A combined linear optimisation methodology for water resources allocation in Alfeios River Basin (Greece) under uncertain and vague system conditions

Abstract

In the present study, a combined linear programming methodology, based
on Li et al. (2010) and Bekri et al. (2012), is employed for optimizing
water allocation under uncertain system conditions in the Alfeios River
Basin, in Greece. The Alfeios River is a water resources system of great
natural, ecological, social and economic importance for Western Greece,
since it has the longest and highest flow rate watercourse in the
Peloponnisos region. Moreover, the river basin was exposed in the last
decades to a plethora of environmental stresses (e.g. hydrogeological
alterations, intensively irrigated agriculture, surface and groundwater
overexploitation and infrastructure developments), resulting in the
degradation of its quantitative and qualitative characteristics. As in
most Mediterranean countries, water resource management in Alfeios River
Basin has been focused up to now on an essentially supply-driven
approach. It is still characterized by a lack of effective operational
strategies. Authority responsibility relationships are fragmented, and
law enforcement and policy implementation are weak. The present
regulated water allocation puzzle entails a mixture of hydropower
generation, irrigation, drinking water supply and recreational
activities. Under these conditions its water resources management is
characterised by high uncertainty and by vague and imprecise data. The
considered methodology has been developed in order to deal with
uncertainties expressed as either probability distributions, or/and
fuzzy boundary intervals, derived by associated α-cut levels. In
this framework a set of deterministic submodels is studied through
linear programming. The ad hoc water resources management and
alternative management patterns in an Alfeios subbasin are analyzed and
evaluated under various scenarios, using the above mentioned
methodology, aiming to promote a sustainable and equitable water
management. Li, Y.P., Huang, G.H. and S.L., Nie, (2010), Planning
water resources management systems using a fuzzy-boundary
interval-stochastic programming method, Elsevier Ltd, Advances in Water
Resources, 33: 1105-1117. doi:10.1016/j.advwatres.2010.06.015 Bekri,
E.S., Disse, M. and P.C.,Yannopoulos, (2012), Methodological framework
for correction of quick river discharge measurements using quality
characteristics, Session of Environmental Hydraulics - Hydrodynamics,
2nd Common Conference of Hellenic Hydrotechnical Association and Greek
Committee for Water Resources Management, Volume: 546-557 (in Greek).

Full text

(1) Environmental Engineering Laboratory, Department of Civil
Engineering, University of Patras, Patras, Greece
(2) Institute of Water Management and Resources Engineering,
Universität der Bundeswehr München, Munich, Germany
A COMBINED LINEAR OPTIMISATION METHODOLOGY
FOR WATER RESOURCES ALLOCATION
IN AN ALFEIOS RIVER SUBBASIN (GREECE)
UNDER UNCERTAIN AND VAGUE SYSTEM CONDITIONS
Eleni Bekri
(1)(2)
, Panayotis Yannopoulos
(1)
& Markus Disse
(2)

Introduction in uncertainties in water resources management
Brief description of applied methodology
(Huang et al., 1992; Li et al., 2010)
Characteristics of the studied Alfeios River Subbasin
Formulation of the optimisation problem
Uncertain variable identification
Results & Conclusions
OVERVIEW

INTRODUCTION
Uncertainties in water resources management in impact factors & system
components :
 Available water resources
 Water Demand / supplies
 Related cost / benefit coefficients
 Sustainability requirements
 Policy regulations
In optimization problem:
Decision variables
Objective function coefficients
Constraints coefficients
Types of uncertainty variables:
Probability distribution
Possibility distribution
Interval (Upper & Lower Value)

DESCRIPTION OF METHODOLOGY
Fuzzy-boundary interval - stochastic programming (Li et al., 2010):
Linear optimization problem
Uncertain variables: (a) favourable (X
ij
+
) & (b) unfavourable (X
ij
-
)
Aim: Identification of optimal water allocation target with minimised
risk of economic penalty from water shortage (water demand)
& opportunity loss from spill water volumes
Two solution methods:
1. “Risk-Prone” or “Optimistic” (best -case model)
2. “Risk-adverse” or “Pessimistic” (worst -case model)
Different solution methods imply
different risk attitudes of decision makers
considering system uncertainties

Discretization of membership grade into α-cut levels (0, 1)
Solving for each solution type and α-cut level:
2
n
deterministic submodels corresponding to all combinations of
lower & upper bound value for n fuzzy / interval variables
For each solution type: f
α
opt
= {f
min
α
, f
max
α
},
where f
min
α
=min{f
1
,f
2
,.., f
2
n
}
f
max
α
=max{f
1
,f
2
,.., f
2
n
}
DESCRIPTION OF METHODOLOGY
0.5
Lower
Bound
Upper
Bound
Lower
Bound
Fuzzy
Interval
Uncertain
Variable
Upper
Bound
α- cut level

EXAMINED ALFEIOS RIVER SUBBASIN
1. Ladhon Dam - HPS
2. Flokas Dam – HPS
- Irrigation canal

LADHON RESERVOIR & HYDROPOWER STATION
Ladhon Reservoir - Dam:
Gross - usable storage: 57.6 ×10
6
- 46.2×10
6
m
3
Main purposes: Irrigation & Hydropower production
Monthly operational curve (target reservoir level)
Ladhon Hydropower Station:
~8 km downstream from Ladhon Dam
Purpose: Satisfy peak energy demand
Total max capacity: 70 MW
Primary & Total Mean Annual Energy: 173 & 340 GWh

