Computational Water, Energy, and Environmental Engineering, 2013, 2, 9-20
http://dx.doi.org/10.4236/cweee.2013.21002 Published Online January 2013 (http://www.scirp.org/journal/cweee)
On the Short-Term Optimisation of a Hydro Basin with
Social Constraints
Gloria Hermida, Edgardo D. Castronuovo
University Carlos III de Madrid, Madrid, Spain
Received November 19, 2012; revised December 20, 2012; accepted January 3, 2013
ABSTRACT
In this paper, an optimisation problem for calculating the best energy bids of a set of hydro power plants in a basin is
proposed. The model is applied to a real Spanish basin for the short-term (24-hour) planning of the operation. The algo-
rithm considers the ecological flows and social consumptions required for the actual operation. One of the hydro plants
is fluent, without direct-control abilities. The results show that the fluent plant can be adequately controlled by using the
storage capacities of the other plants. In the simulations, the costs related to the social consumptions are more signifi-
cant than those due to the ecological requirements. An estimate of the cost of providing water for social uses is per-
formed in the study.
Keywords: Hydro Power Plants; Hydro Generation; Optimisation; Short-Term Planning; Social Resources
1. Introduction
Nowadays, the utilisation of water for electricity produc-
tion is conditioned by many constraints. In Spain, pri-
marily the Kyoto Agreements and the proposals of the
European Commission to 2020 must be considered. The
European Commission have specified a goal of 20% of
the final energy consumption delivered from renewable
sources by 2020 [1]. In Spain, 38.6% of the electricity
generation comes from renewable resources, mainly from
hydro (17.4%) and wind (16.6%) generation [2]. Because
electricity generation has to compensate for other non-
renewable energy consumptions, electricity production
must increase its share of renewable generation. Hydro
production is a mature renewable technology that can
help reach the ambitious objectives proposed by the
European Commission by 2020.
In addition, the exceptionally variable weather condi-
tions of the past few years, most likely due to climate
change, complicate the management of water for elec-
tricity production. The scarcity and the high variability of
water resources have recently reduced the profits in sev-
eral zones [3-6].
Many studies have been performed to calculate the op-
timal operation of a hydro basin. In long-term planning,
Soares and Carneiro [7] consider the operation planning
of a hydrothermal power system in Brazil. The paper
highlights the importance on the control of the head hy-
dro power plants (HPPs) in the basin. Granville et al. [8]
consider the stochastic characteristics of the problem,
including a representation of the market. The solution
algorithm is based on stochastic dual dynamic program-
ming. Cheng [9] applies particle swarm optimisation and
dynamic programming for a large scale hydro system in
China. Oliveira, Binato and Pereira [10] present two
techniques: the extension of a binary disjunctive tech-
nique and screening strategies for planning studies in
Brazil and Bolivia. Fosso et al. [11] give an overview of
the planning tool used in Norway for long, medium and
short horizons. Kanudia and Loulou [12] propose a sto-
chastic version of the extended market allocation model
for a hydro system in Québec, Canada.
In medium- and short-term planning, Habibollahzadeh
and Bubenko [13] compare different mathematical
methods: Heuristic, Benders and Lagrange methods for
hydroelectric generation scheduling in the Swiss system.
Castronuovo and Peças Lopez [14] describe economic
profits of the coordination of wind and hydro energies.
Zhao and Davison [15] analyse the inclusion of storage
facilities in a hydro system, demonstrating the sensitive
dependences between some of the parameters of the hy-
droelectric facility, the expected prices and water inflows.
Pousinho, Mendes and Catalão [16] propose a mixed-
integer quadratic programming approach for the short-
term hydro scheduling problem, considering discontinu-
ous operating regions and discharge ramping constraints.
Simopoulos, Kavatza and Vournas [17] propose a de-
coupling method, dividing the hydrothermal problem into
hydro and thermal sub-problems, which are solved inde-
pendently. A Greek system is analysed in the study. Di-
C
opyright © 2013 SciRes. CWEEE

