Stochastic simulation-optimization framework for energy cost assessment across the water
supply system of Athens
Dionysios Nikolopoulos, Andreas Efstratiadis, George Karavokiros, Nikos
Mamassis, and Christos Makropoulos
Department of Water Resources & Environmental Engineering
National Technical University of Athens, Greece
European Geosciences Union General Assembly
Vienna, Austria, 8-13 April 2018
HS5.7/ERE3.8: Advances in modeling and control of environmental
systems: from drainage and irrigation to hybrid energy generation
Presentation available online: www.itia.ntua.gr/1783/
Nikolopoulos et al., Stochastic simulation-optimization framework for energy cost assessment across the water supply system of Athens 2
How much does the Athens’ raw water cost?
Two companies are involved in Metropolitan Athens’ water:
a public company (Assets EYDAP) for its production and transportation up to the water treatment plants (external water supply system);
a private company (EYDAP S.A.) for the distribution of drinking water to consumers (~ 3.5 million) and wastewater treatment (internal system).
Why this question?
Water cost assessment and retrieval is an obligation by WFD2000/60/EC;
The two companies need to assess a fair cost of raw water in order to regulate their legal agreements.
Breakdown of raw water cost:
Existing infrastructure cost;
Operational and maintenance cost;
Labour and administrative cost;
Environmental cost;
Resource cost.
In the water supply system of Athens, key component of the operational cost is the energy cost, due to pumping, which is not a constant quantity but depends on the time-varying inflows and demands and the water management policy.
Supply cost
Nikolopoulos et al., Stochastic simulation-optimization framework for energy cost assessment across the water supply system of Athens 3
Contrasting the cost of a water bottle to its content
Raw material: plastic or glass
Production fully controllable by the industrial power (assuming unlimited raw material)
Minimal risk of producing faulty products
Steady production cost for a certain amount of bottles
Unit cost decreases as the production of bottles increases (economies of scale)
Unit cost is fully known, at least for a medium-term horizon
Raw material: rainfall and other meteorological drivers
Production depends on rainfall and its transformation to runoff, which are subject to major uncertainties at all temporal scales
Risk of production also depends on complex human drivers, i.e. water uses, constraints and the management policy
The total production cost is expected to increase with demand, particularly when the water is retrieved and transferred via pumping
Providing water to Athens: Evolution of annual demand, population, GDP and infrastructure
Mar
ath
on
dam
Hyl
ike
aqu
edu
ct
Mo
rno
s
Evin
os
tun
nel
Evin
os
dam
1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020
0
1000
2000
3000
4000
5000
0
100
200
300
400
500
1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020
Pop
ula
tio
n (
tho
usa
nd
s)
Wat
er c
on
sum
pti
on
(h
m3)
GD
P (
Bill
ion
$)
Water consumption in AthensGDP of GreecePopulation of Athens
-24%
-63%
-32%
Severe drought
Economic crisis
World War II
Nikolopoulos et al., Stochastic simulation-optimization framework for energy cost assessment across the water supply system of Athens 4
Nikolopoulos et al., Stochastic simulation-optimization framework for energy cost assessment across the water supply system of Athens 5
The water supply system of Athens (~4000 km2)
Mornos (1980) Basin area: 588 km2
Inflows: 239 hm3
Capacity: 630 hm3
Marathon (1932) Basin area: 118 km2
Inflows: 12 hm3
Capacity: 32 hm3
Hylike (1953) Basin area: 2467 km2
Inflows: 288 hm3
Capacity: 585 hm3
Boreholes (1990) Safe yield: 50 hm3
Evinos (2000) Basin area: 352 km2
Inflows: 283 hm3
Capacity: 112 hm3
