Raabe J. Hydro power - the design, use, and function of hydromechanical, hydraulic, and electrical еquipment
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Fig,
3.4.47. Run-of-river power plant at Aschach, Danubc, Austria (owner ~stcrrcichischc Donau-
kraftW~k" AG).
H
=
10 to 18 m;
n
-
68,2 rpm;
P
-
3
.
68
MW
(2
sets Voith,
Z
szts Andritz
-
Sulzcr
Wyss) Runner: 5 blades;
L)
=
8,4
n~. 1 head watcr;
2
tail-race:
3
mean tliil-race IcvcI;
4
Danube;
5
normal head water Icvel;
6
spillway: 7 power house;
8
northcrn lock;
9
lo\\cr port;
10 upper port;
11
southern lock;
12
outdoor switch plant;
13
transmission line. Small macl~inc hall,
,,ass from main crane oi~tdoor by hatch. From
E.
Alosonyi,
see Fig. 3.4.47.
Fig.
3.4.49. Pit power house with elliptic plan of binary pumped storage plant Kiihtai, Austria
(owner Tiroler Wasserkraftwerke, Innsbruck).
TWO
sets with vertical pump-turbines (Voith design)
consisting of a pony motor, 15
MW, 90s start up time, b motor generator
160
kVA,
18 kV,
CPump-turbine,n
=
600rpm,H
=
394to440m,TP
=
115,5to 139
MW,
Pu:P
=
112to 119MW,
maximum submergence
-
50 m; spiral casing self supporting, with Escher Wyss type load cornpen-
Qtor at the inlet, embedded in sponge rubber. Gates operated by single servomotors, electro
controlled, electro hydraulic braking down to stand still; alternator air cooled. d
=
"3nsformer. 160 kVA, 181220 kV.
I
maximum tailrace level,
2
minimum tailracc levc!, 3 grout
Catah,
4
moraine, 5 amphibolitc,
6
slated gneiss,
7
drainage gallery,
8
2
tailrace shafts. (Drawing
CoUrfesy Tiroler Wasserkraftwerke, Innsbruck, Austria)
Thc compact dcsign
of
Fig.
3.4.50
is ot~ly rcstrictcd
to low hcad rnachi~~cs with
parnllcl pla~e spiral casing.
At high
hc;~d
machines,
the
stay
vane
with stre;~nlwiscly
varying span tends to in-
crease
thc clcarance of the
rinp sate's lower seal. More-
over in conscquencc of its
relatively high rotor
weight,
the
uxi:~l
khrusi of a vertical
high hcad machine is not
in-
duced into the hcsd cover.
llence the mcimerlt of the
hydraulic uplift about the
bolt circle on the stay vane
crown, additionally widens
the
clcarance of thc
rilig
gate's lower se.11. Thereby
pres:urizcd v~ater leaks
through
tile ;cal and also
loads
thc ou!er cylindrical
w;~il of the head cover and
thc irlner cylindrical wall of
thc stay vane crown. Re-
lieving the ring
vdve cbanl-
her from
the
pressure of this
leakase may squcexe
:he
seal
into this chamber
and hence
provoke
a
dangero~lsly high
1caknr.e in a power hsase
u~cally undrrgrountl. For
thc reasons rnectionsd
abovc. the radial sections of
sti~y vane crown and head
cover are subject to high
bending moments about
thcir radial nei~tral axes.
Hence high tensile sresses in
tangentiai
direction occur in
the water guide walls
which
usually have
a
high wcar.
Fig.
3-4-50.
Vertical
FT
at Aigle. France (owner
EdF).
Example of
a
ring gate between stay and guide
vanes instead of shut down valve at the lower penstock end.
(9ccausc of highly stressed joint between
stay
rill3 and head c.-,vcr, this dcsign is limitcd to smaller hcads)
I1
=
733
m;
rt
=
143
rpm;
"
P
-;
133
M
W
(design Ncyrpic). Runner:
D
=
4,65
m;
dismantled from underneath. (Drawing courte-
sy
Keyrpic, Grenoble, France)
Fig. 3.4.51. Distribution chamber for penslock bifurcations separated from po\\cr hoase at Lanoux
and Rcsines, France, at power housc Hospitalet, France, with
PTs
and storase pumps (Ki1.a-
~~ur11011t).
