Contribution of Pumped-Hydro Storage to Electrical Grids · Contribution of Pumped-Hydro Storage to Electrical Grids and Improvement Measures José Gonçalo Faria de Sousa Thesis

Contribution of Pumped-Hydro Storage to Electrical Grids

and Improvement Measures

José Gonçalo Faria de Sousa

Thesis to obtain Master’s degree in

Civil Engineering

Supervisor: Profª DrªHelena Margarida Machado da Silva Ramos

Examination Committee

President: Prof. Dr. António Alexandre Trigo Teixeira

Supervisor: Prof.ª Dra.Helena Margarida Machado da Silva Ramos

Members of the Committee: Prof. Dr. José Carlos Páscoa Marques

July 2015

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Acknowledgements

I would like to start by expressing my gratitude to my supervisor Professora Helena Ramos for her

patience and the opportunity to work with her.

To Engº Duarte Nuno Neves, Engº José Luís Pinheiro and EEM for their solicitude, patience and

provided information.

To Francisco Ferreira and IGA for the provided information.

To my family, for the unconditional love, patience, support and encouragement throughout my whole life

and, in particular, throughout my Master degree.

To Carolina, for everything.

To all my colleagues and teachers for their support and knowledge.

And last but not least, to my friends, whose friendship I treasure.

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v

RESUMO

O objectivo deste trabalho é realizar o estudo da importância do armazenamento de energia por

bombagem nos reservatórios de sistemas elevatórios, os seus impactos a nível social, económico e

ambiental, e o estudo das diferentes tecnologias existentes, assim como soluções para optimizar o seu

desempenho.

O aumento da penetração das energias renováveis em redes eléctricas acarreta algumas

contrariedades a nível da segurança e estabilidade das mesmas, pois introduz uma acrescida

variabilidade na curva do diagrama de cargas de produção/consumo, sendo o armazenamento uma

das mais vantajosas possíveis para facer face ao défice e variabilidade na produção/consumo de

energia eléctrica.

Uma análise à presente situação da produção eléctrica a nível global e regional é feita, com foco nas

percentagens de capacidade instalada, impactos ambientais, custos, reservas e previsões para fontes

de energia fósseis, nucleares e renováveis, evidenciando a importância das fontes renováveis e o

armazenamento de energia nas questões de segurança e dependência energética no presente e no

futuro.

O armazenamento por bombagem é estudado, focando-se o estudo nas diferentes tecnologias

existentes, assim como na adopção de alterações que permitam optimizar a sua eficiência. A

variabilidade introduzida nos diagramas de carga pelas energias renováveis e a função dos sistemas

de armazenamento por bombagem no seu equilíbrio são também analisadas.

O caso de estudo do Aproveitamento de Fins Múltiplos dos Socorridos situado, na Ilha da Madeira, é

realizado, com análises ao seu diagrama e modo de funcionamento, atendendo aos impactos na

redução de emissão de gases de efeito de estufa, na penetração de energias renováveis na rede

eléctrica e regulação do diagrama de carga. A introdução de um novo sistema reversível, o Sistema

Hidroeléctrico Reversível da Calheta – Calheta III, é também analisada.

É feita uma operação de optimização recorrendo a modelos desenvolvidos em MATLAB, com o

objectivo de comparar o sistema existente nos Socorridos com a adopção de alterações que visam

optimizar a sua eficiência, nomeadamente a instalação de equipamento com velocidade de rotação

variável, e o uso de condutas separadas entre as operações de bombagem e turbinagem. O

desempenho do sistema é medido através da análise dos custos e dividendos que cada solução gera,

e por fim, os resultados são analisados e comparados.

Palavras-Chave: armazenamento por bombagem, sistemas reversíveis, energias renováveis, rede

eléctrica, velocidade de rotação varíavel, eficiência energética

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ABSTRACT

The purpose of this work is to study the importance of energy storage through pumped-hydro storage

(PHS), as well as its social, economic and environmental impacts, and to study the different PHS

technologies, and the ways in which the performance of such systems can be improved.

The increase of the share of renewable energy generation in electrical grids raises security and stability

problems, as it introduces added variability in the consumption/supply load curves. Storage is one of the

most advantageous possible solutions to address the deficit and variability in the consumption/supply in

the electrical grid.

An analysis to the current global and regional situation of electricity production is drawn, with focus on

share of installed capacity, impacts to the environment, costs, reserves and forecasts for fossil, nuclear

and renewable sources, stressing the importance of renewable energy and energy storage in present

and future security and energy dependency issues.

Pumped hydro storage is studied, focusing on different available technologies and possible system

improvements, in order to make it more efficient. The variability of supply/demand load diagrams which

is introduced by renewable energy sources and the role of PHS in balancing it is studied.

The case study of the Multiple Purpose Socorridos System in Madeira Island is made, with analysis to

its functioning diagram and schedule, its impacts on avoided greenhouse gas emissions, renewable

energy penetration and load diagram balancing. The introduction of a new reversible system, the

Calheta Hydroelectric Reversible System - Calheta III, is also analyzed.

An optimization procedure using MATLAB is done to compare the existing system to the introduction of

different system improvements as described in the previous pumped hydro systems study, namely the

use of adjustable speed equipment, and the use of a separate penstock for pumping and turbining.

Performance is measured through generated revenues and, in the end, results are discussed and

compared.

Keywords: pumped hydro storage, renewable energies, load balancing, electrical grid, adjustable

speed, energy efficiency

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Contents

1. Introduction .................................................................................................................................... 1

1.1 Scope ....................................................................................................................................... 1

1.2 Objectives ................................................................................................................................ 2

2. State of the Art ............................................................................................................................... 3

2.1 Electricity Generation Overview ............................................................................................... 3

2.2 Fossil Fuels in Electricity Generation ....................................................................................... 6

2.2.1 Greenhouse Gas Emissions ............................................................................................... 6

2.2.2 Reserves ............................................................................................................................ 8

2.2.3 Costs .................................................................................................................................. 9

2.2.4 Installed Capacity ............................................................................................................. 13

2.3 Nuclear Fission in Electricity Generation ............................................................................... 14

2.3.1 Greenhouse Gas Emissions ............................................................................................. 14

2.3.2 Reserves .......................................................................................................................... 14

2.3.3 Costs ................................................................................................................................ 15


2.3.5 Radioactive Waste Management ...................................................................................... 16

2.4 Renewable Energy Sources .................................................................................................. 17

2.4.1 Greenhouse Gas Emissions ............................................................................................. 17

2.4.2 Costs ................................................................................................................................ 19


2.4.4 Energy Return on Energy Invested .................................................................................. 24

2.4.5 Security and Dependency ................................................................................................ 25

2.4.6 Energy Storage ................................................................................................................ 28

3. Pumped Storage .......................................................................................................................... 32

3.1 Technology ............................................................................................................................ 34

3.1.1 Conventional Pumped Storage ......................................................................................... 34

3.1.2 Seawater Pumped Storage .............................................................................................. 37

3.1.3 Sea bed Pumped Storage ................................................................................................ 44

3.1.4 Underground Pumped Storage ......................................................................................... 45

3.1.5 System improvements ...................................................................................................... 46

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3.2 Mitigation of variability in RES generation ............................................................................. 50

4. Case Study - Multiple Purpose Socorridos System ...................................................................... 54

4.1 Project description ................................................................................................................. 54

4.2 Madeira’s Renewables Potential ............................................................................................ 62

4.3 Optimization Algorithm ........................................................................................................... 68

4.3.1 Pumped hydro storage with single penstock .................................................................... 70

4.3.2 Pumped hydro storage with double penstock ................................................................... 82

5. Analysis and Comments ............................................................................................................... 85

6. Final Conclusions and Recommendations ................................................................................... 91

6.1 Final Conclusions .................................................................................................................. 91

6.2 Recommendations ................................................................................................................. 92

References ........................................................................................................................................... 95

Appendixes ........................................................................................................................................ 101

A. Script code for Single Penstock Non-Linear Solver .................................................................... 102

B. Script code for Double Penstock Non-Linear Solver .................................................................. 106

C. Objective functions for Single and Double Penstock Non-Linear Solvers .................................. 112

D. Script code for calculating wasted wind energy and energy surplus from the grid ..................... 113

E. Results for Single Penstock ten scenarios simulations .............................................................. 118

F. Results for Double Penstock ten scenarios simulations ............................................................. 120

G. Results for wasted wind energy for single and double penstock for ten scenarios simulations . 123

H. Results for energy surplus from grid, for single and double penstock with synchronous speed

technology, for ten scenarios simulations .......................................................................................... 126

I. Flow histograms for single and double penstock over summer (dry) season ............................. 128

J. Pump station efficiency for adjustable speed ............................................................................. 132

K. Results for consumed/generated energy for double penstock ................................................... 133

L. Results for consumed/generated energy for double penstock ................................................... 140

M. Records from July of 2014 of the Socorridos System: Consumed/generated energy and water level

for the upper and lower reservoirs...................................................................................................... 147

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Figure Contents

Figure 2.1 – (a) World net electricity generation by fuel, 2010-2040; (b) Growth in world total electricity

generation and total delivered energy consumption, 1990-2040 (adapted from EIA (2013)) ................. 3

Figure 2.2 Fossil fuel and cement annual anthropogenic CO2 emissions (in PgC yr–1) from 1750 to 2011

............................................................................................................................................................... 4

Figure 2.3 - Three observational estimates of GMST (black lines) from three different datasets

(HadCRUT4, GISTEMP and MLOST), compared to model simulations (CMIP3 and CMIP5) with (a)

anthropogenic and natural forcings, (b) natural forcings only and (c) greenhouse gas forcing only. Thick

red and blue lines are averages across all available simulations (IPCC, 2013) ..................................... 4

Figure 2.4 - CO2 reduction potential of coal-fired power plants by increased efficiency (adapted from

Christensen et al. (2013)) ....................................................................................................................... 8

Figure 2.5 - The Levelised Cost of Electricity of integrated CCS projects (blue bars) compared to the

reference plants without CCS (green bars) (ZEP, 2011) ...................................................................... 10

Figure 2.6 Fossil-fuel consumption subsidy rates as a proportion of the full cost supply in 2011 (adapted

from IEA (2012)) ................................................................................................................................... 10

Figure 2.7 - State support 1970 – 2012 in Germany in billion € (real prices) (Küchler & Meyer, 2012) 11

Figure 2.8 – Cost of electricity production vs operating hours (adapted from Christensen et al.

(2013) ................................................................................................................................................... 12

Figure 2.9 – Fossil fuel prices in baseline (Constant USD of 2008 per barril of oil equivalent (boe))

(adapted from EC (2009)) .................................................................................................................... 12

Figure 2.10 – Projected and announced power plant capacities in Europe as of 2007, (adapted from

Christensen et al. (2013)) ..................................................................................................................... 13

Figure 2.11 – World identified uranium resources by year (adapted from IAEA (2011)) ...................... 15

Figure 2.12 - World’s existing nuclear power plants, planned shutdowns, new plants and projects

Christensen et al. (2013) ...................................................................................................................... 16

Figure 2.13 - Cumulative emissions reductions for alternative mitigation measures. The figure illustrates

scenarios from four models (AIM, IMAGE, IPAC and MESSAGE) aiming at the stabilization at low (490

to 540ppm CO2-eq) and intermediate levels (650ppm CO2-eq) respectively. The solid bars denote

reductions for a target of 650 ppm CO2-eq and the striped bars denote the additional reductions to

achieve 490 to 540 ppm CO2-eq (IPCC, 2007) .................................................................................... 18

Figure 2.14 – Typical LCOE ranges for renewable power generation technologies, in 2012 and 2020

(adapted from IRENA (2012)) .............................................................................................................. 20

Figure 2.15 - Future development of investment costs for RPGT (Normalised to 2009 cost levels)

(EREC, Greenpeace, GWEC, 2012) .................................................................................................... 20

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Figure 2.16 - (a) Cost trend of land-based wind turbine prices, by contract date; (b) Recent trends in

average price for full-service O&M contracts (EUR/MW/yr) (IEA, 2013) .............................................. 22

Figure 2.17 – (a) World RES share of electricity produced by source in 2012; (b) European Union RES

share of electricity produced by source in 2012 (adapted from Observ'ER (2013)). ............................ 23

Figure 2.18 – (a) Portugal RES share of installed capacity by source in 2012 (adapted from DGEG,

2014); (b) Madeira Island RES share of installed capacity by source in 2011 (adapted from EEM (2011))

............................................................................................................................................................. 23

Figure 2.19 - Daily load curve separated into base, intermediate and peak load (adapted from Cordaro

(2008)) .................................................................................................................................................. 26

Figure 2.20 – Load rates of different power plants (adapted from Inage (2009)) ................................. 27

Figure 2.21 – Demand and supply of wind power in Denmark (Inage, 2009) ...................................... 28

Figure 2.22 - Comparison of the wind power supply and net trade in western Denmark in 2006 (Inage,

2009) .................................................................................................................................................... 29

Figure 2.23 - The relationship of net wind power variation and necessary storage capacities (adapted

from (Inage, 2009)) .............................................................................................................................. 30

Figure 2.24 – Comparison of energy storage technologies (SBC Energy Institute, 2013) ................... 31

Figure 3.1 - Relationship between water volume requirements as a function of net head between

reservoirs, for 1,000 MWh of stored energy (Hearps et al., 2014) ....................................................... 33

Figure 3.2 - Principle of pumped hydro storage systems, showing discharge during the day (left) and

charge during the night (right) (adapted from (Inage, 2009)) ............................................................... 35

Figure 3.3 - Operation and revenues during a sample period (1/1/2008) corresponding to a simulation

with hourly energy prices in South Australia (Hearps, et al., 2014) ...................................................... 35

Figure 3.4 – Marmora Pumped Storage project site before construction (left) and how it will be after the

upper reservoir is built. ......................................................................................................................... 36

Figure 3.5 – Marmora Pumped Storage project schematic profile (adapted from Friesen (2013)) ...... 36

Figure 3.6 – Baixo Sabor Power Plant’s upper (left) and lower (right) reservoirs (adapted from EDP

(2014)) .................................................................................................................................................. 37

Figure 3.7 - Bird’s-Eye View of the Okinawa Seawater Pumped-storage Power Plant (Fujihara et. al,

1998) .................................................................................................................................................... 38

Figure 3.8 – Sectional view of the Okinawa Seawater Pumped-storage Power Plant (Fujihara et. al,

1998) .................................................................................................................................................... 38

Figure 3.9 - Sectional view of the Okinawa Yanbaru Seawater Pumped Storage Power Station pump

turbine (Fujihara et. al, 1998) ............................................................................................................... 41

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Figure 3.10 – Drainage system of the Okinawa Seawater Pumped-storage Power Plant (Japan

Commission on Large Dams, 2001) ..................................................................................................... 42

Figure 3.11 - Schematic diagram of Muuga hydro accumulation power plant (ESTIVO, 2010) ........... 44

Figure 3.12 – Schematic view of a sea bed PSPP (Gangåssæter & Doghouse, 2013) ....................... 44

Figure 3.13 – Schematic view of an underground PSPP (Inage, 2009) ............................................... 46

Figure 3.14 - Comparative Performance of Original and Upgraded Pump/Turbines (Inage, 2009) ..... 47

Figure 3.15 - Operating ranges of fixed-speed (left) and adjustable-speed (right) pumps (adapted from

Krenn et. al (2013)). ............................................................................................................................ 48

Figure 3.16 - System reserve and power storage from variable-speed vs single-speed pumped storage

(Ciocan et. al, 2012) ............................................................................................................................. 48

Figure 3.17 - Operating ranges of fixed-speed (left) and adjustable-speed (right) turbines (adapted from

Krenn et. al (2013)) ............................................................................................................................. 49

Figure 3.18 – Double penstock in system with wind farm powering the pumps (Pálmason, 2010) ...... 50

Figure 3.19 – System load following and frequency regulation. Frequency regulation (red) is the fast

fluctuating component that balances total load (green), (Denholm et. al, 2010) .................................. 50

Figure 3.20 – Impact on net load from increased use of variable generation units (Denholm et. al, 2010)

............................................................................................................................................................. 51

Figure 3.21 – Variable RES generation curtailment in a high RES penetration grid (adapted from

(Denholm et. al, 2010) .......................................................................................................................... 52

Figure 3.22 – Storage as an option for increasing the use of variable RES by decreasing curtailment

(D

enholm et. al, 2010) 53

Figure 4.1 – The Multiple Purpose Socorridos System changes from its initial configuration (IFDR, 2007)

............................................................................................................................................................. 55

Figure 4.2 – Snapshots of the schematic operation of the system in turbine mode (adapted from (EEM,

2006)) ................................................................................................................................................... 56

Figure 4.3 - Snapshots of the schematic operation of the system in pump mode (adapted from (EEM,

2006)) ................................................................................................................................................... 57

Figure 4.4 - Floor plan and two sections of the Socorridos Hydroelectric Station (EEM, Aproveitamento

de Fins Múltiplos da Ribeira dos Socorridos) ....................................................................................... 58

Figure 4.5 – Turbines at Socorridos Hydroelectric station ................................................................... 59

Figure 4.6 - Profile and cross section of the Socorridos Pump Station (CENOR) ................................ 60

Figure 4.7 – Pumps at Socorridos Pump Station ................................................................................. 60

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Figure 4.8 – Profile of the penstock connecting Covão Reservoir to the Socorridos Plant (adapted from

(EEM, Aproveitamento de Fins Múltiplos da Ribeira dos Socorridos)) ................................................. 61

Figure 4.9 – Socorridos reversible system’s effect on the summer load diagram for Madeira Island

(adapted from (EEM, 2006)) ................................................................................................................ 61

Figure 4.10 – CO2 emissions in electricity generation projected comparison between different solutions

in RAM (Vice Presidência do Governo Regional da Madeira, 2008).................................................... 62

Figure 4.11 – Evolution of RES in electricity generation in RAM, from 2007 to 2011 (adapted from (Vice-

Presidência do Governo Regional da Madeira, 2012) ......................................................................... 63

Figure 4.12 – Load diagram in grid without Socorridos Reversible System (adapted from (EEM,

2010)) ................................................................................................................................................... 64

Figure 4.13 – Load diagram in grid with Socorridos Reversible System (adapted from (EEM, 2010)) 64

Figure 4.14 – Projected share of RES in RAM’s electric grid from 2010 to 2020 (Vice-Presidência do

Governo Regional da Madeira, 2012) .................................................................................................. 65

Figure 4.15 – Schematic illustration of the Calheta III Reversible System (Vice-Presidência do Governo

Regional da Madeira, 2008) ................................................................................................................. 67

Figure 4.16 - Load diagram in grid with both Socorridos and Calheta Reversible System (adapted from

EEM, 2010) .......................................................................................................................................... 67

Figure 4.17 –Hourly average wind speed in Loiral - July 2014 ............................................................ 74

Figure 4.18 – VESTAS V90 wind turbine power curve ......................................................................... 74

Figure 4.19 - Hourly percentage of the total generated wind energy that can be fed into the Socorridos

System ................................................................................................................................................. 75

Figure 4.20 – Electricity Tariff (€/kWh) (EEM, 2015) ............................................................................ 75

Figure 4.21 - Average hourly consumption derived water level variation in the upper reservoir (m) .... 76

Figure 4.22 - Average hourly inlet derived water level variation in the upper reservoir (m) ................. 76

Figure 4.23 – Pump efficiency vs Flow ................................................................................................. 78

Figure 4.24 – Operating efficiency of VFD (FLYGT, 2011) .................................................................. 78

Figure 4.25 – Adjustable speed pump station efficiency ...................................................................... 79

Figure 4.26 – Efficiency correlation with discharge for different turbine types, assuming a fixed net head

and rotation speed (Quintela, 2002) ..................................................................................................... 79

Figure 5.1 - Flow histogram over summer season for single penstock ................................................ 85

Figure 5.2 - Results for one scenario simulation of adjustable speed with a single penststock ........... 85

Figure 5.3 - Results for one scenario simulation of synchronous speed with a single penstock .......... 86

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Figure 5.4 - Results for water level of the upper reservoir for one scenario simulation of single penstock

............................................................................................................................................................. 86

Figure 5.5 - Results for hourly water level of the lower reservoir for one scenario simulation of single

penstock ............................................................................................................................................... 86

Figure 5.6 - Flow histogram over summer season for double penstock ............................................... 87

Figure 5.7 - Results for one scenario simulation of adjustable speed with double penststock ............. 87

Figure 5.8 - Results for one scenario simulation of synchronous speed with double penstock ........... 88

Figure 5.9 - Results for hourly water level of the upper reservoir for one scenario simulation of double

speed ................................................................................................................................................... 88

Figure 5.10 - Results for hourly water level of the lower reservoir for one scenario simulation of double

speed ................................................................................................................................................... 88

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Table Contents

Table 2.1 - GHG emissions from electricity generation by fossil fuel source (g CO2eq/kWh) (adapted

from Moomaw et al. (2011)) ................................................................................................................... 7

Table 2.2 - GHG emissions from electricity generation from RES (g CO2eq/kWh) (adapted from Moomaw

et al. (2011)) ......................................................................................................................................... 18