River Basins
Reservoirs
Pumping Stations
Boreholes
Treatment Plants
Aqueducts
Evinos
Mornos
Boeotikos Kephisos
Marathonas
Management challenges and complexity issues
Conflicting objectives
Energy cost due to pumping (to be minimized)
Long-term reliability (to be maximized)
Multiple hydrosystem operation options
Four reservoirs (total useful capacity 1360 hm3, mean annual inflow 820 hm3)
~100 boreholes, used as emergency resources (estimated safe yield 50 hm3)
Multiple water conveyance paths, some of them through pumping
Multiple water uses
Drinking water to Athens (today ~400 hm3)
Local water uses across the water conveyance network (~70 hm3)
Environmental flows through Evinos dam (30 hm3)
Multiple sources of uncertainty
Non-predictable inflows (hydroclimatic uncertainty)
Uncertain demands, subject to uncertain socio-economic conditions
Uncertain losses due to reservoir (Mornos, Ylike) and conveyance leakages
Uncertain technical characteristics of pumps (capacity, efficiency), resulting in approximate estimation of energy consumption
Nikolopoulos et al., Stochastic simulation-optimization framework for energy cost assessment across the water supply system of Athens 6
Stochastic simulation-optimization framework for energy cost assessment
Nikolopoulos et al., Stochastic simulation-optimization framework for energy cost assessment across the water supply system of Athens 7
Multiple Simulations
Model Parameters λ (μλ, ω)
Uncertainty ω
Input Χ(μx, ω) (Decision Space θ)
Output parameters Z=f(Χ(μx, ω), λ(μλ, ω))
Performance Indicator L(Z(Χ(μx, ω), λ(μλ, ω))
Final Performance Indicator J(θ)=E[L(Z(Χ(μx, ω), λ(μλ, ω))]
Simulation
Optimization
System parameterization
Nikolopoulos et al., Stochastic simulation-optimization framework for energy cost assessment across the water supply system of Athens 8
Since inflows are projected through simulation, the target releases are easily estimated, on the basis on the actual storages and the total water demand.
The rules are mathematically expressed using two parameters per reservoir, thus ensuring a parsimonious parameterization of the related optimization problem, where their values depend on the statistical characteristics of inflows.
Total system storage, v
Target storage, si
*
Reservoir capacity, ki
si* = g(ai, bi, ki, v)
Task 1: Schematization of the hydrosystem
Representation of the water resource system in the graphical environment of Hydronomeas
Nikolopoulos et al., Stochastic simulation-optimization framework for energy cost assessment across the water supply system of Athens 9
Task 2: Generation of hydrological inputs
Synthetic time series
of runoff, rainfall and
evaporation losses
Motivation: Historical hydrological records
are too short to estimate extreme
probabilities e.g. up to 99%; this requires
samples of thousands of years length (e.g.,
~10 000 years, to ensure 1% accuracy)
Nikolopoulos et al., Stochastic simulation-optimization framework for energy cost assessment across the water supply system of Athens 10
Task 3: Establishment of the long-term control policy for reservoirs and boreholes
Operation rules to determine the
reservoir releases
Activation thresholds for
boreholes
Nikolopoulos et al., Stochastic simulation-optimization framework for energy cost assessment across the water supply system of Athens 11
Task 4: Optimal allocation of actual fluxes
?
€
Restricted
discharge
capacity
Alternative
flow paths
Cost due to
pumping
To allow
spill or not?
Targets of
different
priorities
Target releases may differ from the actual
ones, because one of the following reasons:
insufficient availability of water
resources to satisfy the total demand;
insufficient capacity of aqueducts;
alternative flow paths;
multiple and conflicting uses and
constraints to be fulfilled;
insufficient reservoir capacity to store
the actual inflows.