G. HERMIDA, E. D. CASTRONUOVO
10
niz and Piñeiro Maceira [18] use a four-dimensional
piecewise linear model for the generation of a hydro
plant as a function of storage, turbined and spilled out-
flows. Shawwash, Thomas and Denis Russell [19] dis-
cuss the optimisation model used in the British Columbia
hydro system for hydrothermal coordination.
Most of the available reports about the optimal pro-
gramming of hydro generation have been published in
countries with abundant water (Norway [11], Brazil [10],
Canada [15], USA [19]). In the algorithms reported by
these studies, the restrictions on the social use of water
and the ecological minimum flows are either minimally
considered or not considered at all, aiming at improving
the utilisation of the abundant resource in a strictly eco-
nomical environment. In Spain, the focus of the present
study, ecological flows and social uses of water must be
considered for the optimal utilisation of the resource.
Pérez-Díaz and Wilhelmi [20] want to assess the eco-
nomic impact of environmental constraints in the opera-
tion of a short-term hydropower plant. For that purpose, a
revenue-driven daily optimisation model based on mix-
edinteger linear programming is applied to calculate the
optimal operation of a HPP in the northwest area of
Spain. In a more recent paper, Pérez-Díaz et al. [21]
propose adding a pumping capability to improve the
economic feasibility of an HPP project, always fulfilling
the environmental constraints imposed on the operation
of the hydropower plant.
This paper presents an optimisation algorithm for cal-
culating the optimal energy bids of a set of HPPs, in-
cluding the economic objectives for energy generation
and the regulations concerning the use of water in the
region. The algorithm is applied to the upper Gua-
dalquivir Basin, an area with scarce resources and vari-
able flows, over a 24-hour horizon. Four HPPs are con-
sidered in the analysis. Three of them have storage ca-
pacity and the other one is run-of-the-river, without di-
rectly controllable alternatives. All of the plants are op-
erated jointly with a unique owner or dispatcher (as in
current practical operation). Actual data from real power
plants and markets are considered in this study, including
the travel times of the water (TTW) between the HPPs.
The results show that the fluent plant can be controlled to
achieve optimal operation by using the upstream HPPs.
Moreover, an estimate of the costs of providing water for
social uses (as a function of reductions in profits from
selling the electricity produced in the market) is made in
this study.
2. Rules Applicable to the Hydro Generation
2.1. Regulations Concerning the Use of Water
for Electricity Generation
The Water Framework Directive [22] establishes a Euro-
pean Community framework for water protection and
management. The objectives of this regulation are the
prevention and reduction of pollution, promotion of sus-
tainable water use, environmental protection, improve-
ment in aquatic ecosystems and floods and drought miti-
gation. This norm was adapted to Spanish regulations by
[23]. In this directive, the priorities regarding the use of
water are fixed. Electricity generation is third in the order
of precedence, after the use of water by the population
and irrigation requirements. Additionally, this norm
specifies the requirement of a Hydrological Plan for each
basin or hydrological zone. In [24], the hydro regulations
for the Andalucia region (the area considered in this
study) are specified. The Guadalquivir Hydrographic
Confederation (http://www.chguadalquivir.es) is the or-
ganisation designed to control the Guadalquivir basin.
This organisation’s website features historical data re-
garding affluences and other hydro information. The
minimum levels of flows (ecological flows) are also
specified for several points of the river.
2.2. The Daily Energy Market
In Spain, the electricity market has been deregulated
since 1997 (Electricity Industry Act [25]). Some renew-
able productions have special incentives for their produc-
tion (Royal Decree 661/2007 [26]). However, large or
pre-existing hydro plants must auction their production in
the conventional market without renewable bonuses and,
practically, without special market regulation. This is the
situation faced by the plants addressed in the present
study.
The Spanish energy market is organised into the fol-
lowing sub-markets: futures market, daily market and
several intra-daily markets. More than 95% of energy
transactions and more than 80% of the economic volume
are traded in the daily market [27]. There are also other
markets that can affect hydroelectric production, such as
the reserve and restriction management. For clarity, in
this work, only daily market participation will be consid-
ered.
In the daily market, producers and consumers make
their offers, in terms of energy quantity and prices for
each hour of the D + 1 day. The Market Operator over-
sees the buying and selling of bids using a simple cass-
ation model [28,29]. The present paper presents a method
to calculate the optimal bids for energy over a 24-hour
horizon of the hydro plants in the basin, assuming that
the expected prices in these hours are known.
3. Mathematical Formulation
3.1. Flow Chart
In Figure 1, the flow chart of the algorithm is presented.

