je že jasno koncipiran
sistem nove elektrarne in posledič no v rač unu
upoštevan verodostojnejši desni robni pogoj –
začetni manever v odvisnosti od č asa,
obratovanje na moč, z upoštevanjem
največ jega možnega odprtja vodilnika, ter
upoštevano zaporedje manevrov odpiranja in
zapiranja turbine. V predhodni študiji je bil
rač un izveden z upoštevanjem obratovanja na
konstantni pretok ter preprostega zaporedja
samo enega zapiranja turbine na predhodno
odpiranje in obratno.
Rezultat hidravlič ne presoje pa je tudi
ugotovitev, da upoštevanje 15-minutnega
č akalnega č asa bistveno ne vpliva na varnost
obratovanja elektrarne, saj je pri največ jem
dvigu gladina v vodostanu nižja le za 3 cm, pri
največ jem padcu pa višja za 34 cm. Dejstvo,
da elektrarna lahko vstopi v pogon v
kateremkoli trenutku, pa ji daje glede na
možnost hitrega prilagajanja trenutni potrebi
po električ ni energiji vsekakor več jo vrednost.
6. CONCLUSION
New values of the HPP Plave II throttle
damping characteristics were evaluated. They
are approximately 10 % higher than the
preliminary ones. The reason is the more
defined concept of the new hydro power plant
and the consecutive consideration of a reliable
right boundary condition – starting manoeuvre
dependant on time, constant power operation
with the highest possible wicket gate opening
and the sequence of opening and closing the
turbine. In the preliminary study, the
calculation was executed by considering the
constant discharge operation and by the simple
sequence opening after starting the closing,
and, vice versa, closing after starting the
opening.
The result of the hydraulic evaluation is
also to the fact, that the 15 minutes waiting
time doesn’t essentially influence operational
safety. The difference between the maximal
water level rise with  and withou the
consideration of waiting time is only 3 cm, and
the difference between the maximal fall is 34
cm. But starting to run anytime to assure the
momentary need for electrical energy is an
advantage which gives higher value to the
hydro power plant.
VIRI - REFERENCES
Krzyk, M., (1994). Analiza nestacionarnih pojavov v dovodnih organih derivacijskih sistemov
hidroelektrarn Doblar II in Plave II (Nonsteady phenomena analyse on the HPP Doblar II and
HPP Plave II derivative systems), Ljubljana (in Slovenian).
Krzyk, M., (1995). Dodatna analiza nestacionarnih pojavov v dovodnih organih derivacijskih
sistemov hidroelektrarn Doblar II in Plave II (Additional nonsteady phenomena analyse on the
HPP Doblar II and HPP Plave II derivative systems), Ljubljana (in Slovenian).
Mosonyi, E., (1991). Water power development, Vol.2, High head power plants, Akadémiai Kiadó,
Budapest, 1091 p.
Rajar, R., (1980). Hidravlika nestalnega toka (Hydraulics of the nonsteady flow),University
textbook, University of Ljubljana, Ljubljana, 279 p., (in Slovenian)
Rodič , P., (2000). Hidravlič na presoja vodostana HE Plave II (Hydraulic evaluation of the HPP
Plave II surge tank), Institute for Hydraulic Research, 25 p. (in Slovenian)
Naslov avtorja - Author's Address
Primož RODIČ Inštitut za hidravlič ne raziskave – Institute for Hydraulic Research
Hajdrihova 28, SI – 1000 Ljubljana