A
distributor main Lanoux in scparate chamber;
B
distributor main Bcsines;
C
joint fgr
Sisca-Baldarques; D motor generators;
E
tnin PTs;
G
storage pumps;
H
spherical valves:
1
Fix point massive concrete; 2 supporting pedestal;
3
manholes: 4 corner nozzle \alve;
5
wedps
valve;
6
drainage duct;
F
low head impulse turbines.
Fig. 3.4.52. Valve chambers up- and downstream
of
power house, at Grand Maison, I'Eau d'Olles,
France (owner
EdF).
1
power house upper stage;
4
vertical 5-nozzle
PT
(Neyrpic).
H
=
8!7,4
to
922,4 m;
n
=
428,7 rpm;
P,
=
4
.
157
M
W;
2
valve chamber: 4 penstocks, 4 spherical valvcs;
3
transport shaft; 4 cable shaft; 5 underground
power house for a pumped storage plant with
tight 4-stage pumpturbincs.
n
=
600
rpm;
H,
=
949
m;
P,,
=
8.
152
M!V;
H,
=
826
m;
PP,,,=
8
160
M
W
(Ncyrpic dcsign);
6
valvc chhm-
her,
2
spherical valves
ill
series; 7 downstream
valve chamber with wedge valve. (Drawing cour-
tesy
EdF)
3.4.1.3.
The substructure
of
the
power
house
The
substructure is dstermined by the type of tailrace conduit. The following arrange-
ments are usually employed for reaction turbines:
'1
Elbow draft tubes for each turbine. Frequently applied in plants
with
KTs
and
FTs
of
low
and medium head (see Fig.
3.4.14),
especially for tl~ose with vertical shaft. Here
Section
A
-
8
iffening devices for bifurcations
a
with
ex-
and joint collar
7-
(Sulzer);
5
with internal
sicklc
1
(Sul~r Eschcr
Wyss):
c
with
bpherical shell;
1
from
pump;
2
to turbine;
3
to
hcad
pond.
Fig.
3.4.54.
Power house at
base of gravity
dam, at
Brntbk, Angara, USSR
(owner
Sowjet State Power
Board). Vertical
FTs
(LMZ
design)
H
=
102
m;
n
=
125
rpm;
P
=
IS
-
230
MW.
Runner:
D
=
5,5
m;
z
14
vanes; integrally cast in
2
l~alves bolted together.
Wcldcd shaft. Weldcd spi-
ral casing. Water-lubricated
guidc bcari~~g.
1
barrage;
2
main crane (hammer head
crane);
3
Raikal Amoor rail-
road:
4
auxiliary crane;
5
power
house.
(Drawing from
Hydro Project Moscow).
,specir?lly in the case of KTs. the large kinctic energy at runner exit requires
n
long draft
tub^
(7
to
8.
D)
and a
considerable
distancc of the bottom of the inner draft tube from
the runner exit (up to 3
-
D).
Effective pressure recovery requires the largest possible draft
tube cxit, whose width is _given by the distance or adjacent sets.
Since such turbines usually are located along the basc of the dam norn~itl to the flow direction, the
flow
in the draft tube outlet continues the flow dircction of thc admission to the set. To obtain a plzne
face separating the adjacent blocks due to sets, the draft tube centre line must be slightly off-centred
in
its plan, thus compensating the eccentric inflow of the spiral casing (see Fig.
3.4.14).
11) Straight draft tube for each set: applied in ti~bular turbines with
a
straight centre line
in elevation and plan, thus facilitatirlg
a
plane separation face of adjacent concrete blocks
from set to set (Fig. 3.4.45).
111) Draft tubes of
FT
with low specific speed and
high
head. Owing to the relatively low kinetic
energy at runner exit, the draft tubes can be kept shorter than above. Here the flow usually
discharges into
a
comnion tail water duct. This may be oriented in the original flow direction at
turbine
inlet or at
90"
to it according to the requirements of the sitz's topography. In consequence
of
the
submergence required, the duct is
a
pressurized tunnel. In the usual plant with
PT
this duct
is not pressurized with a ducking wall to protect the surroundings from the noise.
3.4.2.
Power house design
with
respect
to
distance from dam
I.
Power house close to or within the dam: In low head run-of-river potver plants, the
power house forms together with the spillway part of the damming device and hence is
close to the dam or incorporated within
it.