G. HERMIDA, E. D. CASTRONUOVO 11
Initial
conditions
of the basi
n
Expected
flows
Scenario
Generation
Mathematical
solution
Analysis of results
and generation of
o
p
timal bids
Prices
forecast
Figure 1. Flow chart of the proposed algorithm.
The initial conditions of the basin (level of stored water
in the reservoirs, current flows, etc.) are known at the
beginning of the study. Moreover, the expected flows in
the analysed period can be considered known or esti-
mated. The expected flows are depending also of the
medium term planning for the operation of the basin. In
the present study, an estimation of the prices in the mar-
ket, for all the hours of the next day operation, is required.
This prediction can be obtained from forecasting tools,
outside the scope of the present study. With the knowl-
edge of the initial condition, the price forecast and the
expected flows, a scenario can be developed. In the pre-
sent analysis, a determinist approach is used. However,
the present method can be easily extended for consider-
ing uncertainties in the prices and/or in the expected
flows, by solving many probable scenarios.
When the probable scenario is determined, the optimal
solution for the operation in the hydro plants in the basin
must be calculated. In the present case, ecological and
social constraints are also included in the analysis. In the
next section, a fully representation of the optimization
problem is provided. After the calculation, the optimal
flows of waters and the power and energy optimal bids
are obtained. For achieving the profits presented in the
analysis, it is considered that all the presented bids are
accepted in the market, by offering the hydro production
at low prices.
3.2. Mathematical Representation
The best operation of hydro plants in a basin can be cal-
culated from the solution of an optimisation problem. In
this problem, the restrictions to the operation are repre-
sented as mathematical constraints. The formulation of
the problem is described by Equations (1)-(15).
Max.

,
11
nr nwr T
tit
it
CP





,
(1)
s.t.
,,1, 1,,,
1, ,
AFT C D
itititi tititit
VVV VVVV
inr



(2)
,1,,,,
0
1, ,
AFT CD
iti tititit
VVVVV
inwr


 

(3)



1,1, 1,
1, ,
v
TD
ititt itt
i
VVV
inrnwr






v

r
r
r
(4)
,1,1 1,,
SP
ii
VV in (5)
,,
1,,
SP
iT iT
VVi n (6)
,,,
0 1,,()
T
itit it
PVghi nrnw    (7)




0
,0,1,
23
00
2, 3,
1,,
U
itiiii
UU
ii iii i
hkkVV
kVV kVV
inrnwr
 
  




r

,r
,r
,nr
,r
(8)

min
,
1
1,,
TCCT
it i
t
VV i nrnwr


 (9)

min max
, 1,,
CCC
iiti
VVV inrnw  (10)

min
,, 1,,
TDEC
it iti
VV Vinrnwr  (11)
max
,
0 1,
it i
VV in  (12)
max
,
0 1,
TT
it i
VVi n  (13)
,
099 1,
D
it
Vi  (14)
max
,
0 1,
it i
hh in  (15)
1, ,tT


where the variables indicate the following: Pi,t, the active
power injection to the grid of hydro plant i at hour t; Vi,t,
the useful volume stored in the reservoir of the hydro
plant i in the period t; Vi-1,t, the affluence into reservoir i
at period t, coming through the river from upstream plant
(or plants); , the turbined volume at hour t by plant i;
,
T
it
V
,
D
it
V
,
C
it
V
peri
, the deviated (spilled) volume at hour t by plant i;
, the output water consumption for social uses deliv-
ered by plant i at hour t; and hi,t, the height of reservoir i
at hour t. The following are the parameters in the opti-
misation formulation: ct, the expected market price of
hour t; , the individual affluence into reservoir i at
,
AF
it
V
t, od onsidering the flows coming through the not c