Table 2.3 - Average levelized power generation costs comparison between RES, nuclear and fossil fuel

sources (2011 $/megawatthour) for plants entering service in 2018 (adapted from EIA (2013)) ......... 21

Table 2.4 - Scenarios for shares of RES in electricity (adapted from (REN21, ISEP, 2013)) .............. 24

Table 2.5 - EROEI ratios for different fuel sources in the USA (University of Illinois, 2013) ................ 25

Table 4.1 – Socorridos Hydroelectric Station turbine characteristics ................................................... 58

Table 4.2 – Socorridos Pump Station pump characteristics ................................................................. 59

Table 4.3 – Percentage of RES penetration in the electricity generation mix by year in RAM (Vice-

Presidência do Governo Regional da Madeira, 2012) ......................................................................... 63

Table 4.4 – Hourly water level variations in the upper reservoir for Functions 4.1 and 4.2 .................. 71

Table 4.5 – Hourly water level limits for the upper and lower reservoirs for Functions 4.1 and 4.2 ..... 71

Table 4.6 –Reservoir properties ........................................................................................................... 83

Table 4.7 – Pump and Turbine equipment properties .......................................................................... 83

Table 4.8 – Wind turbine properties ..................................................................................................... 83

Table 4.9 – Hourly input data for the optimization algorithm ................................................................ 84

Table 5.1 - Results for Energy balance by technology ......................................................................... 89

Table 5.2 - Results for Energy surplus by technology .......................................................................... 89

Table 5.3 - Results for Absorbed wind energy by technology .............................................................. 89

Table 5.4 -Results for Costs/Revenues balance by technology ........................................................... 90

Table A 1 – Hourly water level variations in upper reservoir for ten scenarios simulations for single

penstock (m) ...................................................................................................................................... 118

Table A 2 – Hourly water level of the upper reservoir for ten scenarios simulations for single penstock

(m) ...................................................................................................................................................... 118

Table A 3 - Hourly water level of the lower reservoir for ten scenarios simulations for single penstock

(m) ...................................................................................................................................................... 119

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Table A 4 - Hourly water level variations in upper reservoir for ten scenarios simulations for double

penstock (m) ...................................................................................................................................... 120

Table A 5 - Hourly water level of the upper reservoir for ten scenarios simulations for double penstock

(m) ...................................................................................................................................................... 121

Table A 6 - Hourly water level of the lower reservoir for ten scenarios simulations for double penstock

(m) ...................................................................................................................................................... 122

Table A 7 – Hourly wasted wind energy for adjustable speed and single penstock (kWh) ................ 123

Table A 8 - Hourly wasted wind energy for synchronous speed and single penstock (kWh) ............. 123

Table A 9 - Hourly wasted wind energy for adjustable speed and double penstock (kWh) ................ 124

Table A 10 - Hourly wasted wind energy for synchronous speed and double penstock (kWh) .......... 124

Table A 11 – Results for energy surplus from grid, for single penstock and synchronous speed, for ten

scenarios simulations (kWh) .............................................................................................................. 126

Table A 12 - Results for energy surplus from grid, for double penstock and synchronous speed, for ten

scenarios simulations (kWh) .............................................................................................................. 126

Table A 13 – Histogram for single penstock over summer (dry) season ............................................ 128

Table A 14 – Histogram for double penstock over summer (dry) season .......................................... 130

Table A 15 – Pump station efficiency for adjustable speed ................................................................ 132

Table A 16 – Results for specific energy and total energy consumed over summer season for single

penstock ............................................................................................................................................. 133

Table A 17 – Results for specific energy and total energy produced over summer season for single

penstock ............................................................................................................................................. 135

Table A 18 – Results for specific energy and total energy consumed over summer season for double

penstock ............................................................................................................................................. 140

Table A 19 – Results for specific energy and total energy produced over summer season for double

penstock ............................................................................................................................................. 142

xvi

Acronyms

CCGT – Combined Cycle Gas Turbine

CCS – Carbon Capture and Storage

CSP – Concentrated Solar Power

IPCC – Intergovernmental Panel on Climate Change

EEM – Empresa de Electricidade da Madeira

EROEI – Energy Return on Energy Invested

GHG – Greenhouse Gas

GMST – Global Mean Surface Temperature

HLW – High Level Waste

IEA – International Energy Agency

ILW – Intermediate Level Waste

LCOE – Levelised Costs of Electricity

LLW – Low Level Waste

NGCC – Natural Gas Combined Cycle

OECD – Organization for Economic Cooperation and Development

PHS – Pumped Hydro Storage

PSPP – Pumped Storage Power Plant

PV – Photovoltaic

PWM - Pulse width modulation PWM

RAM – Região Autónoma da Madeira

RES – Renewable Energy Sources

RPGT – Renewable Power GenerationTechnologies

1

1. Introduction

1.1 Scope

The ability to produce and provide energy has allowed mankind for giant leaps in its evolution. At the

same time, energy demand has never been greater and will continue to increase in the foreseeable

future, as global population grows and the world evolves, provided that it’s not spoiled it in the meantime.

The ability to produce energy, particularly in the form of electricity is, and has been, highly dependent

on fossil fuels, such as coal, petroleum and gas, which are known to be finite and veiled in uncertainty

regarding their longevity, which is in turn partially related to their successive price oscillations. Other

aspects, such as geopolitical issues, natural disasters and severe climate can affect the functioning of

power plants and thus the energy price volatility. Also associated with fossil fuels burning is the emission

of greenhouse effect gases, particularly CO2, that are linked to the ever growing problematic of global

warming and its increasingly devastating consequences.

Therefore, it is essential to invest in alternative sources of energy, particularly energy from renewable

sources, which stand out for being inexhaustible, with minimum global warming emissions and general

environmental impacts, and for offering stable energy prices, effectively addressing the major problems

with fossil energy sources. In order to compete with fossil energy, renewable energy alternatives have

to deal with its major drawback, which is their production intermittency, as the required conditions for

generation may not always be guaranteed: there will be times in which the wind doesn’t blow or the sun

doesn’t shine, which can raise some problems, like power outages or abrupt changes to the electrical

grid’s frequency. This means that electrical grids with a high renewable energy generation penetration

are subject to these potential hazards. Furthermore, the renewable energy source production may also

exceed the demand for a certain time with the surplus being lost. An efficient way to regulate variability

in the grid and to store this surplus of energy is the use of pumped-storage power plants (PSPP), which

transform it into potential energy through water level: the energy surplus is used to pump the water to a

reservoir that can later be turbinated.

Pumped hydro storage has the ability to “transfer” energy that is stored from low demand hours to

periods when demand is high, smoothing out the daily load diagram. Demand for electrical power varies

throughout the day, with occasional sudden peaks and, because it takes fossil fuels power plants up to

half an hour to crank up to full power, they often operate at full capacity continuously, with spinning

reserves as a backup to meet these peaks. Pumped storage systems can respond to these peaks

immediately, as a mean to minimize energy waste.

2

1.2 Objectives

This dissertation aims at examining the contribution of the connection of pumped hydro storage power

plants to electrical grids, considering economical, ecological and social aspects, and particularly how it

affects renewable energy sources with a variable output, such as wind and photovoltaic, and penetration

degree in the generation mix. A scenario of the current and future world energy situation is drawn, with

existing statistics and forecasts of generation and greenhouse gas emissions by source, to allow for

judicious comparison between the main existing sources of energy and the contribution and

improvements that pumped storage power plants (PSPP) can offer. Other emerging energy complexities

are studied, like energy security, third party dependency and storage. Different existing and in

development phase of PSPP technologies are presented, and improvement methods to some

components are analyzed.

One case study is presented, where the impacts of a PSPP, the Madeira Island’s Multiple Purpose

Socorridos System, are described and analyzed, particularly its importance to renewable energy source

in the grid penetration. The local electricity generation and projections, as wells as the contributions of

existing and future PSPP are also analyzed.

To access how effective the above mentioned improvement methods can be, combined with the use of

free of cost generation sources, in regards to production, to power the pumping station of a reversible

hydro system, objective functions are designed to model these alterations to the original system,

implemented into MATLAB for an optimization procedure, where performance is measured through

generated revenues from the system. At the end, results are presented and discussed, and final

conclusions based on them are made.

3

2. State of the Art

2.1 Electricity Generation Overview

The majority of the electricity generated in the world today comes from fossil fuels, accounting for

approximately 67% of the world’s net electricity estimated in 2010, while nuclear and renewable sources

account for roughly 12% and 21%, respectively (Figure 2.1.a). By 2040, world population is expected to

grow from 7 to 8.8 billion people, mainly from developing economies, such as India and China, while the

world's real gross domestic product rises by an average of 4% per year from 2010 to 2040. These two

factors are the key drivers behind the increase of electricity consumption, being in turn offset by

efficiency gains from new appliance standards and investments in energy efficient equipment. Figure

2.1.b shows the world’s total electricity consumption, which will grow 66% (2.2% per year), and net

generation, which will grow from 20.2 trillion kilowatt-hours in 2010 to 39 trillion kilowatt-hours in 2040,

a 93% increase. With current policies, fossil fuels are estimated to still have the biggest share of the

world’s net electricity generation by 2040, with roughly 62%, with renewable and nuclear sources

increasing to 25% and 13%, respectively, as Figure 2.1.a illustrates (EIA, 2013).

Figure 2.1 – (a) World net electricity generation by fuel, 2010-2040; (b) Growth in world total electricity generation and total delivered energy consumption, 1990-2040 (adapted from EIA (2013))

The overuse of fossil fuels in the generation of electricity presents two main problems: excessive

greenhouse gas emissions and the finite nature of these resources. As of 2011, the electricity and heat

sector was responsible for 42% of the world’s total energy-related CO2 emissions, increasing by 4.4%

over 2010, by far the largest sector - the Industry sector accounted for 21% and transports were

responsbile for 22% (IEA, 2013) – and the intensity of electricity and heat generation CO2 emissions

has grown by 6% since 1990, to 0.5 ton of CO2 emitted per megawatt-hour produced (tCO2/MWh).

Figure 2.2 illustrates the fossil fuel and cement annual anthropogenic CO2 emissions increases in PgC

per year (1 PgC = 1 billion tons of carbon = 3.7 billion tons of CO2), from 1750 to 2011 (IEA, 2011).

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Figure 2.2 Fossil fuel and cement annual anthropogenic CO2 emissions (in PgC yr–1) from 1750 to 2011

(IPCC, 2013)

Global atmospheric concentrations of carbon dioxide, methane and nitrous oxide have increased

markedly as a result of human activities since 1750, and there is a strong consensus within the scientific

community of its correlation with the climate system warming. Thus the unequivocal global mean surface

air temperatures over land and oceans increase throughout the last century, recorded by direct and

indirect observations and measurements, with many of the changes in the last decades presenting

unprecedented values over decades to millennia (based on climate reconstructions): the last three

decades have been successively warmer at the Earth’s surface than any preceding decade since 1850,

and the temperature increase in the upper ocean (0 to 700 m of depth) between 1971 and 2010 is

considered to be virtually certain.

Figure 2.3 shows observational and model simulation data that correlates human activity to global mean

surface temperature (GMST), evidencing the unequivocal correspondence between them.

Figure 2.3 - Three observational estimates of GMST (black lines) from three different datasets (HadCRUT4, GISTEMP and MLOST), compared to model simulations (CMIP3 and CMIP5) with (a) anthropogenic and natural

forcings, (b) natural forcings only and (c) greenhouse gas forcing only. Thick red and blue lines are averages across all available simulations (IPCC, 2013)

5

The observed consequences of global warming include (IPCC, 2007)

:

average atmospheric water vapor content increase;

temperature of the global ocean increase to depths of at least 3000 m;

mountain glaciers and snow cover decline in both hemispheres;

sea level rise due to widespread decreases in glaciers and ice caps;

average arctic temperatures increase at almost twice the global average rate in the past 100

years;

significant increase in precipitation observed in eastern parts of North and South America,

northern Europe and northern and central Asia;

mid-latitude westerly winds strengthening in both hemispheres since the 1960s;

more intense and longer droughts over wider areas since the 1970s, particularly in the tropics

and subtropics;

increased frequency of heavy precipitation events over most land areas;

less frequent cold days, cold nights and frost;

more frequent hot nights and heat waves;

increase in intense tropical cyclone activity in the North Atlantic since about 1970;

decrease in diurnal temperature range.

It is stated in the United Nations’ Copenhagen Accord of 2009 that the increase in global temperature

should be limited to 2 degrees Celsius above pre-industrial era levels, and that leaders of the envolved

nations should therefore take action in reducing global emissions so as to hold the said increase

(UNFCCC, 2009).

It would require cumulative emissions over the entire industrial period to be less than about one trillion

ton of carbon, which corresponds to 3.67x1012 ton of CO2, for a 66% chance of limiting the global mean

temperature increase to less than 2°C, from which about half have already been emitted by 2011. That

leaves roughly 30 years of carbon dioxide emissions at current rates, excluding the significant additional

warming effects of other greenhouse gases and aerosols, and the increasingly growing average annual

growth rates of 1.9% per year in the 1980s, 1.0% per year in the 1990s, and 3.2% per year since 2000

(IPCC, 2013).

The total temperature increase from 1850–1899 to 2001–2005 is set at 0.76°C [0.57°C to 0.95°C], with

GSMT expected to rise about 0.2ºC per decade. Even if the concentrations of all greenhouse gases and

aerosols had been kept constant at year 2000 levels, a further warming of about 0.1°C per decade would

be expected (IPCC, 2007).

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This means a great amount of‘carbon budget’ has already been spent and the mitigation of global

warming is behind schedule.

In an effor to invert the trends that are putting our planet in jeapordise, new policies are continuously

being announced by governments around the world, such as EU's 2009 climate and energy package

(EC, 2009) and the 2012 Energy Efficiency Directive (EU, 2012), which focuses on:

20 % reduction of the EU's GHG emissions compared to 1990;

20 % share of renewable energy in the EU's gross final energy consumption;

20 % increase of the EU's energy efficiency.

Looking beyond these short-term objectives, the EU is determined to achieve much deeper emission

cuts by the middle of the century, commiting to reduce greenhouse gas emissions to 80-95% below

1990 levels by 2050, improving energy efficiency and producing more low-carbon evergy, as stated on

the Energy Roadmap 2050 (EC, 2011).

So far, the EU seems to be on track with the porposed targets, such as the 8% emissions reduction

target, compared to the base level years under the Kyoto Protocol by the EU-15, announcing that total

average emissions in the 2008–2012 period have declined by 12.2 % compared to base‑year levels

(EEA, 2013).

Summarizing, it is not pretentious to state that it’s imperative to decarbonyze the electricity generation

sector with the utmost urgency and look for alternatives to fossil fuels that can face the predicted

increase in demand, without putting the future of the planet at stake.

2.2 Fossil Fuels in Electricity Generation

2.2.1 Greenhouse Gas Emissions

All fossil fuels technologies have associated GHG emissions, but to typically different degrees. Natural

gas is the fossil fuel with the least GHG emissions, and currently the second most commonly used in

electricity generation. Coal is currently the primary fuel for electricity generation and responsible for

roughly 70% of CO2 emissions, which means the most pollutant is also the most commonly used. Oil is

significantly less used in power generation, due mainly to high oil prices, but also has a high emissions

intensity. Table 2.1 compares the GHG emissions from electricity generation by fossil fuel sources

(Moomaw, et al., 2011).

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Table 2.1 - GHG emissions from electricity generation by fossil fuel source (g CO2eq/kWh) (adapted from Moomaw et al. (2011))

Values Natural Gas Oil Coal

Minimum 290 510 675

25th percentile 422 722 877

50th percentile 469 840 1 001

75th percentile 548 907 1 130

Maximum 930 1 110 1 689

CCS min 65 98

CCSmax 245 396

Minimizing emissions is a way to mitigate the problem, while it is not a definitive solution. Technological

development can play a major role in the reducion of CO2 emissions, as the replacement of old plants

with low efficiency (the current average worldwide efficiency is of 33%) with new power plants with high

efficiencies of 45 to 50% could greatly decrease emissions, with multiple resulting benefits (Christensen,

et al., 2013):

Resource protection,

Substantial reduction of CO2 emissions (as shown in Figure 2.4),

Clear reduction of other emissions,

Increased electricity generation from the same fuel amount.

There is also potential to further reduce emissions with technological implementations such as carbon

capture and storage (CCS), a process that consists in the separation of CO2 from industrial and energy-

related sources, transport to a storage location and long-term isolation from the atmosphere. Figure 2.4

shows the potential for reduction in carbon dioxide emissions of coal fired power plants by increasing

their efficiency and with the use of CCS technology. As can be seen, a reduction of as much as 90% in

emissions can be achieved in relation to the world average, by increasing efficiency from 33% to about

50% and using CCS technology. The use of carbon capture technologies, however, comes at a cost to

the overall efficiency of the system, decreasing it by as much as 7% to 12%.

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Figure 2.4 - CO2 reduction potential of coal-fired power plants by increased efficiency (adapted from

Christensen et al. (2013))

2.2.2 Reserves

On the other hand, fossil fuels are finite resources, therefore it is necessary to find ways to supply the

world with energy beyond their availability. The exact amount of how much is left to consume is

uncertain, with estimates evolving accordinglty with new technological achievements, that allow for

extraction at previously inaccessible reserves.

Proven reserves are the estimated quantities that, assuming currently existing technology, economic

and operating conditions, can be recovered economically in future years from known reservoirs,

according to geological and engineering data.

Estimates point for proven resources of conventional oil to be set at around 1.3 trillion barrels and

recoverable sources at about 2.7 trillion barrels. At current consumption levels, reserves-to-production

ratio is in the 40 to 45 years range but will grow as more reserves become exploitable. As for

unconventional oil (produced or extracted using techniques other than the conventional oil well method),

global proven reserves are set at around 400 billion barrels, with estimated recoverable resources of

3.2 trillion barrels.

Conventional gas proven reserves are estimated at around 200 trillion cubic metres (tcm), and remaining

recoverable resources at 440 tcm which on current consumption levels translates into a reserves-to-

production ratio of in the range of 55 to 60 years. Remaining recoverable resources are estimated at

240 tcm.

Proven reserves of hard coal are estimated at 730 gigatonnes (Gt), which renders a reserves-to-

production ratio in the range of 110 to 120 years at current consumption levels, and proven reserves of

lignite are estimated at 280 Gt. The remaining recoverable resources of hard coal and lignite are

estimated at around 18 000 and 4 000 Gt, respectively (IEA, 2013).

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2.2.3 Costs

It seems to be the case that there will be enough fossil fuels to carry the world through the foreseeable

future, but they will become increasingly expensive as conventional reserves become less abundant

and new technologies are required to allow for extraction, thus decreasing profitability.

More so, carbon taxing has been suggested to policymakers as a mean to reduce emissions in a cost-

effective way, based on the principle that the ‘polluter pays’, which also adds to the costs of fossil fuels.

Many countries have already adopted similar measures while others are discussing the option (Bowen,

2011; Pachauri & Reisinger, 2007).

Although CCS will become cheaper in the future, as it has not yet reached full maturity, the cost of

mitigating or avoiding CO2 emissions for a coal-fired power plant fitted with current CCS technology

ranges from US$23-92 per tonne of CO2 and is a little higher for natural gas-fired power plants (Abellera

& Short, 2011).

There are, however, avoided costs that correspond to the emissions trading schemes, in which a cap is

set on the total amount of GHG that can be emitted by the participants, and ‘allowances’ are auctioned,

allocated or traded between pariticipants. If the emissions exceed the allowances, a participant must

purchase from others whose emissions were inferior to their respective allowances, as settled in the

Kyoto protocol emissions trading scheme or smilarly in the European Union Emission Trading System.

Figure 2.5 draws a comparison between the levelised costs of electricity of integrated CCS projects,

including CO2 storage and transport, and reference plants without CSS and their ETS added costs. It is

clear that CCS can be, in some cases, an economically competitive alternative, with obvious GHG

emissions reduction benefits.

There is another factor influencing generation costs which is energy subsidies. Governments use energy

subsidies as a mean to mitigate energy poverty and inequality, and to promote economic development

by enabling access to affordable modern energy services. Figure 2.6 shows fossil fuel consumption

subsidies across the globe, as a proportion of the full cost supply. Subsidies can be of four types (Kitson,

Wooders, & Moerenhout, 2011):

Government provides direct transfer of funds or potential direct transfer of funds or liabilities;

Revenue is foregone or not collected;

Government provides goods or services or purchases goods;

Government provides income or price support.

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Figure 2.5 - The Levelised Cost of Electricity of integrated CCS projects (blue bars) compared to the

reference plants without CCS (green bars) (ZEP, 2011)

Figure 2.6 Fossil-fuel consumption subsidy rates as a proportion of the full cost supply in 2011 (adapted from IEA (2012))

Over the last decades, conventional energy has received substantial subsidies in the form of financial

contributions and tax incentives, along with other favorable treatment, much like in the example depicted

in Figure 2.7, which illustrates state support to electricity generation by source in Germany.