Proximity of the dam exists in the case of a
plant with power house on the base of a dam (Figs.
2.3.4 and 3.4.54), or with an under-
ground power house in the slopes
of
the valley (see Fig. 3.4.55). The incorporation of the
power house into the damming device exists in the case of plant on a river bay (see
Fig.
3.3.1), on both of the river banks, and in an abutment type power plant (see
Fig. 3.3.4). The erection of a power house in the interior of the dam appears in sub-
mersible power plants (Fig.
3.3.3) and in barrages containing the power house, especially
those underneath a spillway of the ski jump type (see Fig. 3.3.5).
11.
Power house at greater distance from the dam: In this type of power station the
diversion section in the form of a channel (see Fig. 3.3.1) or an extended system
of
tunnel,
penstock or pressure shaft is very long. Here the power house may be an open air building
at
the end of the channel or at the base of a slope (see Fig. 3.4.56), linked to the penstock.
Or it may be an underground power house (see Figs. 3.4.52; 55; 57) connected with the
steel-lined pressure shaft at the lower end of the so-called "power drop" of the penstock.
Several varieties of the underground power house
exis!. The lirst is the pit power house
(see Fig. 3.4.49). It is preferred for high head reaction machines needing large submer-
Gcnce. Another type is the earth-covered power house (Fig. 3.4.39). Both are usually
located at the base of a slope, where they are now well protected against avalanches or
rock fall. Both types of power house may be located in boulders or gravel.
The
proper underground power house is usually within an artificial cave in rocky ground
Or
within a natural cave that may exist, e.g. in Jurrasic ground.
The
advantages of an underground power station especially in rock are the following:
I)
No need for an outdoor area which is often both expensive and in short supply, especially in
mOuntainous and densely populated areas, e.g. Switzerland.
2,
No need for the maintenance of the exterior as it exists in an outdoor power house.
.
131
Fig. 3.4.55. An underground power house (cavern) close to a barrage in a river slope. Cabora Bassa, Zambesi, Mozambique, Africa (owner
State
Power
Board Mozambique). 5 sets with vertical Francis turbines.
H,
=
113,5
m,
n
=
107,l rpm;
P
=
5
.
415
MW,
(built by Neyrpic, France, and Voith, West
Germany).
1)
power house cavern, area
A
=
1380
m2,
2)
access tunnel, 3) penstock, 9,7 m,
3)
steel linicg, 5) concrete lining,
6)
transformer gallery,
7) bus bar, 13.5
kV, 8) cable shaft 220 kV,
9)
platform 220 kV with an AC transmission line to converter station where 220 kV is converted into
f
530
kV
DC
covering 1400 km distance to the next consumer in the South African Republic, 10) tail water surge tank,
A
=
350 mZ,
11)
tail race
gallery, 12) exit structure, 13) Zambesi, 14) tailwater,
15)
admission road,
16)
intake and thrash rack, 17) maximum permissible head water levzl,
1s)
minimum permissible head water' level.
Fig.
3.4.56.
Longitudinal section ofa penstock and power house at the base of
a
slope. h.larimbondo,
Rio Grande, Brazil (owner Furnas Centrais Eletricas
SA).
H
=
62
m;
17
=
100
rpm;
P
=
8
-
185
IM\V
(Voith design). (Drawing courtesy Voith)
g.
3.4.57.
Undcrground power house of
:
Montezic pumped storage plant
xner Electricitt de France) with
4
pump-
rbines (design Neyrpic)
n
=
47.8,6
rpm.
rrbining:
H
=
378,9
to
419
m:
P
=
193
MW;
qT,
=
0.888
(guaranteed).
miping:
H
=
384:5
to
423
m;
P
=
218 to
2
M
W;
qPm
=
0,909
(guaranteed). Rotor:
4,01
m;
n,,
=
685
rpm,
1
cavern;
Surge tank shaft,
2
a
upper expansion
xmher of the surge tank,
3
access tunnel
the cavern with an ins~ection tunnel to
'
suction line,
4
suction line,
5
lined sec-
'n
of
the suction line, covered with stell
'1".