G. HERMIDA, E. D. CASTRONUOVO
12
river from the previous plant; tV, the TTW between the
considered HPPs; ,1
SP
i
V and ,
SP
iT
V, the specified volumes
at the beginning at the eof the horizon (respec-
tively) by plant i; ηi, the average efficiency of the hydro
plant i; g, the acceleration of gravity; k0,i, k1,i, k2,i and k3,i,
the coefficients relating volume and height at reservoir i;
U
i
V, the unused volume for electricity generation of res-
ir i; minCT
i
V, the minimum daily requirements of wa-
ter for social uses in hydro plant i; minC
i
V and maxC
i
V,
the minimum and maximum (respectively) hour-
quirements of water for social uses, in plant i; maxEC
i
V,
the minimum (ecological) volume to be maintained in the
river downstream of reservoir i; max
i
V and maxT
i
V, the
maximum useful reserve and capaf prod (re-
spectively) of hydro plant i; and max
i
h, the maximum
height at plant i. In the equations, the number of
hydro plants with reservoirs, nwr is the number of fluent
hydro plants (without reservoir), αi is the set of hydro
plants upstream from the reservoir i and T is the number
of discretisation steps.
The goal of the optim
nd a
analys
nd
ro
go
ervo
cu
ing
ly re
n
is to cal-
by us-
cit
b
y o
nr is
lem (1)-
rithm
uctio
isation p(1
is, the al
4. The Test Case
tion problem (1)-(15) is applied to
matic representation of four hy-
dr
the Daily
M
constraints on electricity
pr
nsumptions and
lows are not considered. The op-
onsumptions are not applied. The
isation problem (1)-(15),
the cases, the same flow (7.944 Hm /day, the
av
5)
is solved
late the optimal production of coordinated hydro plants
in a basin in T periods and considering the expected
prices in the market (1). Equality constraints (2) and (3)
express the energy balances in the hydro plants with and
without a reservoir, respectively. When the hydro plant
has storage capacity (2), the useful volume in the reser-
voir can be increased by the individual affluence (rain,
tributaries, etc.) and the flows coming from the immedi-
ately upstream hydro plants. Additionally, the energy
stored in these plants can be reduced by electricity gen-
eration and social consumption. When large inflows en-
ter the reservoir, a portion of the water can be deviated
by using the spill way to preserve the security of the
plant’s operation. The amounts of useful energy at the
reservoirs at the beginning and end of the programming
horizon (5), (6) are pre-specified quantities. The hydro
production efficiency for power production is expressed
by using a third-order polynomial Equations (7), (8), as a
function of the height. In hydro reservoirs with large
nonlinear relationships between the height and the stored
water (Equation (7)), partial approximations by using third
order polynomial equations for each level of the reservoir
can be adopted. In the present formulation, the social
requirements for water are represented as minimum daily
consumptions (9) and restrictions on hourly water flows
(10). The operation of the hydrological system requires
maintaining the minimum ecological levels of water
flows into the basin (11). In Equations (12)-(15), the
maximum capacities of the equipment of the hydro plants
are expressed.
In the present
Matlab [30]. Equations (1)-(15) constitute a large
nonlinear optimisation problem requiring (T (7nr +
6nwr)) variables, (4T (nr + nwr) + 2nr) equality restric-
tions and (T (16nr + 14nwr)) inequality constraints.
The proposed optimisa
water management in the upper basin of the Guadalquivir
River, Spain. Figure 2 shows a map of the headwaters of
the Guadalquivir River.
Figure 3 shows a sche
o power plants (HPPs). Three of them have a reservoir
(HPP 1, Doña Aldonza; HPP 3, Guadalmena; and HPP 4,
Marmolejo), and the other (HPP 2, Pedro Marín) is run-
of-the-river. The TTW between the plants is shown in the
diagram as Tv. Other important data related to the plants
are presented in Tables 3, 4 of the Appendix.
In the present analysis, typical prices in
arket in March 2011 (a month with medium hydro
production) in Spain are used to simulate the optimal
operation of the hydro system (Figure 4). The accelera-
tion of gravity, g, is 9.81 m/s2.
To analyse the effect of the
oduction, several cases are considered:
 Case A: base case, in which social co
ecological flows are not represented. Therefore, the
optimisation problem is solved without considering
Equations (9)-(11).
 Case B: ecological f
timisation problem is solved without Equation (11).
In this case, the social consumptions are included in
the formulation.
 Case C: social c
optimisation problem is solved without Equations (9)
and (10). In this case, the ecological flows are in-
cluded in the formulation.
 Case D: solution of the optim
considering both social consumptions and ecological
flows.
In all of3
erage flow of March 2011) is considered. The same
flow (3.972 Hm3/day in each HPP) is injected at the
heads of the basin and uniformly distributed over 24
hours (0.1655 Hm3/hour in each HPP). For simplicity in
the analysis, no individual affluences (,
AF
it
V) in HPPs 2
and 4 are considered.
Figure 2. Geographical position of the Guadalquivir basin
and relevant hydro power plants [31].