Maria van der Hoeven, Secretary-General and IEA Executive Director stated that “subsidies to fossil-

fuel consumers often fail to meet their intended objectives: alleviating energy poverty or promoting

economic development, and instead create wasteful use of energy, contribute to price volatility by

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blurring market signals, encourage fuel smuggling and lower competitiveness of renewables and energy

efficient technologies.” (OECD, 2013).

Figure 2.7 - State support 1970 – 2012 in Germany in billion € (real prices) (Küchler & Meyer, 2012)

Fossil-fuel subsidies bulked up to $523 billion in 2011, around six times the level of support to renewable

energy, meaning that 15% of global CO2 emissions have received an incentive of $110 per tonne through

fossil-fuel subsidies, while only 8% were subject to a carbon price. G20 and Asia-Pacific Economic

Cooperation (APEC) member countries have committed to phase out inefficient fossil-fuel subsidies and

many are moving ahead with implementation, which could reduce CO2 emissions by 360 Mt in 2020

(IEA, 2013).

A phase out of fossil-fuel subsidies could also provide an encouragement to investment and growth in

renewable energy and energy efficiency (IEA, 2011).

In paragraph 54 of the European Commission’s Environmental and Energy Aid Guidelines 2014 – 2020

it is stated that:

“To ensure a level playing field and promote the objective of decarburization, the Commission aims at

phasing out environmentally harmful subsidies ("EHS"). In the energy area, this concerns mainly

subsidies to fossil fuels which counteract the objective of promoting RES production and, in fact, require

indirectly even higher subsidies to RES to make them competitive. The debate on EHS is progressing,

but requires a balancing of different effects of subsidies and different EU policy objectives. Work is

undertaken in order to come to operational conclusions. Once such conclusions are available, they can

serve as an element in the review of the guidelines.” (EC, 2013).

The utilization schedules of thermal power plants is also a factor of economical sensitivity. The preferred

consumption of renewable energy sources (RES) based power results in an alteration of the thermal

power plants schedules, thus increasing the power generation cost for fossil power, which is still

indispensable for system stability. The power generation cost for a power plant designed for a given

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operation schedules increases if that schedule is reduced, as shown in Figure 2.8. This is particularly

true for highly efficient, state-of-the-art power plants due to extra financial burden caused by high fixed

cost, i.e. interest and debt payments, and staff as well as maintenance costs.

Figure 2.8 – Cost of electricity production vs operating hours (adapted from Christensen et al. (2013)

Furthermore, thermal power plants using fuels with highly fluctuating prices, as Figure 2.9 illustrates,

have an inherent economic risk as some plants may not be operated economically efficient although

they are technically very efficient.

Figure 2.9 – Fossil fuel prices in baseline (Constant USD of 2008 per barril of oil equivalent (boe)) (adapted from EC (2009))

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2.2.4 Installed Capacity

Coal fuels most of the world’s electricity, with over 40% of the share, though this figure is much higher

in many countries, such as South Africa (93%), Poland (92%), China (79%), India (69%) and the United

States (49%) (Burnard & Bhattacharya, 2011).

By 2040, total world electricity generation from coal is expected to be 73 percent higher than the 2010

level, following a 1.8% percent annual rate growth, despite coal’s share of the electricity market fall to

36 percent in 2040. China and India alone account for 89% of the projected growth in coal-fired

generation while OECD nations reduce their reliance on coal-fired electricity generation.

The projected share of natural gas world’s electricity generation is of 24% in 2040, only 2% more than

in 2010. In the EU, however, natural gas has the highest share of projected and announced power

plants, roughly 33%, reflecting the GHG emissions reduction policies, due to natural gas’ lower

emissions intensity, in contrast with fuel oil, that has virtually no new projected power plants, and coal

and lignite with just 18% of the share, as shown in Figure 2.10.

Figure 2.10 – Projected and announced power plant capacities in Europe as of 2007, (adapted from Christensen et al. (2013))

Of all fossil fuels, oil is the least used in electricity generation, accounting for 5% of the world’s generated

power in 2010, and falling to just 2% in 2040, following the trend of the previous two decades. This is

mostly due to the sustained high oil prices, and since it is a light and energy dense fuel, it is mostly used

in transportation. Even in petroleum rich places, such as the Middle East, the share of total generation

is expected to go down from 34% in 2010 to 14% in 2040, reflecting the intention of maximizing revenues

from exports (EIA, 2013).

In Portugal, as of 2012, the total installed capacity of non-renewable power plants is 9364 MW. Natural

gas has the biggest share, with 53%, followed by oil plus others (including industrial waste, propane,

refined gas, etc) with 27% and coal, with 20% (DGEG, 2014). In Madeira Island there are two thermal

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power plants which currently use fuel oil, amounting for an installed capacity of 248.94 MW. The Vitória

Thermal Power Plant contributes with 212.94 MW (176.80 MW of maximum continuous power) (EEM,

2011), with an undergoing switch to natural gas being done in this power plant since March 2014.

2.3 Nuclear Fission in Electricity Generation

Nuclear fission is a mature technology that was first used to generate electricity in the early 1950s, with

the first commercial nuclear power plants entering operation in the beginning of the 1960s. Following

the oil crisis of the 1970s, governments sought for alternatives to reduce dependence on fossil fuels,

which led to the rapid growth of nuclear capacity in the 1970s and 1980s. Despite this, growth stagnated

in the 1990s, with the exception of Japan and Korea, due to increased concerns with safety following

the Three Mile Island and Chernobyl accidents. Economic factors also played a hand, as higher than

expected construction costs at some nuclear plants, and a return to lower fossil fuel prices took place

(IEA, 2010).

In the early 2000s, a new increase in fossil fuel prices combined with concerns about the environmental

consequences of GHG emissions resulted in a renewed interest in nuclear power. However, the March

2011 disaster at Fukushima Daiichi, Japan; caused a fallout in the nuclear industry worldwide, with

governments abandoning projects due to public pressure, such as OECD Europe that announced

planned retirements of nuclear capacity under current policies, and Japan that significantly reduced its

nuclear generation with 50 nuclear reactors being shut down over the 14 months that followed the

accident. In China processes approval was halted for all new reactors until a complete safety review is

done.


Although nuclear power plants have no direct CO2 emissions, nuclear electricity generation is not totally

carbon-free as some indirect emissions can be attributed to it, mainly from fossil fuel use in the fuel

cycle. However, these emissions are very small when compared to fossil fuels burning, quite similarly

to those attributed to RES, and at least an order of magnitude below direct emissions from fossil fuels

burning. When compared to coal-fired generation, existing nuclear generation in 2009 avoided annual

CO2 emissions of about 2.9 billion ton, or about 24% of annual power sector emissions (IEA, 2010).

2.3.2 Reserves

Nuclear power is fueled by Uranium, a metal that is ubiquitous on Earth, and a constituent of most rocks

and even of the sea but, much like other metals, economically recoverable concentrations are far less

common. An occurrence of mineralization from which the metal is economically recoverable is called an

orebody, and in defining it, assumptions are made about the cost of mining and the market price of the

metal. Uranium resources are therefore calculated as ton recoverable up to a certain cost.

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The total identified uranium resources have grown from 2001 to 2011, as Figure 2.11 shows, but since

the costs of production have also increased, lower cost category resources have been significantly

reduced (IAEA, 2011).

Figure 2.11 – World identified uranium resources by year (adapted from IAEA (2011))

2.3.3 Costs

Nuclear power is a capital-intensive technology. In addition to high investment costs, licensing and public

acceptance issues have delayed construction periods for power plants in many countries, which resulted

in higher than estimated costs of nuclear power and investment risk.

Some reports suggest that subsidies play a major role in the economic success of nuclear power, stating

that since its inception, it has benefited from a vast array of preferential treatment, which started as a

promised short-term stimulus, even to the point of arguing that they wouldn’t be sustainable without the

said subsidies. The most significant support from subsidies consists of a shift in construction-cost and

operating risks from investors to taxpayers and ratepayers (Koplow, 2011).


Overall, nuclear power provides currently around 14% of global electricity, and 21% of electricity in

OECD countries (IAEA, 2011). Figure 2.12 shows the existing power plants across the world today, as

well as planned shutdowns and new plants and projects.

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Figure 2.12 - World’s existing nuclear power plants, planned shutdowns, new plants and projects Christensen et al. (2013)

In Europe only, as of March 2014, there is a total of 185 nuclear power plant units with an installed

electric net capacity of 162 GWe, providing for roughly 28% of the electricity (ENS, 2014). In Portugal,

although were plans to build an 8 000 MW nuclear power plant in 1974, which were later dropped, there

are currently no nuclear power plants, nor plans to construct one.

2.3.5 Radioactive Waste Management

Although CO2 emissions from nuclear electricity generation are reduced, there are still undesirable by-

products, in the form of radioactive waste, becoming the responsibility of the country which uses uranium

to generate power.

Radioactive wastes are classified as:

low-level wastes (LLW) with short-life radioactivity requiring no shielding or geological disposal

(90% nuclear waste volume, 1% radioactivity);

intermediate-level waste (ILW), which requires shielding and disposal in shallow repositories

(5%-7% volume, 4% radioactivity);

high-level waste (HLW) with long life radioactivity and heat production (fission products,

actinides from spent fuel), thus calling for shielding, cooling and deep geological disposal (3%-

5% volume, 95% radioactivity).

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Nuclear power generation power plants worldwide produce each year around 200 000 m3 of low- and

intermediate-level radioactive waste, and about 10 000 m3 of high-level waste, including used fuel

designated as waste. Overall, nuclear wastes comprise less than 1% of total industrial toxic waste.

Over a year, a typical 1-GW power plant produces 200 to 350 m3 of LLW and ILW and 10 to 20 m3 of

HLW (some 1 000 tonnes over a 40-year lifetime), and after recycling, final HLW is reduced to less than

3 m3 of vitrified waste that must be stored for thousands of years (ENEA, 2009).

2.4 Renewable Energy Sources

In all of the projected scenarios for the future of power generation in our planet, renewable energy

sources (RES) play a role of ever growing importance, notably for addressing the two main problems of

fossil fuel sources: their finite nature and acute greenhouse gas (GHG) emissions. By definition, a RES

is a source which is continuously replaced at a rate that is at least equal to the rate at which it is

consumed, and as stated in the Directive 2001/77/EC of the European Parliament: "'renewable energy

sources’ shall mean renewable non-fossil energy sources: wind, solar, geothermal, wave, tidal,

hydropower, biomass, landfill gas, sewage treatment plant gas and biogases”. With the exception of

biomass, landfill gas, sewage treatment plant gas and biogases, these solutions don’t present direct

GHG emissions from power generation. But the list of benefits doesn’t stop there, as RES reduce

external energy dependency, a growing burden for many economies, while offering more flexibility to

power grids and contributing positively for energy security.

However, there are also some pitfalls to RES, as there is no singular perfect energy source. One of the

main issues is reliability of supply, since RES greatly depend, in most cases, on weather conditions, a

trait that makes the addition of more clean energy to an electrical grid a sensitive problem, as it

introduces more variability to the system, making it more likely to incur in blackout situations. Another

disadvantage is that it is difficult to generate a similar quantity of electricity as those produced by

traditional fossil fuel generators. This means it is necessary to either produce more electricity or

consume less, or at least find a way to store any energy surplus for later use. Pumped hydro storage,

in combination with RES, might offer a solution for both of these problems, storing energy surplus from

the said RES for later use. With energy storage, more power generated from variable sources can be

introduced in the electrical grid without compromising security. As so, eolic energy stored in the form of

water level, may be available when the wind isn’t blowing, for example. Conversely, solar energy may

be used when the sun isn’t shining.


Similarly to nuclear energy, although most renewable energies have no directly attributed GHG

emissions, there is still some indirect contribution, which comes as a result of the construction of the

infrastructure and its maintenance, varying significantly from case to case. For example, the carbon

content of photovoltaic cells results from its manufacturing process along with that of the battery that

stores the electricity generated. These are, however, very low rate emissions, as illustrated in Table 2.2.

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The GHG break-even point for a reference 33-unit of 3.0 MW turbines wind farm, which is how soon it

can offset the GHG emitted to build, run and recycle it over a 20-year life cycle, with the GHG avoided

in its power generation, can be as little as 7 weeks (IEA, 2012).

Table 2.2 - GHG emissions from electricity generation from RES (g CO2eq/kWh) (adapted from Moomaw et al. (2011))

Values Bio-

power

Solar Geothermal Energy

Hydropower Ocean Energy

Wind Energy

PV CSP

Minimum -633 5 7 6 0 2 2

25th percentile 360 29 14 20 3 6 8

50th percentile 18 46 22 45 4 8 12

75th percentile 37 80 57 57 7 9 20

Maximum 75 217 89 79 43 23 81

CCS min -1 368 - - - - - -

CCSmax -594 - - - - - -

Figure 2.13 presents cumulative contribution to the reduction of GHG emissions of different actions or

technologies, such as optimized energy efficiency, carbon capture and storage or renewable energies,

by 2030 and 2100, as described by four different models. In this graph, RES show the greatest potential

of all these solutions to reduce GHG on the long run, making it, according to the Intergovernmental

Panel on Climate Change (IPCC), an essential element in the fight against climate change (IPCC, 2007)

Figure 2.13 - Cumulative emissions reductions for alternative mitigation measures. The figure illustrates scenarios from four models (AIM, IMAGE, IPAC and MESSAGE) aiming at the stabilization at low (490 to 540ppm CO2-eq) and intermediate levels (650ppm CO2-eq) respectively. The solid bars denote reductions for a target of 650 ppm CO2-eq and the striped bars denote the additional reductions to achieve 490 to 540 ppm CO2-eq (IPCC, 2007)

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2.4.2 Costs

As previously stated, subsidies to fossil fuel in electricity generation have skewed the balance in their

favor. Nevertheless, renewable power generation technologies (RPGT) have become increasingly cost-

competitive in the last years, and are today, in most cases, the most economic option for off-grid

electrification: the rise in oil prices, combined with the declining costs of RPGT have made the latter the

default option in remote areas with poor or even non-existent infrastructure, where transport costs can

increase the cost of diesel by 10% to 100%. Solar PV, biomass and wind are standardized solutions for

extending access to electricity to remote locations, which helps meet economic and social development

goals

The overall competitiveness of RPGT greatly depends on the locations’ natural resources, but the rapid

deployment and high learning rates have a significant positive impact on costs. As an example, solar

PV modules costs decrease as much as 22% for every doubling in solar PV installed capacity. At the

same time, the rapid growth in installed capacity of RPGT, as well as technology improvements and the

consequential cost reductions mean that data as recent as one or two years old can significantly

overestimate the cost of electricity from these technologies. In locations with great natural resources,

RES can sometimes be the cheapest way to generate electricity, as is the case with hydropower and

geothermal power. For other technologies, like wind, solar PV, CSP and some biomass, the levelised

cost of electricity (LCOE) is steadily declining.

RPGT costs typically follow a hierarchy, while an opposite hierarchy in terms of resources might be

observed on a given location. Generally speaking, biomass, geothermal and hydropower technologies

allow for competitive costs, while onshore wind, solar PV and CSP are usually more costly. On the other

hand, the availability of low‑cost resources for hydropower, geothermal and biomass is limited, to a

greater or lesser extent, and capacity additions cannot be ramped up or down rapidly for the first two,

due to long lead times. Because of the much more prevalent resources for wind and solar power, these

technologies have been deploying rapidly, providing a larger share of power generation from renewables

alone, and thus the LCOE for all renewable technologies is converging, as can be observed in Figure

2.14. In the same image, the range for fossil fuel power costs in OECD countries is shown, evidencing

the competitiveness of RPGT. However, the cost ranges are wide and very site-specific, and therefore

there is no single “best” renewable power generation technology. On the other hand, distributed

renewable technologies, such as rooftop solar PV and small wind, can contribute with new added

capacity and don’t require additional transmission and distribution investment, which means they cannot

be directly compared with large scale renewable solutions. In an increasing number of countries and

regions, RPGT are nowadays the most economical solution for new capacity (IRENA, 2012).

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Figure 2.14 – Typical LCOE ranges for renewable power generation technologies, in 2012 and 2020 (adapted from IRENA (2012))

The cost trends for RPGT, derived from their respective curves, is summarized in Figure 2.15. It is

noticeable that, in all cases, a decrease in relation to the 2009 costs levels is expected, with most

technologies reducing their specific investment costs to between 30% and 60% of 2009 levels upon

achieving full maturity. This decrease is not a function time but of cumulative capacity (production of

units) and, as so, it might be lower or greater, depending on the deployment rate, but steadily leading

directly to reduced LCOE (Energy [R]evolution 2012, Greenpeace, GWEC, EREC, 2012).

Figure 2.15 - Future development of investment costs for RPGT (Normalised to 2009 cost levels) (EREC, Greenpeace, GWEC, 2012)

21

The LCOE for renewable power generation technologies is compared with other power source

technologies in Table 2.3, which shows that, in some cases, they can be an economically competitive

alternative, as previously stated.

Table 2.3 - Average levelized power generation costs comparison between RES, nuclear and fossil fuel sources (2011 $/megawatthour) for plants entering service in 2018 (adapted from EIA (2013))

Plant Type Capacity

factor (%)

Levelized capital

cost

Fixed O&M

Variable O&M

(includIng fuel)

Transmisson investment

Total system

levelized cost

Conventional Coal 85 65.7 4.1 29.2 1.2 100.1

Advanced Coal 85 84.4 6.6 30.7 1.2 123.0

Adv. Coal with CCS 85 88.4 8.8 37.2 12 135.5

Natural Gas-Fired

Conv. Combined Cycle 87 15.8 1.7 484 1.2 67.1

Adv. Combined Cycle 87 17.4 20 450 1.2 65.6

Adv. CC with CCS 87 34.0 4.1 54.1 1.2 93.4

Conv. Combustion Turbine

30 44.2 2.7 80.0 3.4 130.3

Adv. Combustion Turbine 30 30.4 2.6 68.2 3.4 104.6

Advanced Nuclear 90 63.4 11.6 12.3 1.1 108.4

Geothermal 92 76.2 120 0.0 1.4 89.6

Biomass 83 53.2 14.3 42.3 1.2 111.0

Wind 34 70.3 13.1 0 32 86.6

Wind. Offshore 37 193.4 22.4 0.0 5.7 221.5

Solar PV 25 130.4 9.9 0.0 4.0 144.3

Solar Thermal 20 214.2 41.4 0.0 5.9 261.5

Hydro 52 78.1 4.1 6.1 2.0 90.3

In Figure 2.16, a focus on recent cost trends for wind energy is shown. Despite the investment costs

spike that occurred from around 2004 to 2009, which was mostly due to supply constraints on turbines

and components, including gear boxes, blades and bearings, as well as higher commodity costs, such

as steel and copper prices (which also affected conventional power production), investment costs have

fallen steadily along with the reversal of these factors. All factors considered, investment price declined

by 33% or more since late 2008.

Operation and maintenance costs of wind turbines amount for a significant share of the total costs, as

much as 15% to 25%. These include scheduled and unscheduled maintenance, spare parts, insurance,

administration, site rent, consumables and power from the grid, and its frequency and extent can vary

greatly, depending on the age, conservation state and sophistication of the turbine. Electrical and

electronic systems problems are usually the most common causes of wind turbine outages but can be

22

rectified quite quickly, while generator and gearbox failures are fairly less common but generally take

longer to fix and are more costly (IEA, 2013).

Figure 2.16 - (a) Cost trend of land-based wind turbine prices, by contract date; (b) Recent trends in average price for full-service O&M contracts (EUR/MW/yr) (IEA, 2013)


A little over 20% of the world’s generated electricity, as of 2012, is produced from renewable energy

sources, which translates into 4 699.2 TWh, having grown 1 739 TWh in the last ten years,

corresponding to a 4.7% annual growth rate. Of that share, 78% comes from hydropower (including

pumped storage), by far the most predominant power source, while wind power accounts for 11.4%, as

can be seen in Figure 2.17.a. In the EU, the produced electricity from RES is 774.1 TWh in 2012,

corresponding to 23.8% of the total, due to the low carbon emissions policy, with a growth rate of 6%

over the last ten years. Hydro and wind power are also the predominant sources, with a 46% and 25.8%

shares respectively, but biomass and solar present significant shares, with 18.2% and 9.2%

respectively, as shown in Figure 2.17.b (Observ'ER, 2013)

23

Figure 2.17 – (a) World RES share of electricity produced by source in 2012; (b) European Union RES share of electricity produced by source in 2012 (adapted from Observ'ER (2013)).

In Portugal, RES share of installed capacity is considerable, at 54.14% in 2012, mainly due to hydro and

wind power which correspond to 50.1% and 41% of that share respectively, as shown in Figure 2.18.a

(DGEG, 2014). In Madeira Island, RES account for 26.9% of the total installed capacity, with roughly

half of it being hydro and 29.7% wind power, as Figure 2.18.b illustrates.