6
admission pit,
7
access tunnel to
'
Surge tank and the pit
6,
8
drainage
'!cry,
9
drainage pit, 10 tunnel for inspec-
'"f
drainage facilities,
11
ground floor
'cIo~
the machine hall. (Drawing coarte-
Ll
F)
.>I
,<;I\
111g
,;I'
'::.*II
111::
C\;~CL.I:I~I~
111
t;ic
C,I~C
01
:I
scvc~c
c.ii~li.lt~.
c.g Snctlc~i or ~~~ount~~incl~s arca.
4)
i'sotcit;o~~
.~~.lili<t
;~v;tl;t~lc~ilc\
;11111
~~v.-lrfi~l/.
5)
ho
dC\!
rll<llt~!l
t11c
l,lll,l~~
;1j>c,
6)
l'rot<.ctit>~l
;I~,LII~\I
;!ir
r:~iki\
;IIILI
I.!IIC!L-;I~ uar.
7)
l'tic rock c-ut~.:~ctc'cl i'rom tlic cavity c;~n I)c ~lsccl for othcr puroc)scs. c.g. d;im construc!ion (1.541.
Notcs
on
thc
.L;olitlity
ol'
!lie
strr~cinrcs
in
:I
Ilylro
power
~li~~it:
For rc;lson?;
ot'
y~>il
cconon:ji. tlic \v:~tcr rc:tcntiun dcviccs
c.g..
the ul>l>c'r rcscrvoir, the
~;IRI,
the
spillw;~y. po.\sib!ji
;ilt;t>
tlic po..vcrhoirsc.
and
thc watcr~vays have to be wiitc~tight. IIcncc on Jurassic
groulirl,
a
~.-h:rnl!cl
os
a
rcscrvr.)ir clll11ur bc croctcci easily. Ljndcr the c.lctcrior;~ting influclicc cf the
ciirnate (c.?., frost. perma frt)st soil. and stin radi;~tion). this water tigl~tncss has to bc mnintai~~cd
driring tllc uscfal lifo of the plant.
Nevcrt1icl~:ss any ~.calistic stress calculation has to bc biiscd on the assumption of a certuiti sccpage
211d
:h~
i~51iIti11<
~~plirt
011
th~ stri~ct~~re.
Since scc!>ilgc
III;I~
c~lliirgc
thc
danger oisoi! slipp;~gc
;II
the fo3ndation ancl liencc may thrctitcn the
stability of
:iny structure, ;~ny
SCCP;I~C
of thc {vatcrways
;IIIJ
the d;!rnrning deviccs like dam, spillway,
l~iid possibij, ;il>o ~;oivcrl~oi~sc. has to be co?trollcu (c.g., by galleries or
by
ditches occusionally
cquippxl ~iih par~iping st;itions to evacuate thcni).
In
unrc1i;:hic g;-ou!?d
i1;~
scc7:lgc blio~iltl bc limited
by
bpeciill rlevices (gl.out cdrtain. sheet pile).
Thzse Incans iittvc to be applicd cspcciallv during the erection of thc pli~nt's
components
like
powerl:ousc. d.tnl, \\:r!eri\lays and sl>illway.
Thc soil clefi>rnli:tion
(.f
3
';truct;~rc. in consequence of cecpage- or load-induced slippase, should be
continuously conlrolli.ci
t~y
tilr.
mothods
ef
land survey.
-To
compictc thc ttbd~c
not,:
dn
,lams
in
rcli!tion to this topic. solnc considerations must be also given
tc?
thc loads
:II~
thiir coirc\l:or;l~rlg strelhcs
CI,I
spillnay, po\verhousc 2nd their foundaiions.
l'hc cpill:vay
;:~:d
p,tsib!y also t!le po:vcrhc\use have !o translnit tl;c hydraulic thrust from the head
wiltcr into ihc' io~~n~lnticns. the abutment. and the sui: ivithout endangcring the stability of the
structure.
Sii;:~!li;!ncously, spillway anr! pov~~c.rhousc ;ire subject to reaction forces
an3
moments
i~om the soil.
(c'.::..
i~plift
by
si:cp;igc).
As a conscqae11~-t:.
ii:~
;~dl?i\si?lc
v~l
iles
of
ht
rcs. pressure and str2in between soil a116 the concrete
of
thc f~~lidniio!ls
o!'
'uc>ib
C\>J~I~CJIICII~~
ha.e
113
be
accounted
for.