Nikolopoulos et al., Stochastic simulation-optimization framework for energy cost assessment across the water supply system of Athens 12
Task 5: Evaluation and optimization of the hydrosystem operation policy
Failure probability against demands and constraints
Water balance
Annual energy consumption and
related cost for pumping stations
Annual energy consumption and
related cost for borehole groups
Statistical predictions for all fluxes
Nikolopoulos et al., Stochastic simulation-optimization framework for energy cost assessment across the water supply system of Athens 13
Hydronomeas Workflow
Nikolopoulos et al., Stochastic simulation-optimization framework for energy cost assessment across the water supply system of Athens 14
Scenarios & Results
Nikolopoulos et al., Stochastic simulation-optimization framework for energy cost assessment across the water supply system of Athens 15
Four annual demand scenarios: Current state (400 hm3/year) & three future projections (415, 420, 425 hm3/y)
Three sets of optimization weights (management policy): Prioritization of cost, equal importance of cost and reliability and cost double more important than reliability
Results confirm the great effect of management policy to annual reliability and energy cost
As demand increases it is more expensive to provide the same reliability level, thus unit cost of raw water increases too
94%
95%
96%
97%
98%
99%
100%
395 400 405 410 415 420 425 430
Me
an A
nn
ual
Re
liab
ility
Annual Demand (hm3)
2.00
2.50
3.00
3.50
4.00
4.50
5.00
395 400 405 410 415 420 425 430
An
nu
al E
ne
rgy
Co
st (×1
06
€)
Annual Demand (hm3)
Priority: Cost
Equal Significance Cost - Reliability
Cost Double more importnat
Scenarios & Results
Nikolopoulos et al., Stochastic simulation-optimization framework for energy cost assessment across the water supply system of Athens 16
Four annual demand scenarios: Current state (400 hm3/year) & three future projections (415, 420, 425 hm3/y)
Three sets of optimization weights (management policy): Prioritization of cost, equal importance of cost and reliability and cost double more important than reliability
Results confirm the great effect of management policy to annual reliability and energy cost
As demand increases it is more expensive to provide the same reliability level, thus unit cost of raw water increases too
0.004
0.005
0.006
0.007
0.008
0.009
0.010
395 400 405 410 415 420 425 430
Un
it e
ne
rgy
cost
(€
)
Annual Demand (hm3)
Priority: Cost
Equal significance Cost - Reliability
Cost double more important
Conclusions
Economic evaluations and energy assessments are essential elements in the design and management of water resource systems.
Similarly to water and energy fluxes, economic quantities across hydrosystems should also be handled as random variables, since they are driven by uncertain hydrometeorological processes as well as uncertain human-induced demands and constraints.
The cost of raw water of Athens is subject to multiple complexities and uncertainties, and its varies significantly according to the water abstraction and water transfer policy.
In contrast to classical economics, the unit cost of Athens's water does not decrease with the increase of production, since in that case it is essential to activate auxiliary resources requiring pumping, in order to maintain an acceptable reliability level.
The stochastic simulation-optimization framework implemented within the Hydronomeas software allows providing long-term management practices that ensure the minimal energy cost, for a given demand and a given reliability level.
Nikolopoulos et al., Stochastic simulation-optimization framework for energy cost assessment across the water supply system of Athens 17
Related publications Efstratiadis, A., D. Koutsoyiannis, and D. Xenos, Minimising water cost in the water resource management of
Athens, Urban Water Journal, 1(1), 3-15, 2004.
A. Efstratiadis, Y. Dialynas, S. Kozanis, and D. Koutsoyiannis, A multivariate stochastic model for the generation of synthetic time series at multiple time scales reproducing long-term persistence, Environmental Modelling & Software, 62, 139–152, 2014.
Koutsoyiannis, D., A. Efstratiadis, and G. Karavokiros, A decision support tool for the management of multi-reservoir systems, Journal of the American Water Resources Association, 38(4), 945-958, 2002.
Koutsoyiannis, D., and A. Economou, Evaluation of the parameterization-simulation-optimization approach for the control of reservoir systems, Water Resources Research, 39(6), 1170, 1-17, 2003.
Koutsoyiannis, D., G. Karavokiros, A. Efstratiadis, N. Mamassis, A. Koukouvinos, and A. Christofides, A decision support system for the management of the water resource system of Athens, Physics and Chemistry of the Earth, 28(14-15), 599-609, 2003.
Nalbantis, I., and D. Koutsoyiannis, A parametric rule for planning and management of multiple reservoir systems, Water Resources Research, 33(9), 2165-2177, 1997.
Tsoukalas, I., P. Kossieris, A. Efstratiadis, and C. Makropoulos, Surrogate-enhanced evolutionary annealing simplex algorithm for effective and efficient optimization of water resources problems on a budget, Environmental Modelling & Software, 77, 122–142, 2016.