Figure 2.18 – (a) Portugal RES share of installed capacity by source in 2012 (adapted from DGEG, 2014); (b) Madeira Island RES share of installed capacity by source in 2011 (adapted from EEM (2011))

Recent scenarios projected for RES installed capacity and share of generated electricity could be

grouped in three categories: “conservative”, “moderate” and “high renewables”. All scenarios take into

account electricity generation technologies, combined with projected demand and efficiency

improvements, and for every one of them, should total demand be reduced substantially in respect to a

given baseline or projection, higher shares of RES would be made possible more easily. On the same

token, scenarios with high levels of energy efficiency equate to higher shares of RES, even with modest

absolute increases in installed capacity like, for example, on the Greenpeace scenario which has an

energy demand 40% lower than a reference case by 2050, and predicts a share of RES of 82% with

just 6 times the absolute amount of RES of today. Inevitably, there are many lobbies and forces of

interest behind all scenarios, with conservative scenarios being typically drawn by oil and gas

companies. The diverging projections are also explained by different viewpoints on how current policies

will evolve and new ones will be introduced, and other indicators like proven reserves of fossil fuels.

24

In Table 2.4, a compilation of many of these scenarios is made for shares of RES in electricity is

presented (REN21, ISEP, 2013).

Table 2.4 - Scenarios for shares of RES in electricity (adapted from (REN21, ISEP, 2013))

Scenario By Year Electricity

By 2030—2040

ExxonMobil Outlook for energy: A View to 2040 (2012) 2040 0.16

BP Energy Outlook 2030 (2012) 2030 0.25

lEA World Energy Outtook (2012) "new Policies" 2035 0.31

lEA World Energy Outlook(2012) "450" 2035 0.48

Greanpeace (2012) Enegy [R]evolution 2030 0.61

By 2050

lEA Energy Technology Perspectives (2012) "2DS" 2050 0.57

GEA Global Energy Assessment (2012) 2050 0.62

IEA Energy Technology Perspectives (2012) "2DS High Renewables" 2050 0.11

Greenpeace (2012) Energy [R]evolution 2050 0.94

WWF (2011) Ecofys Energy Scenario 2050 1

Whatever one wants to believe the future will hold, there’s a scenario to back it up. But with each day

that passes, RES gain importance, as the consequences of fossil fuel usage become more and more

evident and grave.

2.4.4 Energy Return on Energy Invested

Energy return on energy invested (EROEI) is the ratio of how much energy is returned on a given effort.

Building wind or PV farms, for example, requires high temperatures to process ore, fabricate metals,

allocate materials, etc. This means that the bigger the EROEI ratio is on a given technology, the more

efficient it is. If the EROEI ratio is lower or equal to one, that particular technology becomes an energy

sink, meaning it consumes more energy than it produces. In Table 2.5, a comparison between various

renewable and non-renewable sources EROREI ratios is made, in which hydro stands out and wind

presents a ratio comparable to non-renewable sources. Also noticeable is the fact that the EROEI ratio

for oil and gas has declined over the years (30 for oil and gas in 1970 and 14.5 in 2005), since extraction

is much more difficult nowadays compared to how it was in the past, making it more expensive and

energy demanding. At the time it was first used, one single barrel of oil was enough energy to extract

and process about 100 barrels of oil. This means that, in the future, as technology for RES advances

and fossil fuel reserves decline and become more and more difficult to extract, the EROEI ratio of RES

will increase while decreasing for fossil fuels. It is also evident the remarkable EROEI value of 100 for

hydro technology (University of Illinois, 2013).

25

Table 2.5 - EROEI ratios for different fuel sources in the USA (University of Illinois, 2013)

Ethanol com 1.3

Solar coIlector 1.6

Solar flat plate 1.9

Bitumen tar sands 3.0

EthanoI sugarcane 5.0

Shale oil 5.0

Photovoltaic 6.8

Oil discoveries 8.0

Nuclear 10.0

Oil and gas 2005 14.5

Wind 18.0

Oil and gas 1970 30

World oil production 35.0

Coal 80.0

Hydro 100.0

2.4.5 Security and Dependency

The concept of energy security encompasses providing secure and affordable supply of energy equally,

with minimal environmental impacts. As stated in its Green Paper Towards a European strategy for the

security of energy supply (EC, 2000), the European Commission defines it as “the uninterrupted

physical availability of energy products on the market, at a price which is affordable for all consumers

(private and industrial), while respecting environmental concerns and looking towards sustainable

development”. Consumers expect the power to be always on and that the lights comes on at the flick of

a switch, as it’s considered now a basic necessity. While the positive contributions to the environment

from RES are universally known, other factors to which they contribute are equally relevant, and some

might say, equally important. Security of supply is a major challenge for all economies, since prolonged

disruptions would cause economic and social havoc. Energy security risks include aspects that fall into

different categories (Ölz, Sims, & Kirchner, 2007):

Energy market instabilities caused by unforeseen changes in geopolitical or other external

factors, or compounded by fossil fuel resource concentration;

Technical failures such as power “outages” (blackouts and brownouts) caused by grid or

generation plant malfunction;

Physical security threats such as terrorists, sabotage, theft or piracy, as well as natural

disasters (earthquakes, hurricanes, volcanic eruptions, the effects of climate change etc)

The global distribution of fossil fuel resources is uneven, since the world’s proven oil and gas reserves

are concentrated in a small number of countries. Europe’s dependency on imported coal will grow from

26

about 35 % in 2013, to more than 60 % by 2030, and as much as 81 % for natural gas and 88 % for oil

is expected. Overall, the share of imported energy will increase from about 50 % today to roughly 70 %

by 2030 (Christensen, et al., 2013).

This aggravates the impact on energy market volatility of geopolitical threats. Increasing and diversifying

domestic RES capacity, and thus reducing third party supply dependency, can contribute to electricity

supply security, while safeguarding the economy from widely fluctuating fossil fuel commodity prices,

which primarily affects low-income economies (Ölz, Sims, & Kirchner, 2007).

The supply and demand curves on the electrical grid need to be closely matched, and both can be

dvided into base load, intermediate or middle load and peak load, as depicted in Figure 2.19.

Figure 2.19 - Daily load curve separated into base, intermediate and peak load (adapted from Cordaro (2008))

Base load power sources consist of power plants that generate the minimum level of demand over 24

hours. Power plants with long startup times, such as nuclear and coal plants, are commonly used for

base load supply, producing continuous, reliable and efficient power at low cost. Since they are

somewhat inefficient at less than full output, base load plants run continuously throughout the year and

only stop when there is need for repair or maintenance.

Where available, geothermal power plants can provide continuous base load supply, as variability is not

an issue. However, prime sites are often far from population centers and there are great losses due to

long distance transmission of electricity.

Tidal and wave power outputs are variable but with predictable patterns, albeit with varying degrees of

accuracy, making it a base-load option.

The intermediate demand describes the somewhat predictable variation in demand that happens

throughout the day, and is supplied by plants that are capable of working within minutes to an hour and

have moderate operating costs (typically natural gas combined cycle), and are also commonly called as

“load following” or “cycling” plants.

27

Wind power is commonly used in intermediate load power generation but depends on wind speed and

thus can become unavailable if the wind speed is low, and also when it’s too high. Variation time scales

can go from minutes to hours, or in some cases can also be seasonal. Geographical distribution and

smart grid integration can partly compensate for short term fluctuations, as is the case with solar energy.

Peak load demand describes the sudden increase in consumption that might occur during the day,

posing a risk to energy security. As an extreme example, in the UK, a record breaking power surge of

3000 MW hit the national grid as life returned to normal after a solar eclipse, the equivalent to the

demand of an additional 4 million people, resulting in a power outage (BBC News, 1999). The event

was caused by the slow response of power plants to crank up to meet such sudden demand. In these

situations, a highly flexible power plant that can go to full capacity immediately is needed, typically

NGCC (natural gas combined cycle) or hydropower, as the fast response time of hydro reservoirs can

meet sudden fluctuations in demand, as Figure 2.20 testifies: hydropower has the fastest response time,

being able to go from full power to zero and vice versa within one minute.

Figure 2.20 – Load rates of different power plants (adapted from Inage (2009))

Solar PV technology is much more sensitive to seasonal variation from winter to summer, and diurnal

from dawn to dusk, as well as short-term fluctuations from cloud covering. Because its output cannot be

controlled or scheduled, such possible variations have to be accounted for and compensated by flexible

grids or energy storage. However, solar PV electricity fits well with demand that occurs during daylight

hours, especially where peak demands are due to air-conditioning. Concentrating solar power (CSP)

plants also have the ability to support peak demand due to air-conditioning, and, in some cases, heat

storage can fully cover mid-peak demand during a few hours after sunset.

The availability of organic waste products for biomass combustion isn’t always continuous, which affects

supply security unless storing is a possibility. Cogeneration plants using sugar bagasse, for example,

28

often only operate during the harvesting season. Biomass can, however, serve as a backup for solar

power, mainly during night time, as its response time is slow, making it less adequate to serve as a

backup during the day.

Centralized power generation is exposed to a larger set of supply security risks in relation to distributed

generation. RES can be integrated either into the transmission or the distribution systems. For example,

large hydro or wind farms of up to 300 MW feed in to the high voltage transmission system, in the same

way as conventional thermal plants, while small hydro and wind applications for self-production are

much smaller in capacity and usually widely dispersed geographically, presenting minor risks in terms

of exposure to sabotage or terror attacks. An eventual power outage would only affect a small portion

of the electricity grid, making costly precautionary measures with regard to these specific threats

unnecessary. Centralized power generation present a much bigger risk relative to distributed generation,

since an outage could have significant impacts on electricity supply and society (Ölz, Sims, & Kirchner,

2007).

2.4.6 Energy Storage

As RES capacity and grid penetration increases, so does the challenge of ensuring that supply matches

demand at all times. The Blue Map scenario, as defined by the IEA, aims to cut energy related CO2

emissions in half between 2005 and 2050, which would be achieved to a great extent by an increase on

RES share of installed capacity, with the sum of PV and wind energy rising to 30% of total power. For

these highly variable RES technologies, which depend heavily on season, time and weather conditions,

the challenge is greater. Figure 2.21 shows an example of supply and demand of wind power in

Denmark, in which some unbalances are noticeable.

Figure 2.21 – Demand and supply of wind power in Denmark (Inage, 2009)

Throughout a day, demand varies according to short term fluctuations, which oscillate on a scale of

seconds to several minutes, superimposed on long term fluctuations varying on a scale of several hours,

29

as does the supply of highly variable RES technologies. To deal with such variability, there is the above

mentioned solution of having a backup supply power plant, which can be based on renewable or non-

renewable sources, depending on the case. Interconnection of adjacent power grids may also be a

solution, as happens for instance in Denmark, where effective balancing of supply and demand is

facilitated through electricity trade with other Scandinavian countries, as shown on Figure 2.22. At the

same time, a broad geographical area that is interconnected offers an added smoothing effect of the

generation output: although the output of individual wind or solar plants can vary considerably, wide

geographical dispersal of wind power and PV plants reduces the net variation, since it’s more likely that

at least part of the system is under favorable weather conditions for its functioning. The result is a more

stable energy source which positively contributes to the security of the grid, since the introduced net

variation is much lower.

Figure 2.22 - Comparison of the wind power supply and net trade in western Denmark in 2006 (Inage, 2009)

However, in a geographically close cluster of interconnected systems lying under a single weather

system, with a high share of highly variable RES electricity, trading is not an option for fast access to

additional electricity, since deficits and surpluses among all such systems will coincide to a large extent

and, as so, balance will not be maintained.

A different solution for this problem is the use of large-scale energy storage systems. In the Blue Map

scenario there is an inevitable decrease in system flexibility, due to the high penetration of RES and

nuclear power plants, which means that deficits and surpluses balance will not be possibly maintained

by interconnections alone and internal solutions must be provided, and that’s where large-scale energy

storage can play a major role. Also, the rate at which backup capacity can be brought online is limited,

while stored electricity is available almost instantaneously, contributing to increased security. There is,

therefore, a need to assess the relative amounts of storage against net variability, as expected in 2050.

Electricity can only be stored in other forms, such as chemical, thermal or potential energy. Energy

storing technologies’ main characteristics are:

30

Storage properties: energy density, output density, energy storage efficiency, storage scale and

charge/discharge times;

Operation properties: start-and-stop times, load response, partial load feature, lifetime, and

reliability;

Safety, location, construction time and lead time.

The relative importance and significance of each characteristic varies from case to case, depending on

the purposes of use and desired performance, and of great significance, discharge time. As of 2008, the

existing energy storage capacity in Western EU was of 33 GW, consisting in its majority of pumped-

hydro. Figure 2.23 shows the relationship between the net variation of wind power and the necessary

storage in 2010, 2015 and to comply with the Blue Map scenario’s projections of high RES in 2050,

while attending to energy security, according to a study carried out by the IEA in 2009, which merely

present a framework for such an evaluation. Optimizing interconnectivity over geographically disperse

RES generating units, in order to take the best advantage of the smoothing effect, is the best way to

reduce the total energy storage capacity needed, but net variations are ever present, nevertheless. The

total storage capacity needed is, as so, a function of the net variation ratio of the RES. Wind generation

net variation ratios between 10% and 30% in 2050 correspond to needed storage capacities ranging

from 40 GW to 100 GW, which means that an additional capacity of 7 to 67 GW would be required to

mitigate wind power net variations. Simply put, the more RES installed capacity added, and the more

net variation introduced to the grid, equates an increase in the required energy storage capacity.

Figure 2.23 - The relationship of net wind power variation and necessary storage capacities (adapted from (Inage, 2009))

In Figure 2.24, a comparison between different energy storage technologies and their features is

presented, in which pumped-hydro stands out as being the most efficient for intermittency balancing

31

with a high capacity. It is also the technology with the largest discharge time scale, meaning it can

perform for longer, assuring generation and grid security.

Figure 2.24 – Comparison of energy storage technologies (SBC Energy Institute, 2013)

32

3. Pumped Storage

Pumped hydroelectric storage (PHS or pumped storage) is a mature and widely applied electricity

storage technology that has been commercially deployed around the 1890s. The more recent

widespread of low-carbon or carbon free electricity generation technologies has revived the interest in

developing pumped storage facilities, due to their ability in matching fluctuating power demands. As so,

in 2009, the total worldwide capacity of PHS was 127 GW, with hundreds of stations spread around the

world, with the WEU leading the way with 33 GW, followed by Japan and the USA with around 25 and

21 GW respectively. The world’s largest PHS station is in Virginia, USA, with 2 710 MW of installed

capacity, while the world’s highest pump turbine unit, with a maximum pumping head of 779 m and

turbine output of 800 MW, is the Kazunogawa Pumped Storage Power Station in Japan (Inage, 2009).

Such energy storage facilities allow for a reduced peak generation capacity from thermal plants, since

it’s possible to accumulate energy off peak and discharge when demand is peaking, making for a reliable

and much cleaner back up power. It can also be used to improve transmission and distribution

performance by discharging in congested areas at times of peak demand, and also delay the need for

new transmission and distribution capacity, since these are sized for peak demand and, as demand

grows, new systems must be installed, often only to meet the peak demand for a few hours per year. It

can also provide capacity and energy for a black-start after a system failure, since it requires very little

initial power to start and can provide a large amount of power in a short time scale to help other units

restart, while providing a reference frequency for synchronization.

One of its great advantages is the ability to absorb the excess energy that is generated from renewable

sources in low demand periods, and thus avoiding curtailment of clean energies, allowing for a lower

€/MW ratio from these sources.

Furthermore, modern pumped storage plants are equipped with adjustable speed motor generators,

which provide active power control and frequency regulation in pump mode, and can allow direct

connection to RES generating facilities, as is discussed in the following chapters, which is notably

convenient for off the grid power systems (Beisler, 2013).

Pumped hydro systems are suitable for large capacity energy storage, as described above, and have

long lifetimes of over 40 years. Their efficiency is given by the Equation (1).

η = ηc ∙ ηd = [ηp ∙ ηM (

H − ΔHp

H)] ∙ [ηt ∙ ηG (

H − ΔHt

H)] (1)

where

ηc: charging efficiency

ηd: discharging efficiency

ηp: pumping efficiency

33

ηt: turbine efficiency

ηM: motor efficiency of generator/motor

ηG: generator efficiency of generator/motor

H: head

ΔHp: loss head of water way in pumping operation

ΔHt: loss head of water way in turbine operation.

The energy density of the water in the upper reservoir increases as the turbine head increases, as

Equation (2) shows, meaning that high-head pumped hydro units have a large amount of energy stored

in the upper reservoir. Figure 3.1 shows the relationship between net head and volume in the upper

reservoir to obtain 1 000 MWh of stored energy.

E =

∫ Pdt

ρV= gH (2)

where

E: specific energy or energy density of water (J/kg)

P: power (W)

ρ: water density (kg/m3)

V: volume of water (m3)

g: gravitational acceleration (m/s2)

H: pump turbine head (m).

Figure 3.1 - Relationship between water volume requirements as a function of net head between reservoirs, for 1,000 MWh of stored energy (Hearps et al., 2014)

34

The installed power of the system also increases proportionally with the head and with the discharge,

as Equation (3) shows. Since the specific weight is constant, and the efficiency is a characteristic of the

chosen turbine, the installed power is only a function of the head, H, and the discharge, Q, which means

that different combinations of H and Q can be used to obtain the same installed power. The bigger the

discharge is, the more robust and expensive the turbine system will have to be, leading to a great

increase in the overall price of the investment. For this reason, given that the construction costs of a

higher net head system are the same as a lower one, it will most likely be preferable to opt for the former

with a lower discharge to obtain the same installed power, leading to a lower ratio of €/MW.

P = γ Q Hu η (3)

where

P: installed power (kW)

γ: specific weight of fluid (N/m3)

Q: discharge (m3/s)

Hu: head (m)

η: turbine-generator efficiency

3.1 Technology

3.1.1 Conventional Pumped Storage

In its traditional functioning mode, PHS stations systems consist of two reservoirs, where one is located

at a low level and the other at a higher elevation, with pump and hydropower stations where energy is

either injected or converted with the passage of a water flow. In some cases, large water streams or

water bodies, or even the ocean can be used as one of the reservoirs. Figure 3.2 illustrates a schematic

profile of the principle of PHS systems, showing discharge during the day (left) and charge during the

night (right). Pumped hydro storage systems typically use fresh water, but the pilot project of Okinawa

Yanbaru in Japan has shown, that although challenging, seawater can also be used, which greatly

contributes to the potential and adds to the benefits of this technology

Revenues are generated by the difference between low demand hours electricity price (usually during

the night time, early mornings or during the weekend), when electricity is acquired to pump the water to

the higher reservoir where it is stored, and the sell back price of the electricity generated when the water

is later turbined in peak demand hours (usually during weekdays on late mornings, afternoons, and/or

evenings), effectively selling the same energy that was consumed at a higher price, as Figure 3.3

illustrates.

35

Figure 3.2 - Principle of pumped hydro storage systems, showing discharge during the day (left) and charge during the night (right) (adapted from (Inage, 2009))

Figure 3.3 - Operation and revenues during a sample period (1/1/2008) corresponding to a simulation with hourly energy prices in South Australia (Hearps, et al., 2014)

3.1.1.1 Loop Systems

A loop PSPP system uses two reservoirs that are isolated from a free flowing water source. These

systems can greatly reduce impacts, since there is no transfer from a free flowing source (other than

the potential need for evaporation make up water), particularly regarding impacts on fish passage,

sediment migration and natural course flows. On the other hand they can make perfectly good large

fresh water bodies captive which, in a world where water scarcity is an increasing concern, might deter

future projects. However, an example of a loop PSPP system is the Marmora Pumped Storage project

in Canada, located on an old mining site, where the lower reservoir is the dug part of the mine and the

36

upper one is constructed on a 70 million tons rock waste pile that is the result of the mining, as seen on

Figure 3.4.

Figure 3.4 – Marmora Pumped Storage project site before construction (left) and how it will be after the upper reservoir is built.

The capacity is of 400 MW for 5 hours, and it has an estimated net head of 200 m, as shown in Figure

3.5.

Figure 3.5 – Marmora Pumped Storage project schematic profile (adapted from Friesen (2013))

3.1.1.2 Open Systems Pumped Storage

Systems that operate with an upper or lower reservoir (or both) with a natural source of water are

classified as open. The majority of the PSPP are open systems, but in some cases these systems may

37

operate as a conventional hydro power plant in high water seasons, and use the pumped hydro structure

to meet load only in dry seasons. When these plants are used simultaneously for other purposes, such

as irrigation or public water supply, net head values can be significantly lower for a nevertheless

economically viable system, since they usually allow for high flows.

An example of an open system PSPP there is the Baixo Sabor Power Plant in Portugal, made of 2 dams

built on the Sabor River, as shown in Figure 3.6, each equipped with 2 reversible units amounting to a

171 MW capacity. The project is set to be commissioned in the beginning of 2015 and will contribute

with a storage strategic role to the electricity generation.