Vforcovcr. :he po,~;crhou~t rcccivi:,
iht
weight
of
its cI~:ctro-mcckanic and hyrlraulic cqci,>ment. For
the
loci~~ioi~
of
the !ctte!.
and
the rcsl~!ting s:resses,
tli~
state of erection and repair has to
be
considcrcr!
also.
.l'hc po\;.cr:lousc
is
fi~rtncr loaded by the reaction force and moment of thc
turbine
distributor,
it.;
iervomotor :ictl valve ant\ by the cnrrcsponding loads of the dldt tube.
This
supcrposu.; the prcs5i:rz- ancl temperature-induccd steady loarls of the penstock
(if
any),
of
the
spi:ki casiny. ;tnd ttie uraft tube. the watcr-l~amrncr-. 2nd surge-induced unstcady
loads
of these
elelnents.
and
the vi'uri1to1.y rcacr
ic11
torque
(if
thc altcrri~tor stator, especially in case oi-short circuit.
Also to
b;. accocntcd for arc weight-, hydr;.iulic thrust-, and temperature-induced loads of the
bearil~gs c>n tile pcnvcrhclusc. 1u:ld:; tlur
!G
flcsural
and
torsionill shaft
...
ihriitions, especially at start
up and
rlin:t\it:i!: of the set. The ansteady io;..ds due to the impact of wind
and
possibly of water waves
acd ice flocs. nust bc added.
-i
f
A
po\vcrhouse
on
the bnsc of
a
slope, possibly has also to resist the impact of rockfi~ll
and
avalanches.
In his caw
ti11
C'~I-~I~-COVCI.CJ
oonst~-ucti~ll
01-
;I
pit
I~O\\~~~:IOLISC
may
fit
best.
Tiic st:itic :In<[ :Ivii:l.mic response of the
powerhouse
structure to the above loads, and !he corre-
si-onding stresses
and
str;~i:is,
3\50
i;~
the foi~ndations and
iii
the adjacent :oil, have to be Lcpt
in
;tdniissiblc limits. ,411 cventiial tensilc s:ress, e.g., due to
a
bcnding moment in the wall, requires
a
correspondir,: rcinforccmcnt of the concrete. In
the
c:lse of
a
dangerous rcFonancc, e.g., at
a
power
swing. thc elastic propcr~ics of thc powcr housc
structure,
but also its mass ofconcretc, have to
be
tuned so as to keep the 1-ibratory wiiil nmplit!ldc within adniissible limits. Thesc limits have
to
be
set :v.i,th rcspcc:
to
lo;~J changes clilring tho uscf~tl
lift
oi thc plant, and with rcspcct to the fatigue
cffccts cornbinull 'i~crewiih.
4.
The
layout of river-run
and
storage plants
with respect to optimized figures such as rated discharge,
number of sets
and
their diameter, storage volume,
hydraulic radius
of
the
water
way
and dimensions
of the electric transmission line
4.1.
Introduction
The layout of a hydro power plant has to start from its character whcther
it
is a
run-of-river and a base load plant or a storage and peak load plant, or of
mixed character.
It has to be based, as the case may be, on h~ldrological data such as the
flo\v
duration line
of a river, the catastrophic high water, the topography of the site, the width of the river
bed, the head and hence the machine type, the eventual length of diversion
by
channel
or pipe or both, the electricity rate, amount and structure of demand and the distance of
the next consumer from the site and the geology of the site.
In developing countries with large rivers the exploitation has to start with the erection
of
the barrage
and spil!way, hugc constructions compared with the orignal small energy demand. Hence the main
problem then
arising is the qucstion, how to develop in smaller stages, e.g., by using side valleys to
by-pass the
main river in stcps.
If
this is not feasible. the river must
be
diverted temporarily during
the
erectioli period of the barrage, the spillway and the power hotrse.
Contrary to this in the following chapter the layout is discussed under the assumption
that the
demand exists. Then from the econon~ical point of view the question arises how
to set tlie operating data of the plant and the dimensions of its structural members so as
to make a maximum
the surplus of revenue over initial cost mainly due to the sale of
electricity during the depreciation period of the plant.
Assuming the site, its topography and hydrology and hence also head and
type of
machines to be given, an attempt is here made,
tc;
ascertain the optimum value of
a
certain
device, or an operating figure of a plant, so as to satisfy the requirement above mentioned.