FLOKAS DAM – IRRIGATION
Flokas Dam:
Diversion dam for irrigation purposes
16 km from Kyparissiakos Gulf coastline
97% of Alfeios catchment
Small Hydroelectric Power Station :
Max power capacity : 6.6 MW
Flokas Irrigation canal:
Present irrigated area : 50-60% Total irrigable area (12,250 ha)
Irrigation period : Mid April to Mid October
Crop pattern : Cotton, corn, alfalfa, watermelons, citrus
Surface and drip irrigation

Maximise Total Benefit :
Benefit(HPLadhon) - Penalty(SpillLadhon) +
Benefit(Irrigation+Extra) - Penalty(IrrigationShortage) +
Benefit(HPFlokas) - Penalty(SpillFlokas)
OPTIMISATION PROBLEM
Constraints: 1. Ladhon:
 Water Volume Mass Balance
 Min & Max pumping capacity
 Min & Max reservoir storage capacity
 Evaporation: linear F(average reservoir storage(t))
2. Flokas: (Degree of Ladhon Contribution to Flokas)
 Water Volume Mass Balance
 Min & Max pumping capacity
 Fish ladder flows & Min environmental flows
Objective function:

UNCERTAIN VARIABLES
VariableName
Uncertainty Type
Variable Effect
Unit Benefit HP Ladhon (€/MWh)
Fuzzy: LB (40, 50, 55), UB (60, 65, 75)
Favourable
Unit Benefit HP Flokas (€/MWh)
Interval: (80, 87.75)
-
Unit Benefit Irrigation Flokas (€/m
3
)
Interval: LB (0.19, 0.2), UB (0.24, 0.26)
Favourable
Unit Penalty HP Ladhon (€/MWh)
Fuzzy: LB (90, 115), LB (0.19, 0.2)
Unfavourable
Unit Penalty HP Flokas (€/MWh)
Interval: (120, 130)
-
Unit Penalty Irrigation Flokas (€/m
3
)
Fuzzy: UB (0.29, 0.31), LB (0.36, 0.39)
Unfavourable
Ladhon Contribution To Flokas (%)
Interval: (0.65, 0.71)
-
 For Hydropower Production Unit Benefit/ Penalty:
 operators experience Flokas: Price for small HPS
 Max observed energy sale price of Greek Energy Market
 For Irrigation Unit Benefit/ Penalty (Flokas):
 Net agricultural income per crop + Irrigation water cost
 Net agricultural income per crop + Groundwater pumping costs

RESULTS
2 . Free: No operation rule (Ladhon reservoir)
 Optimisation using LINGO – M. Excel
 Available data: monthly inflows in Ladhon reservoir
(2002-2012)
 Time step / period: Monthly / one year
 Selection of a. wet year (2003)
b. dry year (2007)
 Examined α-cut levels: 0 - 0.5 - 1
 Total number of deterministic submodels: 576
1. Present Water allocation: Min monthly reservoir water level (Ladhon)
 Two alternative scenarios:

0
10.000.000
20.000.000
30.000.000
40.000.000
Present Rule
Free
2007 - Total Benefit (€) for α-cut level 1
Optimistic - Min
Optimistic - Max
Pessimistic - Min
Pessimistic - Max
RESULTS
Total Excess Benefit 36%
Variation of Total Benefit value : up to 32%

0
20.000.000
40.000.000
60.000.000
Present Rule
Free
2003 - Total Benefit (€) for α-cut level 1
Optimistic - Min
Optimistic - Max
Pessimistic - Min
Pessimistic - Max
RESULTS
Total Excess Benefit 9%
Variation of Total Benefit value : up to 29%

CONCLUSIONS
Flexible & efficient incorporation of uncertainties (intervals and fuzzy)
in linear optimisation process through α-cut levels, providing a clear &
comprehensive interpretation of uncertain variable values at each stage.
Assessment & comparison of total benefit range of various water
allocation pattern for a risk-prone and risk-adverse attitudes of decision
makers
Further analysis of uncertain variables: (social benefits and non
consuming water uses i.e. tourism and recreation)
Further investigation of appropriate adjustments incorporating stochastic
water inflows into methodology
OUTLOOK

Thank you for your attention!
When you bend down and look at the waters of the Alfeios river near
Olympia, their clarity is such that your face and soul are mirrored in
them... The nature becomes here spirit. The clarity of waters becomes
clarity of thought ...
Panayiotis Kanellopoulos (1902-1986)
Professor of Sociology, Prime Minister of Greece

We would like to express our gratitude to:
1. Dimitrakopoulos D., Argyrakis I., Mavros I.,
Gatsis K., and Stathas I. from the Hellenic Public
Power Corporation,
2. Panayotopoulos N., Rousakis I.from HPS Flokas,
3. Tzifas V., Altanis T. and Labadaris A.
4. Dr.-Ing Karellas S. from Laboratory of Steam
Boilers and Thermal Plants School of Mechanical
Engineering, National Technical University of
Athens and Dipl.-Ing. Varela Gl., University of
Stuttgart
for their support and for providing necessary data.
This research is also supported by HYDROCRITES
University Network.
(http://www.hydrocrites.upatras.gr)
This research has been co-financed by the
European Union (European Social Fund – ESF)
and Greek national funds through the
Operational Program
"Education and Lifelong Learning" of the
National Strategic Reference Framework (NSRF)
- Research Funding Program: Heracleitus II.
Investing in knowledge society through the
European Social Fund.
ACKNOWLEDGEMENTS:
European Union
European Social Fund