Figure 3.6 – Baixo Sabor Power Plant’s upper (left) and lower (right) reservoirs (adapted from EDP (2014))

3.1.2 Seawater Pumped Storage

The working principle for conventional and seawater pumped storage is the same, with the exception

that seawater is exchanged between the ocean and an upper (or lower) reservoir instead of freshwater,

which makes it an ideal solution for arid coastal regions, where access to fresh water is limited or

rationed. This poses both opportunities and challenges, with an obvious advantage being that

construction of only one upper (or lower) reservoir is needed, while at the bottom (or top) the ocean

works as the lower (or upper) reservoir. As so, in coastal regions it is comparatively easy to find an

appropriate site for a seawater pumped storage plant, since the vast ocean removes the restraints that

could be posed by lower reservoirs, and they can be built in proximity to nuclear or steam power plants,

which reduces the power distribution costs. Taking into account Equations (2) and (3), since seawater

has a higher density and specific weight than fresh water, it is possible to store more energy with a

smaller upper reservoir and to have more installed capacity using this fluid, although the difference might

be negligible. Also, these systems potentially reduce or even avoid environmental impacts to existing

water bodies or rivers, and on land use.

38

On the other hand, seawater PSPPs are conditioned by coastal topography, since a minimum net head

is required, while facing the great challenge of withstanding the aggressive corrosion caused by salt

water. The latter was a matter of great attention in the pilot project of Okinawa Yanbaru in Japan. A

bird’s eye view picture and sectional view of the waterways of the project can be seen in Figure 3.7 and

Figure 3.8 respectively. Construction finished in 1999, and it is still to date the sole seawater PSPP in

operation in the world. This 30 MW plant has 136 m head, 26 m3/s discharge, and 546 000 m3 artificial

effective storage.

Figure 3.7 - Bird’s-Eye View of the Okinawa Seawater Pumped-storage Power Plant (Fujihara et. al, 1998)

Figure 3.8 – Sectional view of the Okinawa Seawater Pumped-storage Power Plant (Fujihara et. al, 1998)

39

In a paper published in 1998, called “Development of Pump Turbine for Seawater Pumped-Storage

Power Plant”, Tetsuo Fujihara, Haruo Imano and Katsuhiro Oshima elaborate on directives for seawater

pumped storage plants based on the Okinawa pilot project. The research work for this project started in

1981, with tests being done since 1984 in Okinawa to three model pump turbines similar in geometry to

the actual one in use, to investigate the corrosion resistance of different materials and preventive

methods, such as corrosive-preventive paint and cathodic protection.

Based on the different materials and methods performance regarding corrosion prevention, as well as

on economic factors, the final solution for the pilot project was settled. For low velocity portions, mild

carbon steel coated with paint was used, while stainless steel was used for high flow velocity portions.

To avoid paint damage and crevice corrosion, cathodic protection was installed, carried out by an

external power source system in order to make the preventive current adjustable accordingly with flow

velocity. The following components are described in more detail regarding their material choice, as

stated in the above mentioned paper.

Spiral case and stay ring

These components were made of rolled steel for welded structures and water passage surfaces were

coated with vinyl-ester-type, extremely thick film paint with glass flakes.

Head cover and discharge ring

Water passage surfaces were made of austenitic stainless steel with a low carbon content. Surfaces

that do not become wet were made of rolled steel for welded structures to maintain low costs.

Wicket gate, runner and main shaft

The wicket gate and runner were made of austenitic stainless steel casting with a low carbon content

plus nitrogen which was added to improve the corrosion resistance. The main shaft was provided with

a slip ring to provide the corrosion preventive current for cathodic protection. The mainshaft was made

of stainless steel forging for the pressure vessel containing nitrogen in austenitic group.

Draft tube

The upper part of the upper draft tube liner was made of austenitic stainless steel with a low carbon

content, while the other parts were made of rolled steel for general structure and coated with vinyl-

ester-type, extremely thick film pain twith glass flakes.

40

Main shaft sealing box

The seal was made of ceramics. Other parts were made of austenitic stainless steel with a low carbon

content. Since the space between the main shaft and the sealing box is narrow, the sacrifice electrode

system was adopted as a corrosion preventive measure.

Besides the meticulously chosen materials used, specific construction procedures were followed to

prevent corrosion:

The pump turbine was made so that the runner could be taken out from below for easy

disassembly and reassembly in maintenance operations, and the water passage surface was

simplified as much as possible to minimize crevice corrosion. ´

Ceramics were used in the main shaft sealing box, and water draining pipes installed to the

drain pit to prevent water leakage on the head cover.

The wicket gate stem packing was doubled to prevent seawater from entering into the bearing

housing, even if water should leak from the upstream side packing. The wicket gate stem was

also made so that the bearing could be replaced without disassembling the head cover and the

discharge ring.

The rubber packing of the seawater pump turbine was jointed to a stainless steel base by rubber

molding process to reduce crevices. In addition, upper and lower facing plates were integrated

into the head cover and the discharge ring to decrease crevice corrosion caused by the space

between the two components, whereas in conventional pump turbines they are tightened by

numerous bolts.

The connection joint between the main shaft and runner was completely sealed by rubber

gaskets so as to isolate seawater from the coupling bolts.

Figure 3.9 shows a sectional view of the project’s pump turbine. Besides corrosion related concerns,

the same paper also elaborated on specific measures to prevent marine organism’s adhesion to the

components. Barnacles are an example of such organisms that could adhere to pump turbine, pipes,

valves, and auxiliary equipment, whenever the flow velocity is less than approximately 5 m/s, and

especially most easily when the flow velocity is around 1 or 2 m/s. Such occurrences can affect the

efficiency of pump turbine systems negatively, clogging pipes and causing other failures. Sections where

the flow is apt to be stagnant, such as the draft tube, the spiral case and pipes, must be carefully

considered.

These organisms secrete a viscid substance when adhering to the surface of an object but this

substance doesn’t adhere so well to surfaces which repel water. As so, critical sections were coated

with an antipollution type of dirt-prevention paint which can repel water.

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Figure 3.9 - Sectional view of the Okinawa Yanbaru Seawater Pumped Storage Power Station pump turbine (Fujihara et. al, 1998)

For the surface lining structure of the upper reservoir, assessments on the durability, mechanical

structure, water holding capacity and ease of installation for alternative materials have been made, by

performing many tests including:

Ozone and ultraviolet ray induced deterioration

Functional deterioration caused by marine organisms (barnacles)

Test for water tightness at bonding parts by adding repeated water pressure

Large field tests for detailed improvements on the actual works

Confirmation of stability under a strong wind (typhoon) through the field tests

An ethylene propylene diene monomer (EPDM) rubber sheet was chosen for the lining, which has

proven to have excellent weather-resistance characteristics, and can be easily repaired if damaged. A

sheet of 2.0 mm thick EPDM was installed. A drainage layer with 20 mm was constructed using gravel.

http://en.wikipedia.org/wiki/Pumped-storage_hydroelectricity

42

To prevent damage from the angular parts of gravels, a cushioning material made of nonwoven spun

bonded fabric of polyester was laid. On slopes, the span of sheet anchors was set at a standard of

8.5 m.

Should any damage to the sheet occur, seawater leakage is detected by seawater sensors and pressure

gauges, both of which were installed in the pipes connected to the drainage layer in each zone. The

detector emits an alarm to indicate seawater leakage, and at the same time the pump will recharge

leaked seawater to the upper pond system, preventing seawater from leaking into the neighboring

environment. Figure 3.10 shows a schematic view of the drainage system with the various layers and a

field test of materials.

Figure 3.10 – Drainage system of the Okinawa Seawater Pumped-storage Power Plant (Japan Commission on Large Dams, 2001)

Besides concerns with the safety of the system itself and its structure, impacts to the surrounding

environment were also a matter of great importance, in order to prove the viability of such a project.

Environmental impacts mitigation were undertaken, given that there were 16 species of birds and

amphibians considered to be biologically important in the surrounding areas of the upper reservoir. In

order to preserve the habitats of these animals and the coral formations.

43

As so, the following measures were implemented (New Energy Foundation, 2006)):

Reduction of the discharge velocity in order to mitigate the impact of seawater discharge from

power generation on coral. A breakwater of precast concrete blocks (with 350 pieces of 50 tons

and 550 pieces of 32 tons) was installed around the outer circumference of the out-let structure,

reducing the seawater velocity at the time of power generation to approximately 10 cm/s.

Installation of approximately 30 cm high polyethylene nets along 8 km of the outer perimeter of

the construction area in order to prevent small animals such as turtles from entering the

construction area from outside and being harmed by construction vehicles.

Installation of slope-type side ditches which enables small animals such as land turtles and

young birds so that animals will be guided toward natural ground, while also thus playing a role

in promoting traffic safety.

Treatments of muddy water for the purpose of preventing damage during construction works.

All muddy water generated at construction sites was collected and chemically treated before

discharge into natural streams.

Planting seedlings of indigenous trees was done in order to repair the living environment for

plants and animals in the areas that were used as disposal yards and temporary work yards.

Despite the challenges that seawater PSPPs face, there are reportedly new projects being considered

a bit all over the world, namely Monte Goa in Cape Verde Islands, Glinsk in Ireland, Lanai in Hawaii,

and Muuga in Tallin, Estonia.

The Muuga Hydroelectric Pumped Storage Power Plant project reverses the process for seawater

pumped storage by using the sea as the upper reservoir. It would have a capacity of 500 MW, using

three reversible vertical shaft Francis-type pump-turbine assemblies (1x100 MW, 2x175 MW) and one

50 MW vertical-shaft Francis-type turbine, by use of a net head of approximately 500 m, and maximum

flow rate by power generation of 110 m3/s. The delivery conduit would have a 7 m diameter, feeding an

escavated lower reservoir with 12 hour operation at full capacity, equivalent to approximately 4.75 Mm3.

The project was listed as a “potential project of common interest in energy infrastructure” in a European

Comission publication in July 27th 2012. In Figure 3.11 a schematic diagram of the project, situated in

the Mugga Harbour Industrial Park is shown. The water intake is located at the northern slope of the

Muuga Harbour eastern breakwater, and the total covered area is 56 000 m2. The complex buried

underground should incorporate the hydro accumulation power plant control center and a substation

where the main transformers should be. The turbine hall, situated below the lower reservoir, should be

close to the ventilation shaft intended for the entrance of people and equipment and for the air inlet.

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Figure 3.11 - Schematic diagram of Muuga hydro accumulation power plant (ESTIVO, 2010)

3.1.3 Sea bed Pumped Storage

The concept for a sea bed PSPP is arising, but for now it’s still just an idea and not an existing

technology. It would use the water pressure at the sea bed level to make water flow through a valve

fitted turbine that would open when electricity was needed, and flood an underwater tank, at a depth of

400 to 800 m. A schematic profile of a sea bed pumped storage plant is shown in Figure 3.12.

Figure 3.12 – Schematic view of a sea bed PSPP (Gangåssæter & Doghouse, 2013)

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The greatest advantages to these systems would be that there would be virtually no limit to the number

of tanks used in these high head systems, which could provide storage for a large amount of energy,

without land use impacts. The tanks would be emptied by pumping the water out of them, as if charging

a “battery” like in a conventional PSPP, but on this case emptying the reservoir.

The idea is reportedly being considered for implementation in Norway, which has a deep enough shore

to make the systems profitable, according to the company behind the idea, SINTEF, who claims that it

could be used in many parts of the world where great water depths are located close inshore, such as

the marine areas around Italy, Portugal and Spain, as well as North and South America.

One of the great challenges posed by the concept is the reservoir construction and design, which would

have to be built in a material both appropriate for the highly inhospitable climate and cheap enough to

ensure profitability, and this is currently the factor withholding the technology.

3.1.4 Underground Pumped Storage

The concept of underground pumped storage is also the same as conventional pumped storage, with

the exception that the lower reservoir and generation units are underground. Much like the sea bed

pumped storage and sea water concepts, it offers the advantage of minimizing impacts on land use and

natural scenery, since only one of the reservoirs is at the surface. There is also the possibility of using

existing abandoned quarries, mines or underground caverns as the lower reservoir, and using existing

water bodies or even the ocean as the upper reservoir. Figure 3.13 shows schematic view of an

underground PSPP.

The challenges for these systems would obviously be the construction of the lower reservoir or security

reinforcements done to existing underground cavities, which could be very costly, and also maintenance

and repair jobs, which would be made very difficult to accomplish due to the great depths of such

systems.

With this in mind, the Agency of Natural Resources and Energy of Ministry of International Trade and

Industry in Japan investigated from 1997 to 2002, as part of a project to realize underground PSPPs,

the following items:

Rational design and construction of an underground pumped hydro power station that utilizes

space deep underground, aiming for more economical efficiency.

Development of a pump turbine for use with seawater and establishment of technologies for

casting, forging, rolling and welding a new stainless steel that can withstand seawater.

Design of a generator motor to be used for an ultra-high-head pump turbine.

Development of instruments for surveying geological conditions deep underground (1 000 m).

Development of geological research and evaluation methods for deep underground

environments.

Environmental evaluation of the impact of a deep underground pumped hydro power plant.

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Project specifications for this study stated that the output capacity had a maximum of 2 000 MW during

7 hours, with an effective head of 800 m, maximum flow rate of 296 m3/s and an effective storage of 8M

m3 (Inage, 2009).

Being a new technology, pilot projects on a demonstration scale are being undertaken internationally in

Norway (Utsira), Canada (Ramea and Oprisan 2007) and several projects in the UK (the HARI project

in Loughborough, the Yorkshire hydrogen project and several Scottish projects (Energy Storage and

Mangement Study, Scottish Government, 2010). Figure 3.13 shows a schematic view of an underground

PSPP.

Figure 3.13 – Schematic view of an underground PSPP (Inage, 2009)

3.1.5 System improvements

The capacity of the pump is usually smaller than the capacity of the water turbine in reversible pump-

turbines, which means that the water pumping process requires more time than the generation process.

The addition of water pumping capacity can increase the efficiency of the whole system, by speeding

up the pumping process and thus allowing for more generation by extending the period where water is

available to be turbinated. In such types of upgrades, however, damage to the turbine runner has been

reported in some cases. A successful example of an upgraded pumped hydro plant by increase of the

pumping capacity is the Blenheim-Gilboa pumped storage power plant, located in the New York state in

the USA. Figure 3.14 compares the performance of the original versus the upgraded pump turbines

when operating as turbines, showing that efficiency was increased significantly.

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Figure 3.14 - Comparative Performance of Original and Upgraded Pump/Turbines (Inage, 2009)

Another improvement that can be made to pumped storage systems is the use of adjustable-speed (also

commonly referred to as variable-speed) pump turbine units and motor generators, which can operate

over a larger range of rotation speeds. In these equipment, static frequency convertors are used to

adjust its speed. For units of up to 50 MW a synchronous generator can be linked to the grid by a static

frequency convertor, while in larger units a double fed induction machine with a static frequency feeding

the rotor are commonly used, which consists in creating a rotating magnetic field on the rotor, allowing

the unit to be operated over a range of rotating speeds around the synchronous speed, while attached

to a fixed frequency network.

Traditional synchronous machines are directly connected to the grid and operate at a constant speed

and constant input pumping power, which means frequency regulation while in pump mode is not

possible. Adjustable speed systems, on the other hand, allow the power consumed in the pumping mode

to be varied over a range of outputs, enabling them to perform frequency regulation, since the power

absorbed can be varied at fixed head, as Figure 3.15 shows. Cavitation problems can be bypassed by

simply changing the speed of the pump: at maximum head the pump comes close to the suction side of

cavitation, speed can be reduced to allow pump inflow angles match runner blade angles, while at

minimum head speed can be increased to avoid pressure side cavitation (Krenn et. al (2013)). As so,

by adjusting inflow angles pumps can always be operated at their best efficiency. Since less flow is

required for the same pump power input, water resources usage impacts are reduced. Variation can be

up to 30% of the absorbed power. This feature enables the use of fluctuating renewable wind or solar

energies to pump water to the upper reservoir and to reduce use of “spinning” capacity.

Figure 3.16 illustrates how adjustable-speed technology is able to store more energy than single-speed.

The purple colored areas represent the extra energy that a variable-speed technology could storage,

versus the red areas that show the energy that synchronous speed technology can storage. It is possible

to observe that variable-speed not only offers more ability to store energy, but also that it can offer

network balancing during pump mode and that requires less starts and stops, due to the added flexibility.

48

Figure 3.15 - Operating ranges of fixed-speed (left) and adjustable-speed (right) pumps (adapted from Krenn et. al (2013)).

Figure 3.16 - System reserve and power storage from variable-speed vs single-speed pumped storage (Ciocan et. al, 2012)

Adjustable-speed also allows for the turbine to operate at peak efficiency power over a larger portion of

its operating spectrum. In a publication from the Electric Power Research Institute - Application of

Adjustable-Speed Machines in Conventional and Pumped-Storage Hydro Projects, EPRI, 1995 – turbine

efficiency improvement is considered very minor for Pelton turbines, minor for Kaplan, and some

improvement for Propeller turbines, but a very significant improvement is attributed to Francis turbines.

Furthermore, the rate of changing the output is faster than synchronous speed systems. The rotational

speed can also be adjusted to avoid resonances and cavitation modes in the water flow, leading to

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longer life and less maintenance done to the system. The overall more efficient use of the equipment,

enabled by adjustable speed, further reduces the need for thermal plant “spinning” units, thus avoiding

GHG emissions (Inage, 2009).

The net head in turbine operation is obtained by subtracting the head losses form the static head, while

in pump operation the head losses are added to the static head, therefore making the pump mode net

head larger. Consequently, a pump-turbine is always too large to operate as a turbine, meaning that the

best efficiencies of the turbine characteristics are outside the actual operating range of the machine in

a single speed configuration as Figure 3.17 shows, where the operating range (red area) of fixed and

adjustable speed turbine are compared.

Figure 3.17 - Operating ranges of fixed-speed (left) and adjustable-speed (right) turbines (adapted from Krenn et. al (2013))

Another option for system improvement is the use of separate parallel circuits for pumping and turbining,

which might or not be an improvement, depending on the case. Either way, while a single penstock is a

cheaper solution, a double penstock can offer operational flexibility, since pumping or turbining become

independent operations, and allows for a quick response operation of the turbine when needed. This

could be advantageous if a wind power unit, or other variable generating unit, is directly connected to

the pump, for example, as could happen in an off the grid system, in a similar scheme to the one shown

in Figure 3.18. The available energy from the wind power units could be stored via pumping action, while

the turbine is working. In this case the pumped storage plant acts as an effective energy filter through

which the fluctuating wind production is transformed to a stable and controllable hydroelectric production

(Anagnostopoulos & Papantonis, 2012). On the other hand a double penstock doesn’t offer any

advantage when not coupled to a “free” of costs source of energy, since if it was connected to the grid,

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the unit would be consuming and selling electricity at the same price, not to mention energy losses of

the process.

Figure 3.18 – Double penstock in system with wind farm powering the pumps (Pálmason, 2010)

3.2 Mitigation of variability in RES generation

As discussed in previous chapters, one of the greatest challenges in a high RES penetration grid is the

unpredictable and potentially high variability of its output, especially with wind and solar technologies.

Demand fluctuates through the day and utilities must keep additional plants available to meet

unforeseen increases, losses of conventional plants and/or transmission lines, and other contingencies.

Frequency regulation (the ability to respond to small, random fluctuations around the normal load) and

contingency reserves require units that can rapidly change output. When demand rises above

generation, the frequency declines, while the inverse happens when generation is higher than demand.

Figure 3.19 illustrates frequency regulation (red), total load (green) and load following, which is longer

term ramping requirements (blue). In this example the morning load increases smoothly by about 400

MW in two hours, during which rapid short-term ramps of +/- 50 MW within a few minutes are noticeable.

Figure 3.19 – System load following and frequency regulation. Frequency regulation (red) is the fast fluctuating component that balances total load (green), (Denholm et. al, 2010)

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The fast nature of these fluctuations require fast response of regulation reserves, which are often

provided by plants that are online and “spinning”, commonly known as spinning reserves. Keeping these

plants spinning can be very costly and diminishes the overall efficiency of the system, since the need

for operating reserves and the large variation in demand restricts the contribution from low-cost base

load units and increases the need for units that can vary output to provide load-following.

The variable input of RES to the grid can be interpreted as a source of demand reduction with unique

temporal characteristics, so conventional generators provide the “residual load” of normal demand

minus the electricity produced by renewable generators.

Figure 3.20 illustrates how a renewable generation is subtracted from the normal load, showing the

“residual” or net load that the system would need to meet with other sources. The reduction implies a

reduction in fuel use (and associated emissions) from these sources.

However, the use of variable generation also has negative impacts on the grid. Because it increases

ramping rate, and short term variability, there is an increased need for frequency regulation. The ramping

range – the difference between the daily minimum and the maximum demand - also increases, with the

associated reduction in minimum load, which can force base load generating units to reduce output or

even force them to cycle off during periods of high wind output. Finally, the unpredictable nature of a

variable source reflects on the resulting net load. When put all together, the increased variability of the

net load resulting from the use of variable generation requires a greater amount of flexibility and

operating reserves in the system, with more ramping capability to meet both the predicted and

unpredicted variability.