G. HERMIDA, E. D. CASTRONUOVO 13
Figure 3. Spatial distribution of the reservoirs in tpper
Guadalquivir basin.
he u
0510 15 20 25
50
55
60
65
70
75
80
85
90
periodo de programación
precio horario
Pri
ce
c€/
k
W
hour
Figure 4. Typical spanish next-day market prices in mah
2011.
this sample basin, assuming 24 hours of operation
n
se, without Social Consumption and
In Fproduction of the four hydro
the be-
gi
d (Fig-
ur
y Social
Consumption
.
Socies are required in all of the
capacity of
H
rc
For
ad hourly discretisation, the formulation described by
(1)-(15) implies 648 variables, 390 inequality constraints
and 1488 inequality restrictions.
5. Results
5.1. Base Ca
Ecological Flows
igure 5, the optimal
plants is shown. The hydro plants at the head of basin
(HPPs 1 and 3) put the resources into circulation, if pos-
sible, during the high-price periods in the morning.
However, the behaviour of these two plants is quite dif-
ferent due to the TTW between the plants in the basin
and the type of plants downstream. The production of
HPP 1 is limited by the capacity of the run-of-the-river
HPP 2 located downstream. In this scheme, all of the
water entering HPP 2 is turbined, obtaining the maxi-
mum possible profit in the combined operation. HPP3,
with a controllable power plant downstream (HPP 4),
generates electricity during the early hours of the day at
the highest prices and full capacity. The resources com-
ing from HPP 2 and HPP 3 reach HPP 4 in time to be
turbined at full power during the hours of maximum
daily price. A small quantity of water is turbined by HPP
3 at the hour of the maximum price of the day, hour 21,
without reaching HPP 4 during the daily horizon.
As shown in Figure 6, hydro plants HPP 1 and HPP 3
(at the heads of the basin) use the water stored at
nning of the day to increase production during the first
hours. The inflows in the heads in the evening help re-
cover the specified final values of stored energy at the
end of the day. As expected, HPP 2 has no storage ca-
pacity. HPP 4 utilises its storage capabilities to wait for
higher prices to sell its production in the market.
The reduced storage capacity of HPP 2 distributes the
profits throughout the entire programming perio
e 7). A higher generation capacity in the plants would
centralise the revenue only at the peaks of the price curve.
The profit of the joint operation is 165.6 M€.
5.2. Optimal Operation Considering onl
In this case, the effect of social consumption is studied
al-consumption valu
plants. The daily minimum consumption and the hourly
limit at each plant are specified in Table 3 of the Appen-
dix, fifth and twelfth columns, respectively.
Figure 8 shows that at the beginning of the day HPP 1
turbines more than the maximum generation
PP 2, delivering water for social consumption to HPP 2
and HPP 4. This period has the lowest prices of the day.
In the other head plant (HPP 3), social requests are sup-
plied using water with less economic efficiency, elimi-
nating HPP 3 generation at hour 21 (Figure 5). Figure 9
shows the delivery of water for social uses for the four
hydro plants. The upstream plants, HPPs 1, 2 and 3,
transfer the volumes for social consumption at the begin-
ning of the day, the period with lowest prices. HPP 4,
without individual inflows, must yield to this restriction
along the following minima of the price curve (hours 16
and 24). HPP 3, with the largest social consumption, also
uses the minimum price at hour 24 to fulfil the social
requirements. The profile of incremental profits is similar,
considering (Figure 10) or without considering (Figure
7) social consumption. However, the final profits are
Figure 5. Production in the four hydro plants, Case A.

