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1 Introduction
In the field of controlling of reservoirs systems, it is often

very difficult to formulate a reliable system of criteria. Control
is usually defined as optimisation of structures and systems in
terms of these appropriate criteria. This proper aims to assess
the possibility of using risk analysis to define control criteria
both in the phase of design and in the phase of operating hy-
draulic structures and systems of reservoirs.

Risk is defined in various ways in the literature. It is mostly
explained as a combination of hazards, vulnerability and ex-
posure. Vulnerability is obviously defined as the aptness of
a structure or system to failure as a result of low resistibility.
Exposure characterises the time period during which the
structure or system is exposed to hazard. Hazards are charac-
terised as the threat of an event, that tends to put the system
into an undesirable state (mortality, economic losses, infra-
structure failure, etc.). Hazards can be divided into natural
hazards, caused generally by natural disasters (earthquakes,
floods, tornados, fire, etc.), and hazards causes by human
actions.

Risk can also be expressed by the theory of reliability. If
the reliability is defined as the probability of the trouble-free
state of the system, then the risk is given by the closeness of
this probability to a certain event. Risk assessment is generally
a very difficult problem. The following relation is often used:

R P C� � , (1)

where R is the risk quantifier, P is the probability of the occur-
rence of losses, and C is monetary loss.

In water management, risk analysis is broadly developed
in the field of dam construction. During the 20th Interna-
tional Congress on Large Dams in Beijing [1] significant
attention was given to risk analysis. Most of the papers dealt
with the analysis of dam failure. The safety of dams using risk
analysis was studied by Nilkens et al [2]. The capacity of the
risk analysis for EIA is described by Riha [3].

A system of reservoirs is usually defined as a system of
water management elements that are mutually linked by
inner and outer connections in a purpose-built complex.
Combined elements are given by reservoirs, river sections,

dams, weirs, hydropower plants, water treatment plants and
other hydraulic structures. These elements also include the
rainfall system, the run-off system, the ground water system,
etc., etc.

Reservoirs and reservoir systems usually serve many pur-
poses at the same time. According to their main purpose,
reservoirs can be categorised as follows:
� water supply (drinking water, industry),
� flood control,
� irrigation,
� navigation,
� recreation,
� environmental function, etc.

2 Methods
Two basic phases need to be distinguished when dealing

with reservoirs and reservoir system. The first phase, from the
system point of view, is the design, while the second phase is
the control and operation of existing systems and structures.
Both phases involve the optimisation problem for the previ-
ously defined set of criteria. Optimisation of the dynamic
system is then called control. Control is often defined as a sys-
tematic action on a control object that satisfies given aims. In
the phase of reservoir design we generally talk about strategic
control, and we are interested in optimising systems or struc-
tures from the long-term point of view. This phase aims at
determining particular reservoir volumes in order to guaran-
tee given reservoir purposes.

In the phase of real operation of previously designed
reservoirs we usually try to optimise the system during all
possible operating situations, namely during extremes such as
floods, hydrological droughts, water quality control, etc. This
kind of optimisation is called real time control, and we try to
satisfy particular reservoir purposes taking into account given
criteria, which can be formulated by minimising the measure
of risk. In a period of hydrological drought, the risk of water
supply failure rises, and it can be losses that can affect society.
There are known approaches for assessing the risk from
floods, hydropower production failure, etc. It is evident that

52 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/

Acta Polytechnica Vol. 44 No. 2/2004

Control of Systems of Reservoirs with
the Use of Risk Analysis
P. Fošumpaur, L. Satrapa

A system of reservoirs is usually defined as a system of water management elements, that are mutually linked by inner and outer connections
in a purpose-built complex. Combined elements consist of reservoirs, river sections, dams, weirs, hydropower plants, water treatment plants
and other hydraulic structures. These elements also include the rainfall system, the run-off system, the ground water system, etc. A system of
reservoirs serves many purposes, which result from the basic functions of water reservoirs: storage, flood control and environmental
functions. Most reservoirs serve several purposes at the same time. They are so called multi-purposes reservoirs. Optimum design and
control of a system of reservoirs depends strongly on identifying the particular purposes. In order to assess these purposes and to evaluate the
appropriate set of criteria, risk analysis can be used. Design and control of water reservoir functions is consequently solved with the use of
multi-objective optimisation. This paper deals with the use of the risk analysis to determine criteria for controlling the system. This approach
is tested on a case study of the Pastviny dam in the Czech Republic.

Keywords: risk analysis, system of reservoirs, multi-objective optimisation, water supply, hydropower plant, fuzzy logic.

risk analysis is a very powerful tool in the area of controlling
reservoir systems.

When carrying out a risk assessment it is very important to
make a loss estimation, which can be deterministic or stochas-
tic. The deterministic approach involves loss estimation for
only one previously measured event. By contrast to the sto-
chastic approach includes the probability distribution of the
studied events. This approach requires the simulation of
numerous scenarios with the use of the Monte-Carlo method.

Determination of the risk with respect to the set of qualita-
tive criteria is a very complicated problem in the area of the
risk assessment. The criteria include the risk of exceeding
the value of a minimum permissible maintained discharge
downstream of the dam, the risk of deteriorating the environ-
mental conditions in the downstream area, and the risk of a
negative impact on the recreation function of a reservoir. In
order to optimise a set of criteria which involves a certain
number of qualitative requirements, we can use fuzzy set
theory and the fuzzy logic theory put forward by Zadeh [4].

In our case study we deal with optimisation of the strategic
control of a reservoir with respect to the following criteria:
� maintenance of the minimum discharge downstream of the

dam,
� flood control,
� hydropower production,
� recreation.

