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.