G. HERMIDA, E. D. CASTRONUOVO
14
Figure 6. Energy storage in the hydro plants, Case A.
Figure 7. Incremental profits in the basin, Case A.
Figure 8. Production in the four hydro plants, Case B.
Figure 10. Incremental profits in the basin, Case B.
restrictions (minimum flows in the river) on the profits
are analysed. In the prese
nt simulations, this restriction
can only be imposed at the head plants (HPPs 1 and 3). A
ered.
With minimum ecological flows in all of
3) generate electricity at all hours of the day. As in Case
A, the generation of HPP 1 is restricted by the limited
capacity of HPP 2, and HPP 3 mainly generates electric-
ity during the first high-price periods of the day. The
ecological restrictions (minimum flow at all hours) make
the slope of income almost constant (Figure 12). The
profile of the volume turbined becomes flatter, and
therefore, there are fewer resources for producing at the
hours of maximum price. The optimal profit in this case
reaches 163.14 M€ (1.5% less than that without ecologi-
cal ic-
ons on minimum flows in the river do not significantly
5.
constant value of 16 m3/s for each plant is consid
this value, the
the basins can be maintained [32], considering TTW.
Figure 11 shows that the two head plants (HPPs 1 and
restrictions). In the present simulations, the restr
ti
reduce the profit of operation. It must be stressed that
these restrictions are not consumptive; they only change
the generation times of head HPPs 1 and 3. However,
theincrease in the amount of ecological flow can reduce
the total profits.
4. Optimal Operation with Social Consumption
and Ecological Constraints
In this case, the effects of the two types of constraints
(social consumption and minimum flows) are analysed.
In this case (Figure 13), the optimal profiles of genera-
tion are similar to those observed in Case B (Figure 8).
However, some differences must be highlighted. First,
the ecological minimum flows require generation at
HPPs 1 and 3 during all periods. The distribution of so-
cial consumption is also dissimilar (Figure 14). In Case
B (with social consumption but without considering eco-
logical restrictions, Figure 9), the volumes for social
consumption are assigned to hours 2 to 5 in HPPs 1 and 2.
The ecological flow requirement shifts the delivery of
HPP 1 to hours 2 and 7 and the release of HPP 2 to the
end of the day (hours 19 to 24). In HPP 3, delivery for
Figure 9. Energy storage in the hydro plants, Case B.
different. When considering social requirements, the total
revenue is 137.09 M€, 17.20% lower than without human
consumption in the basin.
5.3. Optimal Operation with only Ecological
Constraints
In this case, the individual impacts of the environmental