To quantify the measure of risk of the first three criteria,
the time-based reliability (Re) of water supply according to
duration is used [5]:

Re �
�

�
T t

T
�

100 [%], (2)

where T is the duration of the time series and � t is the sum of
the duration of all failures that occurred in the series. The risk

is then equal to a certain event (100%). To quantify the recre-
ation benefits of a reservoir, fuzzy set theory was used.

3 Case study
Multi-objective optimisation of strategic control with the

use of risk analysis was tested on the Pastviny dam on the
Divoka Orlice river (Czech Republic). This is a stone ma-
sonry arch dam built in 1939. The total storage capacity is
11×106 m3, including a flood control capacity of 2×106 m3.
There are six spillways consisting of a fixed sill and located at
three different elevations. The dam is equipped with two
bottom outlets with an inner diameter of 1.4 m. The Pastviny
dam is a typical multipurpose dam. Its primary purpose
is flood control, while the secondary purposes are: produc-

tion of hydroelectric power, discharge regulation in the
downstream part of the Divoka Orlice river, and sport and
recreation.

The criteria for minimum discharge maintenance, flood
control and hydropower production were solved by using
their reliability according to relation (2). The criterion for the
recreation purpose was accomplished by using four fuzzy sets
according to Fig.1. Each fuzzy set describes the quality of rec-
reation by the membership degree index � for the range of

Acta Polytechnica Vol. 44 No. 2/2004

Fig. 1: Fuzzification of the recreation criterion

Fig. 2: Scenarios of the total reservoir volume allocation

water levels in a reservoir. Fig. 1 shows that these are excellent
conditions for recreation in the area around the full active
storage capacity (altitude: 469 m) and as the water level de-
creases the recreation conditions become worse.

Fig.2 shows selected scenarios of the total reservoir vol-
ume allocation to the flood control capacity and the active
storage capacity. The maximum water level in the reservoir is
473 m, and different active storage capacitiesare defined for
the summer and winter periods.

As not all the particular criteria are mutually scalable they
should be normalised into the interval of (0,1). Secondly, pref-
erential weights should be chosen that agree with the order of
significance of particular reservoir purposes. In actual opera-
tion, the order of significance order of particular reservoir
purposes is established in the operating schedule of each
dam. Our research also deals with the sensitivity analysis of
the weight determination. Particular scenarios was performed
with the use of the stochastic dynamic programming. Proba-
bility distribution of the input time series was adopted from

the measured variables from the 1938–1995 period. Fig. 3
shows the dependence of the mean annual hydropower pro-
duction E on the choice of the active storage capacity level Ma.
The hydropower production values are related to the current
level of mean annual production (100%).

Fig.4 shows ratio of the flood control capacity Vr and the
flood volume with given return period N with respect to the
altitude of the water level of the active storage capacity Ma.

The suitability of particular scenarios according to the
recreation purpose of the reservoir was evaluated with the
use of the membership degree of the actual water level to
each fuzzy set during the simulation (Fig.1). The optimum
scenario was then found by standard multi-objective optimi-
sation methods.

4 Conclusions
We studied the use of risk analysis to quantify a suitable

set of criteria for multi-objective optimisation of reservoirs
and reservoir systems, which are usually intended to satisfy

54 © Czech Technical University Publishing House http://ctn.cvut.cz/ap/

Acta Polytechnica Vol. 44 No. 2/2004

100

462 463 464 465 466 467 468 469 470

Ma [m]

V
r
/W

N
[%

] W100

W50
W20

W10

Fig. 4: Dependence of the ratio of the flood control capacity Vr and the flood volume WN with a given return period N with respect to the
altitude of the water level of the active storage capacity Ma

80.0%

85.0%

90.0%

95.0%

100.0%

105.0%

462 463 464 465 466 467 468 469 470

Ma [m]

E
[%

]

Fig. 3: Dependence of mean annual hydropower production on the choice of water level Ma of the active storage capacity

several purposes at the same time. These purposes can be in
contradiction with each other. The described methodological
approach of multi-objective optimisation was applied to a
case study of the Pastviny dam in the Czech Republic, which
serves for flood control, hydropower production, discharge
regulation, and recreation purposes. Reliability theory was
used for risk assessment of quantifiable criteria. The research
has proved that fuzzy set theory is efficient for quantifying
fully qualitative criteria, such as the recreation or environ-
mental function of reservoirs.

5 Acknowledgment
This research has been supported by grant No.

103/02/0606 and grant No. 103/02/D049 of the Grant Agency
of the Czech Republic.

References
[1] 20th International Congress on Large Dams. Vol. 1, Ques-

tion 76, Beijing China, Paris: ICOLD 2000, p. 896.
[2] Nilkens B., Rettemeier K.: “Risk Assessment Procedure

for German Dams”. In: Workshop on the occasion of the
69th Annual Meeting of ICOLD in Dresden, 2001.

[3] Riha J.: Evaluation of Investment Impacts on Environment.
Multipurpose Analysis EIA, Prague, Academia, 1995.

[4] Zadeh L. A.: Fuzzy sets. Information and control. Vol. 8,
(1965), p.338–353.

[5] Votruba L., Broža V.: Water Management in Reservoirs.
Elsevier: Prague SNTL, 1989.

Dr. Ing. Pavel Fošumpaur
phone: +420 224 354 425
e-mail: fosump@fsv.cvut.cz

Ass. Prof. ing. Ladislav Satrapa, Ph.D.
phone: +420 224 354 618
e-mail: satrapa@fsv.cvut.cz

Department of Hydrotechnics

Czech Technical University in Prague
Faculty of Civil Engineering
Thákurova 7
166 29 Prague 6, Czech Republic

Acta Polytechnica Vol. 44 No. 2/2004

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Speech Signal Recovery in Communication Networks 59
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