Figure 3.20 – Impact on net load from increased use of variable generation units (Denholm et. al, 2010)

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At higher penetration of variable RES generation, the ability of conventional generators to reduce output

becomes an increasing concern. In Figure 3.21, variable RES generation shows periods (the first 12

hours of each day) where it reduces demand so much that it begins to displace units that usually work

with a constant output, and whose ability to reduce output is somewhat constrained. If the base load

generators cannot reduce output (and some other use cannot be found for this “excess generation”),

then wind energy will need to be curtailed– this occurs in the above mentioned periods of the first 12

hours of each day. While modern wind turbines can reliably curtail output, it is a largely undesirable

practice because it throws to waste a cost-free (in regards to production) and emissions-free energy.

Curtailment reduces the net capacity factor of wind and solar generators, which implies an increased

generating cost for the energy that is actually produced from that source.

A solution to avoid curtailment is provided by energy storing facilities, by absorbing otherwise unusable

generation and moving it to times of high net system load (where net load is defined as normal load

minus variable generation), as Figure 3.22 shows. Energy that is stored from the surplus of wind power

generation, for example, can be shifted to high demand hours. The additional flexibility that pumped

storage adds to the system is also of significant importance: by providing operating reserves, it reduces

the need for partially loaded thermal generators which may otherwise restrict the contribution of variable

RES generation. Finally, by providing firm capacity and energy derived from variable RES sources,

pumped storage can effectively replace base load generation, which reduces the minimum loading

limitations.

Figure 3.21 – Variable RES generation curtailment in a high RES penetration grid (adapted from (Denholm et. al, 2010)

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Figure 3.22 – Storage as an option for increasing the use of variable RES by decreasing curtailment (Denholm et. al, 2010)

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4. Case Study - Multiple Purpose Socorridos System

4.1 Project description

Located in Madeira Island, which has approximately 262 000 habitants, the Multi-Purpose Socorridos

Hydroelectric System began operating in 1995 under an initial configuration that featured a 15.5 km long

string of hydro tunnels and canals, allowing the transfer of water collected on the higher altitude and

more pluvious northern side of the island, to the southern side of the island, a loading chamber in Covão

with a maximum capacity of just 7 500 m3, and a hydroelectric station with three 8 MW turbines. Another

branch of the system connects to the Stª Quitéria mini hydropower station, which is equipped with a

single Pelton turbine with a nominal flow of 1 m3/s

The small capacity loading chamber could only provide guaranteed power during winter, which led to

the improvement of the system in the period between 2004 and 2006, with the introduction of four main

new features:

Transformation of the hydroelectric station into a reversible system with the installation of 3

working pumps of 3.75 MW, 0.65 m3/s flow and a peak of 457 m each, plus a similar one as a

backup;

Addition of a 5 243 m long tunnel between Covão and Campanário with a 32 500 m3 water

storage capacity, which supplies irrigation water on both of its ends, and provides storage, in

order to ensure a reliable water supply and electricity production;

Addition of a storage gallery with 40 000 m3 capacity in Socorridos, which accumulates the

turbined water and feeds the pumping station;

Renovation of the Encumeada (2 850 m) and Canal do Norte (2 768 m) tunnels, and installation

of gates to regulate water flow, allowing the storage of up to 55 000 m3 of water.

With these changes, the project’s objectives were:

to guarantee that 24 MW of power and 44 MWh are available daily;

to cut energy losses, which were estimated at 2.54 GWh per year;

to introduce additional wind power estimated at 25 MW;

to reduce the use of fossil fuels in power generation;

to reduce GHG emissions in power generation;

to improve the management of hydroelectric resources;

to increase reliability of the water supply system to the populations of Funchal (through the

Water Treatment Station at Stª Quitéria) and Câmara de Lobos (through the Water Treatment

Station at Covão);

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to deliver 65% of irrigation water to the distribution facilities at Covão and Campanário,

minimizing estimated losses by some 1 300 m³/day in the Canal do Norte (southern section)

between the Serra de Água power station and Campanário.

The introduction of Loiral and Pedras wind farms alone, made possible by the Socorridos reversible

system, allowed for a reduction of 27 600 tonnes of CO2 (carbon dioxide), 116 tonnes of SO2 (sulfur

dioxide), 478 tonnes of NOx (nitric oxide) and 7 tonnes of particles.

In Figure 4.1 it is possible to see the changes in the system from the initial configuration to the current

one: Encumeada (1) and Canal do Norte (2) tunnel renovations, addition of the Covão (3) tunnel,

Socorridos gallery (7) and reversible hydro station (8). Following that, the functioning sequence of the

system is explained.

Figure 4.1 – The Multiple Purpose Socorridos System changes from its initial configuration (IFDR, 2007)

In dry seasons, during the day, water stored between the Encumeada (1) and Canal do Norte (2) tunnels,

and in Covão (3) loading chamber and tunnel can be turbined at Stª Quitéria (4) and Socorridos (5) to

generate electricity. At Stª Quitéria, all of the water that is turbined is used for public supply after going

through a water treatment station. At Covão, part of the water is diverted for irrigation and water

treatment plants for public supply. Likewise, at Campanário (6), part of the water is diverted for irrigation.

All of the water that is turbined during peak periods at Socorridos hydroelectric power station (5) is stored

in the Socorridos storage gallery (7). At night water is pumped back (8) to the Covão tunnel (3) so that

it can be used again the next day, completing the cycle.

Snapshots of the schematic operation of the system in the summer are displayed in Figure 4.2,

corresponding to the turbine mode, and Figure 4.3, corresponding to the pumping mode.

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Figure 4.2 – Snapshots of the schematic operation of the system in turbine mode (adapted from (EEM, 2006))

57

Figure 4.3 - Snapshots of the schematic operation of the system in pump mode (adapted from (EEM, 2006))

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In reversible systems with big stream flows and small elevations, Francis turbines are commonly used,

but due to the large head of this station (the gross head is 456.9 m, as Figure 4.8 illustrates, where a

profile of the penstock can be seen), Pelton turbines were installed, at a topographic level of 89 m,

where the hydropower station sits. The turbines characteristics of the turbines are listed in Table 4.1.

A floor plan and two sections of the hydropower plant are presented in Figure 4.4, and a picture of the

turbines is shown in Figure 4.5.

Table 4.1 – Socorridos Hydroelectric Station turbine characteristics

Turbines

Number of units 3

Type Pelton

Gross Head (m) 457

Net Head (m) 450/433

Number of Paddles per Wheel 19

Nominal Wheel Diameter (m) 1.118

Maximum Flow (m3/s) 2

Nominal Speed (r.p.m.) 750

Nominal Power (kW) 8 000

Constructor Noell

Figure 4.4 - Floor plan and two sections of the Socorridos Hydroelectric Station (EEM, Aproveitamento de Fins Múltiplos da Ribeira dos Socorridos)

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Figure 4.5 – Turbines at Socorridos Hydroelectric station

The use of reversible turbines to pump the water back to Covão was inadequate, considering the range

of power and head required and, as so, an autonomous pumping system was installed in parallel, using

the same hydraulic infrastructure (penstock and intake/discharge chambers). The pump station is

buried, and sits at a topographic of level 85 m, using four pumps with the characteristics listed in Table

4.2, with one of them serving as a backup. It was designed to pump as much as 40 000 m3 of water

stored in Socorridos gallery during electricity low demand hours (from 0 to 6 am). In Figure 4.6, a profile

and cross section of the pump station is presented, and in Figure 4.7 a picture of the pumps is shown.

Table 4.2 – Socorridos Pump Station pump characteristics

Pumps

Type Centrifugal

Number of Units 3+1(backup)

Installed power (kW) 3 750

Head (m) 457

Maximum Flow (m3/s) 0.65

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Figure 4.6 - Profile and cross section of the Socorridos Pump Station (CENOR)

Figure 4.7 – Pumps at Socorridos Pump Station

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Figure 4.8 – Profile of the penstock connecting Covão Reservoir to the Socorridos Plant (adapted from (EEM, Aproveitamento de Fins Múltiplos da Ribeira dos Socorridos))

Figure 4.9 shows how the load diagram is smoothed out by the Socorridos reversible system: in low

demand hours the system absorbs energy from wind power, and in peak hours that same absorbed

energy is used to meet peak demand over roughly 125 MW, meaning as much as 24 MW of spinning

reserves can be avoided (although the graph shows roughly 10 MW of maximum avoided spinning

reserves).

Figure 4.9 – Socorridos reversible system’s effect on the summer load diagram for Madeira Island (adapted from (EEM, 2006))

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4.2 Madeira’s Renewables Potential

As part of the EU, the Região Autónoma da Madeira (RAM) has ambitious goals for greenhouse gas

emissions reduction and the use of renewable sources in power generation, which is all the more

important considering the isolation and third party energy dependence that such remote islands are

usually subjected to. An important step towards cutting GHG emissions and reducing the effects of third

party dependency is being given with the substitution of the Vitória Thermal Power Plant’s fuel from fuel-

oil to natural gas which, as previously seen, has an overall lower emission rate, besides being cheaper

and less prone to price oscillations. As a reference point, with an energy production of 400 GWh, which

corresponds to roughly 55% of the thermal energy production in the RAM in 2005, the introduction of

natural gas translates into a reduction of 156 000 tonnes of carbon dioxide (equivalent to the subtraction

of 78 000 automobiles), 20 000 tonnes of sulfur, 680 000 tonnes of nitric oxide, and 20 tonnes of

particles. Figure 4.10 draws a comparison between projected CO2 emissions for different combinations

of energy sources in RAM. The projections were made with the commissioning year of 2011 in mind

when in fact the natural gas use only started in March 2014. Nevertheless, the difference in the projected

emissions between the sole use of fuel oil and the use of natural gas and RES is strikingly accentuated.

Figure 4.10 – CO2 emissions in electricity generation projected comparison between different solutions in RAM (Vice Presidência do Governo Regional da Madeira, 2008)

The RAM government committed to a 20% reduction in CO2 emissions by 2020, below 1990 values,

and to raise the share of RES in the energy mix up to at least 20% by the same deadline, by signing in

to the Pact of Islands. In recent years the evolution has been significantly positive, having already

surpassed the 20% RES share mark 11 years ahead of schedule, as Table 4.3 shows.

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Table 4.3 – Percentage of RES penetration in the electricity generation mix by year in RAM (Vice-Presidência do Governo Regional da Madeira, 2012)

Year 2007 2008 2009 2010 2011

Madeira Island 13.1% 14.4% 23.0% 26.3% 26.9%

Porto Santo Island 5.1% 5.7% 5.1% 13.0% 14.3%

RAM 12.8% 14.1% 22.4% 25.8% 26.5%

The introduction of the new wind turbine parks of Paul da Serra (6.0 MW), Pedras (10.20 MW), Fonte

do Juncal (8.1 MW), Loiral (5.1 MW) and Loiral II (6.0 MW), between 2008 and 2011, increased by

almost 5 times the installed power for this source, for a total of 45 MW. In 2011, solar panel parks were

also installed in Loiral (9.0 MW) which raised the total installed capacity of this source up to 17 MW.

Figure 4.11 shows how these additions contributed to the evolution of the electricity produced by RES

in RAM between 2007 and 2011, allowing it to more than double in just 4 years.

Figure 4.11 – Evolution of RES in electricity generation in RAM, from 2007 to 2011 (adapted from (Vice-Presidência do Governo Regional da Madeira, 2012)

This increase was made possible with the commissioning of the Multiple Purpose Socorridos System

reversible functioning mode. In fact, without a hydro power plant to regulate peak demand, the system

would be left with only one major thermal power plant serving as base, middle and peak load. In such a

situation, system stability is heavily compromised with the introduction of variable generation as was

previously shown. Not only that, spinning reserves have to be higher to meet peaks in demand and

regulate frequency, which means more fuel is consumed and generation is, in turn, more expensive.

Figure 4.12 and Figure 4.13 illustrate how the Socorridos System affects the daily load diagram in

autumn, showing how wind penetration is maximized due to pumping in low peak demand hours, and

thermal generation is substituted for hydro production in peak hours, which is allowed by storage,

effectively “smoothing” out the load diagram. As so, less spinning reserves are required.

64

Figure 4.12 – Load diagram in grid without Socorridos Reversible System (adapted from (EEM, 2010))

Figure 4.13 – Load diagram in grid with Socorridos Reversible System (adapted from (EEM, 2010))

The projected share of RES in electricity generation in RAM is expected to grow even higher, as Figure

4.14 illustrates, to as much as 52% by 2020, a very high figure. This will be achieved mainly with more

wind power capacity (up to 150 MW), and solar power capacity (up to 20 MW) by 2020.

65

Figure 4.14 – Projected share of RES in RAM’s electric grid from 2010 to 2020 (Vice-Presidência do Governo Regional da Madeira, 2012)

Soon more storage capacity will be needed, to ensure grid security to variation in generation.

As so, and through the accumulated experience and confidence with Socorridos system, a new

reversible project in Calheta (Calheta Hydroelectric Reversible System - Calheta III) is currently

under construction. The project’s main components are (Calheta Hydroelectric System:

Calheta III – New Reversible System, EEM, 2011):

Pico da Urze Dam

o 31 meters height

o 1 000 000 m3 of storage capacity

o Flooded area of 7 ha

Calheta Dam

o 34.5 m height

o 73 750 m3 total storage volume for the retention of the water turbinated in Calheta III,

for subsequent pumping to Pico da Urze’s reservoir

o Flooded area of 6 360 m2

Calheta III Hydroelectric Power Plant and Calheta Pumping Station

o 2 generators with 15 MW of power each (2x15 MW)

o 3 pumps for Calheta Pumping Station, each one with 4.9 MW

Penstocks

o 1500 mm steel tubing

o 3.460 m length, from Calheta and Paul stations to Pico da Urze’s bayou)

66

Water Pumping Station of Paul

o 2x150 kW electric pumps to pump the collected water by Paul I water channel (Levada

do Paul I), below the Pico da Urze dam, and also by Paul II water channel (Levada do

Paul II), both to Pico da Urze bayou.

Paul II Water Channel (Levada do Paul) Expansion

o 10.6 km length between the Juncal stream (Ribeira do Juncal) and the forebay of Paul,

by raising the side walls to increase transport capacity

Paul Old Water Channel (Levada Velha do Paul) Expansion

o main source of supply to Pico da Urze’s bayou

o 1 600 m length , between the Lajeado stream (Ribeira do Lajeado - where it takes in

the water) and the Alecrim stream (where it gives back the intake water)

o building of a channel in order to increase the carrying capacity

Lombo Salão Water Channel (Levada do Lombo do Salão) Renewal

o 1 690 m long, located between Calheta I Hydroelectric Power Plant and Lombo do

Salão forebay

o aims at reducing water flow losses during its path, in order to improve the water delivery

to irrigation and adduction to Calheta II Hydroelectric Power Plant (Central de Inverno

da Calheta - Calheta II)

This project is expected to generate an added 29 GWh of annual average hydropower production, of

which 18 GWh will derive from direct water exploration and the remaining 11 GWh will be a result of the

pumped water storage usage, and it will allow for the inclusion of as much as 25 MW of added variable

generation, namely wind power (Figueira, Calheta Hydroelectric System - Calheta III – New Reversible

System, 2011).

A schematic illustration of the system and its functioning is displayed in Figure 4.15. The working

schedule is supposed to follow the same protocol as the Socorridos system: pumping occurs during low

demand hours (during the night) and water is available to be turbinated during the day.

The projected daily load diagram of the RAM’s electricity grid with the inclusion of the Calheta reversible

system is shown in Figure 4.16. As expected, the load diagram is further smoothed out in comparison

with the one displayed in Figure 4.13 where only the Socorridos system was considered, with increased

RES penetration possibility, of up to 30% of the electricity production share, and reduced need for

spinning reserves. This results in the avoidance of 81 400 tonnes of fuel oil importing, which corresponds

to a 3.8 M€ savings per year, and to an avoided emission of 253 000 tonnes of CO2.

67

Figure 4.15 – Schematic illustration of the Calheta III Reversible System (Vice-Presidência do Governo Regional da Madeira, 2008)

Figure 4.16 - Load diagram in grid with both Socorridos and Calheta Reversible System (adapted from EEM, 2010)

68

4.3 Optimization Algorithm

In order to draw a comparison between different technology solutions in PHS systems, an optimization

procedure is developed using MATLAB, with objective functions that represent the Multiple Purpose

Socorridos System in its real configuration and with alterations that aim to improve it, such as the ones

that are mentioned in chapter 3.1.5: the use of adjustable-speed pump and turbine equipment, and the

installation of a double penstock. This is an adaptation of a previously done study to the same system

by Ramos and Vieira - Hybrid solution and pump-storage optimization in water supply system efficiency:

A case study, Ramos and Vieira, 2008 - where wind energy integration to power the pump station is

studied.

Performance of each alternative is measured and classified accordingly with its generated revenues,

meaning that costs are minimized and benefits are maximized in the optimization procedure, and by

accounting RES integration ability and surplus of energy which is provided by the electrical grid. Costs

of installation, operation and maintenance works of these alterations, as well as of the wind park are out

of the scope of this exercise and, therefore, not considered, meaning that only performance is compared.

The objective functions are solved for water level variation, since it is directly correlated to the amount

of energy that is either consumed or produced, provided that the system remains unchanged throughout

the modelling time period. With this optimization procedure, a schedule for the best possible

performance is obtained, being energy tariff and wind energy availability the criteria for the algorithm to

either store or generate energy, within the set boundaries. The results indicate the ideal water level

variations for each hour, which are to be used in the following calculations.

Nonlinear MATLAB algorithm solvers are used, which stop when a local minimum is found. In order to

get as close as possible to the global minimum one is faced with two options: provide an initial point that

is as close as possible to the global minimum or run the simulation multiple times and pick the best

solution. Since the solution is largely unknown, the script is run in a loop a hundred times with randomly

generated initial points, and the best solution is automatically picked out and worked in EXCEL.

Some considerations and simplifications are implemented in the system in order to make the modelling

simpler, without compromising the proposed comparison:

The modelling is common to both adjustable and synchronous technologies, meaning the

schedule obtained is the same for both. The results are, however, treated independently;

The top and bottom reservoirs are considered identical, with a rectangular parallelepiped shape,

and effective dimensions of 100 x 100 x 4 [m3] amounting for 40 000 m3 of water storage

capacity, meaning the maximum level is 4 m, while the minimum is set at 0.5 m for the upper

reservoir, and 0,1 m for the lower reservoir;

Although wind speed and water inlet and consumption were collected for both winter (wet) and

summer (dry) seasons, only the dry season is considered. This is justified by observing that

during wet season the pump is never or very rarely used, from gathered data of the functioning

of the system;

69

The electricity tariff is adapted from the 2015 real tariff from EEM (Empresa de Electricidade da

Madeira) to “final clients in medium tension”, so that the peak to low (and vice versa) period

switch occurs on the hour, instead of on the half hour, to make it compatible with the time step

increments of the modelled systems. No criteria was used in choosing the tariff since it will affect

all alternatives equally, except that it corresponds to the dry season period;

The equipment is considered to work as a unit in the modelling phase, meaning all 3 turbines

and pumps work as a single unit. Later on they are accounted for separately, considering the

efficiency of each pump and turbine;

For the wind integration simulation, it is considered that there is one park with 6 VESTAS V90

wind tower turbines of 3000 kW each in Loiral (same as the Loiral II wind park but with two

additional wind towers), due to the more detailed available information about the average wind

speed values for typical winter and summer conditions on that station, and wind turbine power

curves of the model V90 from Vestas;

The wind speed data is compiled from a monthly record for February and July in 2014, one from

each season (wet and dry);

It is considered that not all the wind energy that is produced is available to use in the Socorridos

System, but a percentage of it, since part of it is directly consumed by the electrical grid, namely

during high peak demand hours

The net head is considered fixed, for all calculations, at 457 m;

Ten simulations are run with different initial levels for the reservoirs, starting at the minimum

level for the upper reservoir and ending at 1 m above that. These are considered to occur with

equal probability in further calculations;

In order to ensure spinning reserve capacity at peak demand hours, a minimum upper reservoir

level is required to be verified at 10 am and 8 pm;

During peak demand hours, only the turbine station can operate, and during low demand hours

only the pump station can operate.

A Microsoft Excel file is used as the input for the MATLAB optimization, to allow it to be flexible and

adaptable to different situations. The inputs for the modelling are:

Hourly water consumption in the upper reservoir (m) - NCU

Hourly water inlet in the upper reservoir (m) - NIU

Hourly water consumption in the lower reservoir (m) - NCL

Hourly water inlet in the lower reservoir (m) - NIL

Electricity tariff (€) - c

Initial water level in the upper reservoir (m) - NINITU

Initial water level in the lower reservoir (m) - NINITL

70

Maximum water level in the upper reservoir (m) - NMAXU

Maximum water level in the lower reservoir (m) - NMAXL

Minimum water level in the upper reservoir (m) - NMINU

Minimum water level in the lower reservoir (m) - NMINL

Water level rise/decrease for each time step (determined by pump/turbine flows – dNh

Volume per meter in height in the reservoirs (dependent from their dimensions) (m3/m)- Vu

Net head - Hu

Pumping station efficiency - ηP

Maximum water level rise in upper reservoir – NQP

Maximum water level decrease in upper reservoir - NQT

Generating station efficiency – ηT

Wind speed curve

Wind turbine power curve

Wind energy powered water level variation available on each hour - dNh_w

4.3.1 Pumped hydro storage with single penstock

To model the single penstock system Function 4.1 is used:

∑ [|(𝑑𝑁ℎ,𝑊 𝑑𝑁ℎ⁄ ) − 1| ×

𝐶𝑃,ℎ

𝜂𝑃(

𝑑𝑁ℎ + |𝑑𝑁ℎ|

2) + 𝐶𝑇,ℎ 𝜂𝑇 (

𝑑𝑁ℎ − |𝑑𝑁ℎ|

2) ]

24

ℎ=1

(4.1)

where

CP,h - electricity tariff for each hour (€/kWh);

dNh- water level variation in the upper reservoir (Covão) (m);

dNh,W - water level variation that can be produced by wind energy in the upper reservoir (Covão) (m);

CT,h - produced hydroelectricity selling price for each hour (€/kWh);

ηP- pump efficiency (%);

ηT - turbine efficiency (%);

h - hour of the day.