G. HERMIDA, E. D. CASTRONUOVO 15
Figure 11. Production in the hydro plants, Case C.
Figure 12. Incremental profits in the basin, Case C.
Figure 13. Production in the hydro plants, Case D.
Figure 14. Social consumptions, Case D.
social consumption is increased at hour 19 and elimi-
nated at hour 24. HPP 4 continues to provide for social
consumption at the end of the day (hour 24) but shifts to
small delivery from hour 16 to 15. These changes opti-
mise the utilisation resources, increasing the combined
profit of the operation. However, the optimal income
this case is 129.90 M€, 21.54% less than that of the base
caseon-
straints).
5.5. Comparison of the Analysed Cases
As previously discussed, the economic results of the pre-
vious section depend on the type of restrictions added to
the base case. Minimum flows in the river can be main-
tained without a loss of resources, only changing the time
of generation. However, the social uses of water are
consumptive constraints, extracting resources from the
basin. Mction of
the amouree dif-
sent simulations, the ecological requirements of
evaluated
nstraints de-
pends on the amount of resources injected to the basin. In
gical cost
(EC) f the affluence is presented.
tively ten times
m
ers the costs of water delivered for social consumption.
in
(without social restrictions and ecological c
oreover, the economic results are a fun
nt of available resources. Therefore, th
ferent scenarios are compared here: dry, medium and wet
scenarios, for the two types of restrictions. The medium
value coincides with the previous affluence (7.94
Hm3/day). For comparison purposes, all of the results are
obtained by maintaining the data previously used, in par-
ticular, the price profile shown in Figure 3.
5.1.1. Results Considering Only Ecological
Constraints
In the pre
Table 1 (1.6 m3/s in HPPs 1 and 3) are maintained. How-
ever, the effect of the ecological constraints is
in three different situations of affluence.
In Table 1, the first column shows the total inflow in
the basin injected in head HPPs 1 and 3. The second and
third columns show the optimal incomes obtained with-
out considering or including the ecological constraints
(Equations (9)-(11)), respectively. The economic differ-
ence between the two previous cases is represented in the
fourth column. In the fifth column of the table, the rela-
tive cost of the ecological constraints, for each Hm3 of
inflow in the head HPPs, is calculated. Finally, the sixth
column shows the relative cost of the ecological con-
straints, for each Hm3 of minimum flow requested at the
head HPPs of the basin. In this table, it can be seen that
the cost of maintaining the ecological co
Figure 15, the curve of variation in the ecolo
as a function o
As shown in Table 2 and Figure 15, the cost of
maintaining the ecological requirements is far more im-
portant in dry scenarios. In fact, maintaining the same
ecological flow of 3.42 Hm3/day is rela
ore expensive than maintaining a flow of 12.47
Hm3/day.
5.1.2. Results Considering only Social Consumptions
In the present section, the effect of social consumption
(as specified in Table 3, Appendix) in the three previous
scenarios of affluence is considered.
Table 2 has the same structure as Table 1 but consid-

G. HERMIDA, E. D. CASTRONUOVO
16
qui
co
((€/Hm3) (€/Hm3)
Table 1. Costs of ecological re
Flow in HPPs 1 and 3
(Hm3/da)
Income, Case A.
(M€)
Income, Case C.
(M€)
In
rements for different inflows.
me Gap.
M€)
Relative Ecological Costs, Relative Ecological Cost,
12.47 228 227 1.4 112,549 507,646
7.94 166 163
3.42 80 67
3 305,253 877,073
13 3,801,169 4,947,837
Table 2. Social consumptio
Flow in HPPs 1 and 3 Income, Case Income, Case Income G
n c
(Hm3/da) A. (M
ap. Relative Social Consumption Relative Social Consumption
Cost, (M€/Hm3)
osts for different inflows.
€) B. (M€) (M€) Costs, (M€/Hm3)
12.47 228 208 20 2 9
7.94 166 137 29 4
3.38 42 12
13
42 80 19
Accordto the two tablthe costs of er allo-
ated for social uses are larger than those of maintaining
ological constraints. In fac
nario, the reduction in profit due to the social uses of
wr reae
the ecconstrainl usesresourc
from the basin; the ecological constraint request
modi- fication in the proof generatbut the r
source re- mains in the river.
In Figure 16, the relativcial consumon costs f
e three scenarios of affluence are shown. The curve SC,
So
ing es, wat
c
the ec
t, for the medium sce-
ater is 967% greate
ological
than the dec
ts. Socia
se in revenu
extract
due to
es
s only a
file ion, e-
e soptior
th
cial Consum., shows the cost of delivering 1 Hm3 of
water from the basin for social uses in the simulated sce-
narios. The values of this curve can be used to calculate
the price of water allocated for human use in the basin as
a function of the profits lost in electricity generation.
6. Conclusions
This paper presents an optimisation method to calculate
the
Figure 16. Social consumption (sc) costs for different in-
flows.
The algorithm allows for control over the actions of
fluent HPPs, modifying the operation of controllable
HPPs. The method calculates the maximum profit elec-
tricity generation in the daily power market, considering
ecological constraints and the social use of water.
The study of different inflow states shows that in this
ver, initial evaluations of the costs of provi-
g water for social uses are performed. The proposed
algorithm can be easily extended to consider other opera-
tional restrictions on the hydro systems.
7. Acknowledgements
The authors would like to acknowledge the Ministry of
Science and Technology of Spain (Projects IT2009-0063,
ENE2010-16074 and CENIT-CONSOLIDA) for suppor-
ting this work.
] “Concerning Common Rules for the Internal Market in
optimal operation of a basin with both controllable
and non-controllable hydro power plants. This program
considers both social and ecological restrictions, assess-
ing the economic weight of each of them in the manage-
ment of resources.
case the relative value of the social consumption of water
is larger than that of maintaining ecological flows in the
asin. Moreob
din
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Figure 15. Cost of ecological ruirements (EC) for differ-
ent inflows.
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Appendix
Table 3. Hydro plants data.
HPP Type Prev. HPP Tv [h]
In Table 3, Prev. HPP is the number of the HPP up-
stream to the current HPP (i.e., upstream HPP 4 there are
the HPP’s 2 and 3).
Table 4. Coefficients volume-height of the hydro plants.
HPP k0 [m] k
1 [m−2] k 2 [m−5] k 3 [m−8]
min 3
Hm
CT
i
V