Such an optimization may be attained with respect to rated discharge in a run-of-river
hydro power plant, with respect to size and number of sets, with respect to
the coefficient
of rotor blade speed, the hydraulic radius of the waterway (if there is one) such as channel
or pipeline, the diameter of the electric conductor for power transmission and the distance
between adjacent towers on this line.
This
optimization includes many cost terms, e.g. fabrication, earth excavation, super-
Structure and substructure of the power house and spillway costs and accounting for the
losses of the hydraulic machine, and, in case of a. reaction machine, for its ground
excavation required due to ccvitaticn, as a function of the machine's size.
For the layout of a storage plant on
a
river, the topography of the site, the target release
due
to the river and the power demand are assumed
as
known values. For the case of a
pu:npt.d storryc
pl;int,
which only consumcs clcctric energy. t!ie p~.ohlcm
arises
how
to
set the electricity
rate during
b:isc
Ic.2d
and
pcnk
loricl
hours
so
as
to
make
n
surplus by
s;ile
of peak loat1 energy.
The hrcnk down of
a
plnnt economy into lincarly intcrrclatcd coniponcllts is ntlmittcdly difficult
and
rem;iins often only all cstimatc. To obt;iin, c.g. thc spccific cost of the coniponcnts from a rcal schcnie,
scale effects. often unknown due to size, position, inflation, degrec of devclol)nicnt, local state of the
art. and impondcrabilitics such as tl\c political ambition of the plnnncr or owncr, Iiavc to bz
scparatcd, to obtain actual informatien
[4.
I].
In
this chapter the assignment of the electric machine and the hydraulic machine to eacli
other with respect to thc limits of output and spccd (see chapter
11.4)
is ignored.
In
any
plant, it is expected that, at least for a sufficient and reasonable number of
days in the
average year, the plant operates with
ratcd head and rated discharge at the
bcp
of the
mzchines.
It is important to know that thc opcratir~g point of a rnachinc results from the
intersection
of two
curves. The one is tnz head as function of the rivcr flow that results from the hydrograph, the
topography of
tlie site, and the gcomctry of the watcr way, which is often infliienccd by scdimen-
tation. The other curve is the head as a function of the flow, which passes the machine at a certain
speed and a certain gate opening.
If the intersection point of both the curves
misscs the bep of the machinc, then there may be litigation
to seek for the person
responsible.
7'he only thing a court can do in this case is to obtain the opinion
of
3
consulta~~t on the base of careful research and field tests.
On the one hand, the faulty construction may result from wrong surveying, or a faulty reading of
the hydrograph by the planner. Also
a
wrong evaluaiion of the friction in the water ways, Qr an
crioncous estimation of the depositing scdiments may have led the planner to wrong conclusions
about back
water effects etc.
On
the other hand thc maker of the machixie can make a mistake either in designing,machining, or
controlling
thc machine he has supplied.
In general the maker has an interest to meet the bcp, as a bad elTiciency would be a bad recorr~men-
dation for his business. But also the user of the plant, which is usually also the planner, must be
interested in a high revenue. On no account can the maker
be madc responsible for !laving adopted
a \vrong hydrograph or head since such measurements are too time-consuming, in this respect he
,-
must trust the planner. This holds true especially for the manufacturer of the set.
T11e plznnin? of a hydro power plant is also made difficult by the fact, that two random
effects must coincide with the best efficiency point of the machine characteristics.
One is the available annual output of the
plafit, which can be predicted (especially
in
a
run-of-river plant) only as a time-averaged value. This results from observations over
many years.
The other is the prediction of the annual output of the plant during its useful life. This
car1 be only derived from the preceding development and may undergo unpreclictable
variations in the future. The consequences of this uncertainty may be further complicated
when the
plani supplies a grid by itself or when its annual output is relatively large
conipared to that of the interlinked
grid.
Finally the planning of
a
hydropovxr plant in
the way described here is characterized by
the fact that its rated capacity which equals
the energy
demaild, exists only at a certain moment
during
its useful life.
To overcome
this
discrepancy, the plnnt may be developcd either in stages, or certain limiting
working
data, e.g.. the current density or the velocity in the water way, are reached at the end of its
useful life. In this chapter, the concept
oi thc capitalized cash value of energy loss is app!ied. Thir
needs some comment, since this cost term is neither an asset nor
a
liability in the csual economic