71

This function represents the sum of the water level variation in the upper reservoir multiplied by the

electricity costs/selling price, throughout 24 hours. It is separated in two terms, one for the pump

operation, and one for the turbine. When the water level rises (dNh>0), the pump is operating, with an

associated cost for each hour (CP,h), and the turbine term is equal to zero due to the factor (𝑑𝑁ℎ− |𝑑𝑁ℎ|

2) .

Conversely, when the water level declines (dNh<0) the turbine is operating, and energy can be sold at

an associated price for each hour (CT,h), while the pump term is equal to zero due to the factor

(𝑑𝑁ℎ+ |𝑑𝑁ℎ|

2).

Additionally, the factor |(𝑑𝑁ℎ,𝑊 𝑑𝑁ℎ⁄ ) − 1| introduces a condition in which if the pump uses exactly the

wind energy available in a given hour, then the cost of operation is equal to zero. Should the pump use

more than that energy, then there is a price to be paid for the operation, since the pump needs to use

the electrical grid to work. If, instead, the pump uses less than that energy, then there is also a price to

be paid for, as that means that wind energy is being wasted. Since we are minimizing the function, the

solver will always try to use exactly the amount of wind energy available, to bring the pumping operation

cost down to zero, and use the turbine the most when the electricity tariff is higher.

The restrictions to the hourly water level variations are shown in Tables 4.4 and 4.5. In addition to these

hourly restrictions, there are other constraints set to occur at specific hours, as previously mentioned:

spinning reserves must be guaranteed at 10 am and 8 pm, and only the turbine can operate on peak

demand hours.

Table 4.4 – Hourly water level variations in the upper reservoir for Functions 4.1 and 4.2

Operation Limits

Turbine [NQT, 0]

Pump [0, NQP]

Table 4.5 – Hourly water level limits for the upper and lower reservoirs for Functions 4.1 and 4.2

Maximum water level in the upper reservoir (m) NMAXU

Maximum water level in the lower reservoir (m) NMINU

Minimum water level in the upper reservoir (m) NMAXL

Minimum water level in the lower reservoir (m) NMINL

These restrictions are mathematically translated as follows:

1. Guarantee supply in the upper reservoir by maintaining its minimum required level.

For any given time, the sum of the variation of the water level on the upper reservoir (∑ dN) with

the initial level in the upper reservoir (NINITU) and the difference between the sum of the water

72

inlet in the upper reservoir (∑ NIU) and the sum of the hourly water consumption (∑ NCU) has to

be equal or superior to the minimum water level for the upper reservoir (NMINU):

∑[𝑑𝑁ℎ + 𝑁𝐼𝑁𝐼𝑇𝑈 + (𝑁𝐼𝑈ℎ− 𝑁𝐶𝑈ℎ

)]

ℎ

𝑡=1

≥ 𝑁𝑀𝐼𝑁𝑈

2. Guarantee that the upper reservoir doesn’t spill over.

For any given time, the sum of the variation of the water level on the upper reservoir (∑ dN) with

the initial level in the upper reservoir (NINITU) and the difference between the sum of the water

inlet in the upper reservoir (∑ NIU) and the sum of the hourly water consumption (∑ NCU) has to

be equal or inferior to the maximum water level for the upper reservoir (NMINU):


)]

ℎ

𝑡=1

≤ 𝑁𝑀𝐴𝑋𝑈

3. Guarantee supply in the lower reservoir by maintaining its minimum required level.

For any given time, the sum of the variation of the water level on the lower reservoir (− ∑ dN)

with the initial level in the lower reservoir (NINITL) and the difference between the sum of the

water inlet in the lower reservoir (∑ NIL) and the sum of the hourly water consumption (∑ NCL)

has to be equal or superior to the minimum water level for the lower reservoir (NMINL). Positive

values of dN correspond to a decrease in the lower water level, hence the negative value

adopted on this sum:

∑[(−𝑑𝑁ℎ) + 𝑁𝐼𝑁𝐼𝑇𝐿 + (𝑁𝐼𝐿ℎ− 𝑁𝐶𝐿ℎ

)]

ℎ

𝑡=1

≥ 𝑁𝑀𝐼𝑁𝐿

4. Guarantee that the lower reservoir doesn’t spill over.

For any given time, the sum of the variation of the water level on the lower reservoir (− ∑ dN)

with the initial level in the lower reservoir (NINITL) and the difference between the sum of the

water inlet in the lower reservoir (∑ NIL) and the sum of the hourly water consumption (∑ NCL)

has to be equal or inferior to the maximum water level for the lower reservoir (NMINL). Once

again, positive values of dN correspond to a decrease in the lower water level, hence the

negative value adopted on this sum:

∑[(−𝑑𝑁ℎ) + 𝑁𝐼𝑁𝐼𝑇𝐿 + (𝑁𝐼𝐿ℎ− 𝑁𝐶𝐿ℎ

)]

ℎ

𝑡=1

≤ 𝑁𝑀𝐴𝑋𝐿

73

5. Guarantee spinning reserves at 10 am:

At the end of the first 10 hours of the day, the sum of the variation of the water level on the

upper reservoir (∑ dN) with the initial level in the upper reservoir (NINITU) and the difference

between the sum of the water inlet in the upper reservoir (∑ NIU) and the sum of the hourly water

consumption (∑ NCU) has to be equal or superior to the difference between the maximum water

level for the upper reservoir (NMINU) and the minimum water level for the upper reservoir (NMINU):


)]

10

𝑡=1

≥ (𝑁𝑀𝐴𝑋𝑈 − 𝑁𝑀𝐼𝑁𝑈)

6. Guarantee spinning reserves at 8 pm:







)]

21

𝑡=1


7. Guarantee that only the turbine can work in peak demand hours

Peak demand hours occur between 10 am and 1 pm and between 8 and 10 pm. As so dN has

to be equal or inferior to zero on these hours:

𝑑𝑁10 ≤ 0; and

𝑑𝑁11 ≤ 0; and

𝑑𝑁12 ≤ 0; and

𝑑𝑁20 ≤ 0; and

𝑑𝑁21 ≤ 0.

Wind data was collected from Loiral’s weather station record of July of 2014. The data consists of 10

minute interval records of the wind speed throughout the days which were then compiled into hourly

averages, and subsequently daily hourly averages. The results are presented in Figure 4.17. With the

wind speed records, and using VESTAS V90 power curve, shown in Figure 4.18, the data was converted

into kW, and subsequently to water level variation (in meters) using Equation (4).

74

P = γ Q Hu η⁄ (4)

where

P: installed power (kW);

γ: specific weight of fluid (N/m3);

Q: discharge (m3/s);

Hu: head (m);

η: pump efficiency.

That is to say that a given wind speed produces a given power that is capable to elevate a given amount

of water, represented by 𝑑𝑁ℎ𝑤.

Figure 4.17 –Hourly average wind speed in Loiral - July 2014

Figure 4.18 – VESTAS V90 wind turbine power curve

4.00

5.00

6.00

7.00

8.00

9.00

10.00

11.00

12.00

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

m/s Hourly average wind speed in Loiral - July 2014

75

Since there is the possibility that the available wind energy is higher than the maximum flow the pump

is capable of producing, a curtailment procedure is done in MATLAB. Therefore, if the available wind

energy exceeds that threshold, the value will be reduced to the maximum value that the pump can

elevate.

The hourly percentage of the total generated wind energy that can be fed into the Socorridos System is

shown in Figure 4.19.

Figure 4.19 - Hourly percentage of the total generated wind energy that can be fed into the Socorridos System

The electricity tariff is adapted from the 2015 real tariff from EEM to “final clients in medium tension”,

and it is presented in Figure 4.20.

Figure 4.20 – Electricity Tariff (€/kWh) (EEM, 2015)

The data for the hourly consumption derived water level variations in the upper reservoir was compiled

from a record of the hourly flows to the water treatment plants of Stª Quitéria and Covão, and the

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

Hourly percentage of the total generated wind energy that can be fed into the Socorridos System

0.0724 0.07240.0674 0.0674 0.0674 0.0674

0.0724 0.0724 0.0724

0.1027

0.1195 0.1195 0.1195

0.1027 0.1027 0.1027 0.1027 0.1027 0.1027 0.1027

0.1195 0.1195

0.1027

0.0724

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

Electricity Tariff (€/kWh)

76

irrigation flows Stª Quitéria for Ameixeira, Campanário and Covão. There is no data record for the hourly

inlet derived water level variations in the upper reservoir, so it is considered constant and equal to the

total amount of water consumed in a day. The water consumption and inlet in the lower reservoir is set

to zero. The average hourly consumption and inlet derived water level variation in the upper reservoir is

shown in Figure 4.21 and Figure 4.22.

Figure 4.21 - Average hourly consumption derived water level variation in the upper reservoir (m)

Figure 4.22 - Average hourly inlet derived water level variation in the upper reservoir (m)

The algorithm runs in two loops, one which sets the initial water level in the upper reservoir in ten

different levels, starting from its minimum level and increasing in 0.1 m intervals. The thought behind

this is that in most days, water will be discharged by the end of the day from the upper reservoir to the

lower reservoir, in order to generate electricity and revenues, but it may not fully discharge. The results

for the ten scenarios are, therefore, considered to happen with equal probability.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

Average hourly consumption derived water level variation in the upper reservoir (m)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

Average hourly inlet derived water level variation in the upper reservoir (m)

77

The second loop happens within each of these ten scenarios, and runs the algorithm a hundred times,

minimizing the objective function, in order to get as close to the global minimum as possible, since the

nonlinear solver stops running when a local minimum is found.

The best results are stored in MATLAB’s memory and later output to an excel spread sheet. The output

contains the hourly water level variation and both reservoirs’ water levels for all of the 10 scenarios,

where it is treated separately for adjustable and synchronous speed technologies. A histogram is made

from the results, where an average of the 10 scenarios is multiplied by 183 days, corresponding to the

dry season, which tells us the number of hours the equipment has worked at a given flow on that period

of time.

The specific energy that is consumed or generated by moving a certain volume of water through the

system is calculated as shown in Equation (5).

𝐸𝑠 =𝐸𝑛𝑒𝑟𝑔𝑦

𝑉𝑜𝑙𝑢𝑚𝑒 =

𝑇𝑖𝑚𝑒×𝐻×𝑄×𝑔×𝜌

𝑇𝑖𝑚𝑒×𝑔 (5)

where

E: specific energy (J/m3)

Time: time (s)

Q: discharge (m3/s)

gu: gravitational acceleration (m/s2)

ρ: fluid density (kg/m3)

For pumping and turbining operation, and considering water with a density of 1000 kg/m3, Equation (5)

translates as Equation (6) and (7) respectively

𝐸𝑠 =𝐻 × 𝑔

3600 × 𝜂𝑝 (6)

𝐸𝑠 =𝐻 × 𝑔 × 𝜂𝑡

3600 (7)

where

E: specific energy (kWh/m3);

ηp: pump efficiency;

ηt: turbine efficiency.

78

The pump efficiency curve was obtained from a test done to one of the pumps installed in the Socorridos

system, and it is shown in Figure 4.24. For the calculations regarding adjustable speed technology, the

efficiency of the motor and variable frequency drive (VFD) have to be taken in consideration. Pulse width

modulation (PWM) is a commonly used way to control the speed of the motor. A PWM frequency

converter works by alternating the voltage between discrete amplitudes, normally full positive and

negative voltage and zero voltage. Voltage values are commonly either proportional to the frequency or

proportional to the square of the frequency. When the VFD has an output voltage proportional to the

frequency, the motor torque remains constant while the frequency decreases. Therefore, it is desirable

to use VFD that has an output voltage proportional to the square of the frequency, since motor torque

is then proportional to the square of the frequency. Figure 4.25 shows the operating efficiency of VFD.

To obtain the efficiency of the pump with adjustable speed motor, one has to multiply the efficiencies of

both of these.

Figure 4.23 – Pump efficiency vs Flow

Figure 4.24 – Operating efficiency of VFD (FLYGT, 2011)

79

Since there are three pumps in the system, the efficiency will rise and fall as the flow varies an additional

pump is turned on or off. The overall efficiency for the adjustable speed pump station is shown in Figure

4.26. The efficiency for the synchronous pump station is considered constant and equal to 0.84 at

nominal flow.

Figure 4.25 – Adjustable speed pump station efficiency

With a Pelton turbine there aren’t much improvements in efficiency by using adjustable speed

technology, since its efficiency is almost constant even for low discharges, as shown in Figure 4.27. As

so, the efficiency is considered equal in both technologies in turbine operation.

Figure 4.26 – Efficiency correlation with discharge for different turbine types, assuming a fixed net head and rotation speed (Quintela, 2002)

0.70

0.75

0.80

0.85

0.90

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Effi

cien

cy (

%)

Flow (m3/s)

Adjustable speed pump station efficiency

80

Hence, the specific energy for every flow possible is calculated. It is worth mentioning that the specific

energy in a synchronous system is constant since its efficiency is always maximum.

To calculate the energy consumed and generated by the pump and turbine station respectively, one has

to use Equation (8).

∑ 𝐸𝑠,𝑖 × 𝑇𝑖 × 𝑄𝑖

𝑖

(8)

where

Es,i: specific energy corresponding to the flow Qi (kWh/m3);

Ti: number of hours for which the flow Qi occurred;

Qi: flow (m3/s).

For calculating the energy that is consumed with a synchronous pump station, it is necessary to

determine the time for which the pump operates throughout an hour, at a fixed flow value, to produce

the equivalent water level variation. For example, if the results schedule shows that there was a water

level variation of half the nominal flow of the synchronous pump at a given time step of one hour, it

means that the pump only worked for half an hour during that time step.

In the adjustable speed pump station, the time is considered to be always one hour, meaning the pump

operates continuously during that time step. The only exception to this is for values below 0.33 m3/s,

since below that threshold the efficiency drops considerably. For those values, it is considered that the

adjustable speed pump station operates similarly to the synchronous equipment.

4.3.1.1 Absorbed wind energy by technology

The amount of wind energy absorbed is determined by subtracting the energy the pump has used from

wind energy from the total wind energy available. For this, a second MATLAB model is used, which

gathers data from the previously generated optimized schedule and calculates the time for which the

pump station worked for synchronous and adjustable technologies.

The synchronous pump station will only operate for a fraction of the time step, which means some of

the wind energy will be lost.

To determine the time the pump operates for synchronous technology, the script follows the procedure:

If 𝑓𝑙𝑜𝑤 ≤ 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑓𝑙𝑜𝑤 𝑜𝑓 𝑜𝑛𝑒 𝑝𝑢𝑚𝑝

81

o Then 𝑡𝑖𝑚𝑒 = 𝑓𝑙𝑜𝑤 × 3600 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑓𝑙𝑜𝑤 𝑜𝑓 𝑜𝑛𝑒 𝑝𝑢𝑚𝑝⁄

o Else

If 𝑓𝑙𝑜𝑤 ≤ 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑓𝑙𝑜𝑤 𝑜𝑓 𝑡𝑤𝑜 𝑝𝑢𝑚𝑝s

Then 𝑡𝑖𝑚𝑒 = 𝑓𝑙𝑜𝑤 × 3600 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑓𝑙𝑜𝑤 𝑜𝑓 𝑡𝑤𝑜 𝑝𝑢𝑚𝑝⁄ s

Else

o 𝑡𝑖𝑚𝑒 = 𝑓𝑙𝑜𝑤 × 3600 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑓𝑙𝑜𝑤 𝑜𝑓 𝑡ℎ𝑟𝑒𝑒 𝑝𝑢𝑚𝑝𝑠⁄

For adjustable technology, the script follows the procedure:

If 𝑓𝑙𝑜𝑤 ≤ 0,33 𝑚3/𝑠

o Then 𝑡𝑖𝑚𝑒 = 𝑓𝑙𝑜𝑤 × 3600 0,33 𝑚3/𝑠⁄

o Else

𝑡𝑖𝑚𝑒 = 3600

The wasted wind is calculated with the Equation (9):

𝑊𝑊𝐸 = 𝑊𝐸𝑃 − 𝑓𝑙𝑜𝑤 ∗𝑡𝑖𝑚𝑒

3600+ 𝑇𝑊𝐸 × (1 − 𝑡𝑖𝑚𝑒) (9)

where

WWE: Wasted wind energy

WEP: Wind energy available during pumping hours

TWE: Total available wind energy

At this point, results are again exported to an excel data spread sheet where they are converted from

water level variation to kWh and averaged.

4.3.1.2 Energy surplus from the grid

For synchronous pump operation, the electrical grid will have to provide a surplus of energy to power

the pump station when the wind energy is not enough to power it by itself, since it will only operate at

nominal power. This surplus is determined with the following procedure:

If 𝑓𝑙𝑜𝑤 ≤ 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑓𝑙𝑜𝑤 𝑜𝑓 𝑜𝑛𝑒 𝑝𝑢𝑚𝑝

o Then 𝑠𝑢𝑟𝑝𝑙𝑢𝑠 = 𝑡𝑖𝑚𝑒 3600 × (𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑓𝑙𝑜𝑤 𝑜𝑓 𝑜𝑛𝑒 𝑝𝑢𝑚𝑝 − 𝑓𝑙𝑜𝑤)⁄

o Else

If 𝑓𝑙𝑜𝑤 ≤ 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑓𝑙𝑜𝑤 𝑜𝑓 𝑡𝑤𝑜 𝑝𝑢𝑚𝑝s

82

Then 𝑠𝑢𝑟𝑝𝑙𝑢𝑠 = 𝑡𝑖𝑚𝑒 3600 × (𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑓𝑙𝑜𝑤 𝑜𝑓 𝑡𝑤𝑜 𝑝𝑢𝑚𝑝 − 𝑓𝑙𝑜𝑤)⁄

Else 𝑠𝑢𝑟𝑝𝑙𝑢𝑠 = 𝑡𝑖𝑚𝑒 3600 × (𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑓𝑙𝑜𝑤 𝑜𝑓 𝑡ℎ𝑟𝑒𝑒 𝑝𝑢𝑚𝑝𝑠 − 𝑓𝑙𝑜𝑤)⁄

The results are exported to an excel spread sheet where they are converted from water level variation

to kWh and averaged.

4.3.2 Pumped hydro storage with double penstock

For modelling a double penstock system, a similar procedure is done, but with all the variables converted

into a 48 sequence time steps in the MATLAB script, in which the odd number sequence steps

correspond to the pump operation and the even number sequence steps correspond to the turbine

operation. This way it is possible to attribute the same restrictions applied to the single penstock model,

except for restriction number 7, which no longer makes sense, and restrictions 5 and 6, which need

minor adjustments. Instead, a new restriction is used to ensure that pumping and turbining occur in the

appropriate sequence steps, as follows:

5. Guarantee spinning reserves at 10 am:







)]

20

𝑡=1


6. Guarantee spinning reserves at 8 pm:







)]

40

𝑡=1


7. Guarantee separate penstocks for pump and turbine

83

Pumping occurs on odd number sequence steps (i) and turbining occurs on even number

sequence steps (j).

𝑑𝑁𝑖 ≥ 0; and

𝑑𝑁𝑗 ≤ 0.

The consumption and inlet derived water level variations is simply divided into equal parts for each

sequence step, while the electrical tariff remains the same for both pump and turbine related time steps.

The available wind energy derived water level variations on the upper reservoir is converted so that it is

zero on even number time steps.

The objective Function 4.2 and the rest of the calculations are also adjusted to 48 sequence steps.

∑ [|(𝑑𝑁ℎ,𝑊 𝑑𝑁ℎ⁄ ) − 1| ×𝐶𝑃,ℎ

𝜂𝑃(

𝑑𝑁ℎ + |𝑑𝑁ℎ|

2) + 𝐶𝑇,ℎ 𝜂𝑇 (

𝑑𝑁ℎ − |𝑑𝑁ℎ|

2) ]

48

ℎ=1

(4.2)

The following tables contain the input that is fed to the MATLAB scripts, namely Table 4.6, Table 4.7,

Table 4.8 and Table 4.9.