max m
i
h
1 R - - 0.5 13
2 F 1 2 0.3 -
3 R - - 0.8 82
4 R 2, 3 6, 8 0.6 7
1 −3.58E + 014.94E + 00 −1.07E − 01 1.02E − 07
2 25 0 0 0
3 2.53E + 004.75E − 01 −6.85E − 04 1.03E − 07
4 9.63E − 013.71E − 01 −3.90E − 04 1.05E − 07
HPP max 3
Hm
i
V

max 3
Hm
T
i
V

3
,1 Hm
SP
i
V



 3
,Hm
SP
iT
V
 3
Hm
U
i
V




1 23 0.513 1.3 1.3 20
2 19 0.206 0 0 11
3
347 0.839 0.8 0.8 -
4 13 0.850 0 0 10
HPP ηi
max 3
Hm
C
i
V

min 3
Hm /h
EC
i
V




1 0.3 0.7 0.0576
2 0.1 0.79 0
3 0.5 0.796 0.0576
4 0.4 0.7962 0

G. HERMIDA, E. D. CASTRONUOVO
20
Biographies
Gloria Hermid), received her
Bgree Inng from University of
Lrhster degree in Electrical,
Electronics and tomation Engineg (2011
UnersiCarlosde Mrid. Sheworking -
sistant Prsor i the Deartment of Electrical Engi-
neering of University Carlos III de Md. Her research
interests includeoptim r resources and
peration planning.
Edgardo D.tronuovo received a B.S. degree
() in Electrical Engineering from the National Uni-
ve
d performed Post-Doctorate
005) at INESC-Porto, Portugal. He worked at the Pow-
er
Portugal. Currently, Dr. Castronuovo is an Asso
Prr ateparEngg,
Unisity ine
in optimization methods applied to power system prob-
lemrenewabroductio storage a deregulation of
the ctric soo-
ior Member of IEEE.
a was born in Coruña (1973
.S de
a Co
in
uña (2007) and
dustrial Engineeri
er Ma
Auerin) from
ivty
ofes
III
n
ad
p
is as As
adri
the ization of wate
o
Cas
1995
rsity of La Plata, Argentina; both M.Sc. (1997) and
Ph.D. (2001) degrees from the Federal University of
Santa Catarina, Brazil, an
(2
System areas of CEPEL, Brazil, and INESC-Porto,
ciate
ineerinofesso the Dtment of Electrical
ver Carlos III of Madrid, Spain. His terests ar
s, le pn,nd
eleal energyystems. Prf. Castronuvo is Sen