Table 4.6 –Reservoir properties

Upper Reservoir

Volume (m3) 40 000

Dimensions (m) 100*100*4

Volume/m 10 000

Maximum level (m) 4

Minimum level (m) 0.5

Initial level 0.5

Lower Reservoir

Volume (m3) 40 000

Dimensions (m) 100*100*4

Volume/m 10 000

Maximum level (m) 4

Minimum level (m) 0.1

Initial level 3.5

Table 4.7 – Pump and Turbine equipment properties

Pumps

Power (kW) 11 250

Flow (m3/s) 2

NQP (m/h) 0.72

Efficiency (%) 0.84

Turbines

Power (kW) 24 000

Flow (m3/s) 6

NQT (m/h) -2.16

Efficiency (%) 0.91

Table 4.8 – Wind turbine properties

Wind Turbines

Model Vestas V90

Units 6

Power (kW) 3 000

84

Table 4.9 – Hourly input data for the optimization algorithm

Time Electricity

tariff (€/kWh)

Water inlet in upper reservoir

(m)

Water consumption

in upper reservoir (m)

Water inlet in lower reservoir

(m)

Water consumption

in lower reservoir (m)

Wind speed (m/s)

Generated Power by wind turbine

(kW) %

Curtailed (kW)

Generated Wind Power (kW)

dNh,w (m)

00:00 0.0724 0.16 0.16 0 0 7.82 1090 1 1090 6450 0.447

01:00 0.0724 0.16 0.17 0 0 7.47 1000 1 1000 6000 0.410

02:00 0.0674 0.16 0.17 0 0 7.76 1080 1 1080 6480 0.443

03:00 0.0674 0.16 0.17 0 0 7.78 1080 1 1080 6480 0.443

04:00 0.0674 0.16 0.17 0 0 7.63 1060 1 1060 6360 0.435

05:00 0.0674 0.16 0.17 0 0 7.59 1050 1 1050 6300 0.430

06:00 0.0724 0.16 0.16 0 0 7.43 1000 1 1000 6000 0.410

07:00 0.0724 0.16 0.16 0 0 7.09 800 0.8 640 3840 0.262

08:00 0.0724 0.16 0.17 0 0 6.73 700 0.6 420 2520 0.172

09:00 0.1027 0.16 0.17 0 0 6.29 550 0.1 55 330 0.023

10:00 0.1195 0.16 0.17 0 0 5.67 380 0.005 1.9 11.4 0.001

11:00 0.1195 0.16 0.15 0 0 5.56 320 0.005 1.6 9.6 0.001

12:00 0.1195 0.16 0.14 0 0 5.39 300 0.005 1.5 9 0.001

13:00 0.1027 0.16 0.17 0 0 5.38 300 0.005 1.5 9 0.001

14:00 0.1027 0.16 0.18 0 0 5.58 320 0.005 1.6 9.6 0.001

15:00 0.1027 0.16 0.18 0 0 5.59 320 0.4 128 768 0.052

16:00 0.1027 0.16 0.18 0 0 5.87 420 0.8 336 2016 0.138

17:00 0.1027 0.16 0.17 0 0 6.43 650 0.6 390 2340 0.160

18:00 0.1027 0.16 0.16 0 0 6.94 750 0.6 450 2700 0.184

19:00 0.1027 0.16 0.16 0 0 7.58 1050 0.4 420 2520 0.172

20:00 0.1195 0.16 0.16 0 0 8.43 1400 0.005 7 42 0.003

21:00 0.1195 0.16 0.12 0 0 8.62 1500 0.005 7.5 45 0.003

22:00 0.1027 0.16 0.13 0 0 8.50 1450 0.2 290 1740 0.119

23:00 0.0724 0.16 0.15 0 0 8.04 1200 0.4 480 2880 0.197

85

5. Analysis and Comments

The output of the 10 initial level for the reservoirs scenarios modelling for single penstock is presented

in Figure 5.1 in an histogram, consisting of the number of hours that the equipment operated with a

given flown over the time period of dry season, where 183 days are considered. The histogram suggests

that only 2 pumps with 0.65 m3/s of nominal flow are effectively necessary, since the maximum

registered flow is of 1.28 m3/s. On the other hand, the number of turbines is seemingly adequate.

Figure 5.1 - Flow histogram over summer season for single penstock

A more detailed view of one of the simulated scenarios for single penstock and adjustable speed is

shown in Figure 5.2, while Figure 5-3 shows the same simulation but with the use of synchronous speed

equipment. By comparing the two figures, it is possible to observe that to deliver the same hourly water

level variations, synchronous speed equipment must often operate with a higher flow over less time.

The consequence of this is that there are gaps in which wind energy is wasted. Also, a surplus of energy

over the available wind energy, must be provided by the electrical grid in order for the pump station to

operate, as is indicated in Figure 5.3.

Figure 5.2 - Results for one scenario simulation of adjustable speed with a single penststock

0

50

100

150

200

250

300

350

400

450

-6.00 -5.50 -5.00 -4.50 -4.00 -3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00

Nu

mb

er o

f h

ou

rs

Flow (m3/s)

Flow histogram over summer season for single penstock

-6

-5

-4

-3

-2

-1

0

1

2

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

Flow (m3/s) Adjustable speed - single penstock

86

Figure 5.3 - Results for one scenario simulation of synchronous speed with a single penstock

The water level in the upper and lower reservoirs for the same scenario and single penstock is presented

in Figure 5.4 and Figure 5.5. It is possible to identify from these illustrations the hours for which the

pump and turbine stations operate, which are seemingly coherent with the previous graphics, and also

with the modelling constraints.

Figure 5.4 - Results for water level of the upper reservoir for one scenario simulation of single penstock

Figure 5.5 - Results for hourly water level of the lower reservoir for one scenario simulation of single penstock

-6

-5

-4

-3

-2

-1

0

1

2

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

Flow (m3/s) Synchronous speed - single penstock

0.00

1.00

2.00

3.00

4.00

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

(m) Upper Reservoir Water Level - single penstock

0.00

1.00

2.00

3.00

4.00

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

(m) Lower Reservoir Water Level - single penstock

Energy surplus from grid

Wasted wind energy Wasted wind energy

Energy surplus from grid

87

The histogram for double penstock is presented in Figure 5.6, while an overview for one scenario of

adjustable and synchronous speed equipment is shown in Figure 5.7 and Figure 5.8, respectively. The

same behavior as single penstock is largely observed in pumping operation, shown in blue, indicating

that 2 pumps of 0.65 m3/s of nominal flow would be sufficient.

Because more water is pumped to the upper reservoir, due to the permanent availability of pumping

operation, there is enough for the turbine station to operate at maximum capacity while maintaining the

modelling constraints.

It is also possible to observe that, similarly to the case of single penstock, adjustable speed technology

allows for more wind power to be absorbed, while only using wind energy to feed the pumps.

Figure 5.6 - Flow histogram over summer season for double penstock

Figure 5.7 - Results for one scenario simulation of adjustable speed with double penststock

0

50

100

150

200

250

300

350

400

-6.00 -5.50 -5.00 -4.50 -4.00 -3.50 -3.00 -2.50 -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00

Nu

mb

er o

f h

ou

rs

Flow (m3/s)

Flow histogram over summer season for double penstock

-6

-5

-4

-3

-2

-1

0

1

2

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

Flow (m3/s) Adjustable speed - double penstock

Pump operation

Turbine operation

88

Figure 5.8 - Results for one scenario simulation of synchronous speed with double penstock

Figure 5.9 and Figure 5.10 show the upper and lower reservoir water levels throughout the simulation

of the same scenario, where it is possible to observe that the modelling constraints are respected.

Figure 5.9 - Results for hourly water level of the upper reservoir for one scenario simulation of double speed

Figure 5.10 - Results for hourly water level of the lower reservoir for one scenario simulation of double speed

-6

-5

-4

-3

-2

-1

0

1

2

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

Flow (m3/s) Synchronous speed - double penstock

0.00

1.00

2.00

3.00

4.00

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

(m) Upper Reservoir Water Level - double penstock

0.00

1.00

2.00

3.00

4.00

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

(m) Lower Reservoir Water Level - double penstock

Energy surplus from grid Energy surplus from grid

Wasted wind energy Wasted wind energy

89

Taking into account the efficiency for adjustable and synchronous speed pump equipment, it is no

surprise to observe in Table 5.1 that adjustable speed pumping spends more energy than synchronous

speed. However, jumping to the conclusion that adjustable speed is therefore less profitable is a

mistake, for there are other expenditures to be accounted for.

Table 5.1 - Results for Energy balance by technology

Energy balance by Technology

Pump Turbine

Single Penstock Double Penstock Single Penstock Double Penstock

Adjustable Synchronous Adjustable Synchronous - -

Summer season (GWh) -11308 -10697 -13351 -12595 8507 9917

Electricity Tariff (€) 0.0724 0.0724 0.0724 0.0724 0.1027 0.1027

Costs/revenues (€) -818725 -774493 -966631 -911849 873709 1018461

Table 5.2 shows the results for the surplus of energy that synchronous speed equipment require, while

Table 5.3 shows the percentage of wind energy that each technology can absorb. This surplus is directly

taken from the electrical grid and, as so, comes at a cost.

It is remarkable that adjustable speed is able to absorb more wind energy with a single penstock than

synchronous speed is with a double penstock, as Table 5.3 shows. As so, even though it consumes

more energy overall, adjustable speed avoids the waste of fossil fuel generation by absorbing more wind

power.

The combination of a double penstock with adjustable speed equipment absorbs as much as 97% of

the available wind energy, which is a clear indication of its adequacy to off grid systems, such as existent

in isolated regions.

Table 5.2 - Results for Energy surplus by technology

Energy Surplus by Technology

Single Penstock Double Penstock

Adjustable Synchronous Adjustable Synchronous

Daily (kWh) - 10 584 - 12 421

Summer season (kWh) 1 936 809 2 273 024

Costs (€) 70 112 82 283

Table 5.3 - Results for Absorbed wind energy by technology

Absorbed Wind Energy by Technology Total Available Wind Energy Single Penstock Double Penstock

Adjustable Synchronous Adjustable Synchronous -

Daily (kWh) 55 129 45 265 64 012 53 478 65 950

Summer season (kWh) 10 088 642 8 283 505 11 714 192 9 786 434 12 068 777

Total percentage 0.84 0.69 0.97 0.81 -

90

The total balance of costs and revenues by technology is shown in Table 5.4. With this table, it is clearer

that adjustable speed can offer a globally more profitable solution. Not only does it generate more

revenues, it absorbs more wind energy, a step closer to an ideal situation in the electricity generation.

Another conclusion to be made is that a double penstock can be less profitable than a single one, which

suggests that it is only suitable for isolated regions or off the grid connections.

There are another expenditures that are not accounted for in this study which could further justify the

use of adjustable speed technology, which are spinning reserves capacity from fossil fuel avoidance,

and consequently GHG emissions avoidance, and the ability to provide frequency and load balance

control to the grid while in pump mode.

Table 5.4 -Results for Costs/Revenues balance by technology

Costs/Revenues Balance by Technology

Single Penstock Double Penstock

Adjustable Synchronous Adjustable Synchronous

operation (€) 54 984 99 217 51 830 106 612

surplus (€) - -70 112 - -82 283

total (€) 54 984 29 104 51 830 24 328

91

6. Final Conclusions and Recommendations

6.1 Final Conclusions

Due to the unequivocal evidence of global warming as a consequence of the burning of fossil fuels, it is

critical to switch to energy sources that are GHG emissions free, namely RES. The intermittency of RES

generation results in an added variability that is introduced in the electrical grids, which presents security

problems to supply. If that variability is accounted for with more spinning reserves, the initial purpose of

adding clean renewable energy to mitigate GHG emissions is defeated, since more fossil fuels are

burned to waste.

The interconnection of renewable source units over a vast geographical area comes as a solution, as

the climate conditions are less likely to affect a greater area all at once. However, it is not enough to

raise renewable energy penetration to a desirable proportion.

Pumped hydro storage is the element that will allow for renewable energy to safely increase its

penetration in electrical grids, without compromising security or requiring the use of added spinning

reserves, while making them a more competitive energy source. The storage of energy allows PHS to

regulate load diagrams, absorbing the variability that is introduced by RES, and distributing it through

time. It can be implemented in a variety of situations and configurations: with a traditional configuration

of two reservoirs on a closed or open loop, using a large water body or stream as the lower or upper

reservoir, with one of the reservoirs buried underground or even using saltwater, which presents an

opportunity for coastal regions, with the ocean working as one of the reservoirs.

Some improvements can be implemented to PHS systems, namely the use of adjustable speed

equipment, or the use of a separate penstock for the pumping and turbining operations. These

alterations can increase the overall system ability to provide ancillary services and absorb RES energy

that would otherwise go to waste, which results in a cut in costs and in a potential reduction in GHG

emissions.

The case study presented confirmed the claims of the initial study. With the introduction of the Multiple

Purpose Socorridos System, safe renewable penetration was increased by 17 MW, corresponding to a

GHG emissions reduction of 27 600 tonnes of CO2 (carbon dioxide), 116 tonnes of SO2 (sulfur dioxide),

478 tonnes of NOx (nitric oxide) and 7 tonnes of particles. In conjunction with the Calheta Hydroelectric

Reversible System - Calheta III, renewable production is expected to reach 30% of the electricity

production share, which results in the reduction of spinning reserve, avoiding 81 400 tonnes of fuel oil

importing, corresponding to a 3.8 M€ savings per year, and to an avoided emission of 253 000 tonnes

of CO2.

The optimization algorithm further enlightens the potential for improvement by using adjustable speed

equipment, with the results showing that it absorbs 15% more wind energy with a single penstock, and

16% more with a double penstock. By avoiding the use of a surplus of energy provided by the electrical

grid, it can be over twice as profitable with a double penstock, and just under two times as profitable

with a single penstock. Furthermore, results show that the use of adjustable speed combined with a

92

double penstock is the ideal setting for an off the grid system, since it absorbs 97% of the available wind

energy.

6.2 Recommendations

The main focus of the case study on this work is on the role of PHS in renewable energy grid penetration

and ways to improve it, by improving its efficiency with the use of adjustable speed technology and/or

the use of a double penstock.

The study of other aspects that benefit with such alterations would be pertinent and complementar to

this dissertation, such as the assessment of avoided spinning reserves/GHG emissions and its

associated costs, and the improvement in the ability to provide ancilliary services such as frequency

regulation or avoided additional transmission and distribution investment. It would also further enlighten

the impact of PHS in RES’ competitiveness versus fossil fuels, and on energy secutiry and

independance.

Due to the isolated nature and limited resources of Madeira Island, it would be very interesting to study

the possibility, as well as the economic aspects and environmental impacts of building a seawater PSPP

on the island, which wouldn’t depend on pluviosity and thus be available to work all year round, and

require the construction of only one reservoir.

However important PHS may be for the future of the planet, nothing motivates decision makers more

than the economic aspects. The responsibility is on the scientific world’s side to make PHS and RES

more competitive and appealing.

93

94

95

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101

APPENDIXES

102

A. Script code for Single Penstock Non-Linear Solver

%% _____________________________________________________________________|>| % Single Penstock Non Linear Programming Solver % ______________________________________________________________________

% Load values from excel file. % NOTE: make sure all numbers in the excel file are in number format filename = 'single_penstock.xls'; sheet = 'Input'; [status,sheets,xlFormat] = xlsfinfo(filename); % tt = xlsread(filename,sheet,'B3'); costs = xlsread(filename,sheet,'C3:C26'); % electricity tariff eta_P = xlsread(filename,sheet,'C54'); % Pumping station efficiency eta_T = xlsread(filename,sheet,'H54'); % Generation station efficiency NQP = xlsread(filename,sheet,'C53'); % Maximum water level rise in upper

reservoir NQT = xlsread(filename,sheet,'H53'); % Maximum water level decrease in

upper reservoir NMINU = xlsread(filename,sheet,'C42'); % Minimum water level in the upper

reservoir NMAXU = xlsread(filename,sheet,'C41'); % Maximum water level in the upper

reservoir NMINL = xlsread(filename,sheet,'H42'); % Minimum water level in the lower

reservoir NMAXL = xlsread(filename,sheet,'H41'); % Maximum water level in the lower

reservoir NCU = xlsread(filename,sheet,'E3:E26'); % Hourly water consumption in the

upper reservoir NIU = xlsread(filename,sheet,'D3:D26'); % Hourly water inlet in the upper

reservoir NCL = xlsread(filename,sheet,'G3:G26'); % Hourly water consumption in the

lower reservoir NIL = xlsread(filename,sheet,'F3:F26'); % Hourly water inlet in the lower

reservoir Vu = xlsread(filename,sheet,'C40'); % Volume per meter in height in the

reservoirs Hu = xlsread(filename,sheet,'L36'); % Head dNh_w = xlsread(filename,sheet,'Q3:Q26'); % Available hourly water level

variation in the upper reservoir as a result of wind energy powered pumping

% Number of scenarios with different initial levels for the upper % reservoir num_scenarios = (((NMAXU-NMINU-NMINL)/0.1)+1);

% Initial level for the upper reservoir for the different scenarios for n=1:num_scenarios N_INIT_U = NMINU+n*0.1-0.1; N_INIT_L = NMAXL - N_INIT_U;

% Variables. num_variables = 24;

%Wind Curtailment for i=1:num_variables

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if dNh_w(i)>NQP dNh_w(i)=NQP; end end

% Inequality constraints. % Guarantee suply in the upper reservoir by maintaining its minimum

required % level for i = 1:num_variables A1(i,:) = [-1*ones(1,i) zeros(1,num_variables-i)]; B1(i) = N_INIT_U-NMINU-sum(NCU(1:i))+sum(NIU(1:i)); end

% Guarantee that the upper reservoir doesn't spill over for i = 1:num_variables A2(i,:) = [1*ones(1,i) zeros(1,num_variables-i)]; B2(i) = NMAXU-N_INIT_U+sum(NCU(1:i))-sum(NIU(1:i)); end

% Guarantee supply in the lower reservoir by maintaining its minimum % required level

for i = 1:num_variables A3(i,:)=[1*ones(1,i) zeros(1,num_variables-i)]; B3(i) = N_INIT_L-NMINL-sum(NCL(1:i))+sum(NIL(1:i)); end

% Guarantee that the lower reservoir doesn't spill over for i = 1:num_variables A4(i,:) = [-1*ones(1,i) zeros(1,num_variables-i)]; B4(i) = NMAXL-N_INIT_L+sum(NCL(1:i))-sum(NIL(1:i)); end

% Guarantee spinning reserve at 10 am A5 = [-1*ones(1,10) zeros(1,14)]; B5 = -1*(NMAXU-NMINU-N_INIT_U)+sum(NIU(1:11))-sum(NCU(1:11));

% Guarantee spinning reserve at 8 pm A6 = [-1*ones(1,20) zeros(1,4)]; B6 = -1*(NMAXU-NMINU-N_INIT_U)+sum(NIU(1:21))-sum(NCU(1:21));

% Turbine in the peak load hours v = [zeros(1,2) -1*ones(1,4) zeros(1,4) ones(1,3) zeros(1,7) ones(1,2)

zeros(1,2)]; A7 = diag(v); B7 = [zeros(1,24)];

A = [A1;A2;A3;A4;A5;A6;A7]; b = [B1.';B2.';B3.';B4.';B5.';B6.';B7.'].';

% Equality constraints.

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Aeq = []; beq = [];

% Bound constraints: lower and upper bounds of the variables. lb = [ones(1,num_variables)*NQT]; ub = [dNh_w'];

ResultsdN=zeros(24,100); ResultsFinal=zeros(1,100); ResultsNU=zeros(24,100); ResultsNL=zeros(24,100);

for z=1:100

% Initial point (initial approximation). x0 = (NQT + (NQP-NQT).*rand(24,1))';

% Objective function: param = [costs; eta_P; eta_T; dNh_w]; func = @(x)cost_function_single_penstock(x,param);

%Optimization solver options. options =

optimset('Algorithm','sqp','LargeScale','off','MaxFunEvals',10000, ... 'Tolcon',1e-10,'TolX',1e-10,'Tolfun',1e-10);

% Optimization solver. [x,fval,exitflag,output,lambda,grad,hessian]=

fmincon(func,x0,A,b,Aeq,beq,lb,ub,[],options); dN = x';

%RESERVOIR'S LEVELS %Lower Reservoir NL(1) = N_INIT_L-dN(1)-NCL(1)+NIL(1); for i = 2:num_variables NL(i) = NL(i-1)-dN(i)-NCL(i)+NIL(i); end %Upper Reservoir NU(1) = N_INIT_U+dN(1)-NCU(1)+NIU(1); for i = 2:num_variables NU(i) = NU(i-1)+dN(i)-NCU(i)+NIU(i); end

%Wind contribution to generation for i=1:num_variables dNw(i) = ((abs(dN(i))+dN(i))/(2*dN(i)))*dNh_w(i); end

for i=1:num_variables if dN(i)>= dNw(i) dNt(i) = dN(i) - dNw(i); else if dN(i)<0 dNt(i)=dN(i); else dNt (i) = 0;

105

end end end

for i = 1:num_variables BAL (i,:) = (0.5*(dNt(i) + abs(dNt(i))))*costs(i)*(-9.8*Vu*Hu/3600)/eta_P -

... (0.5*(dNt(i) - abs(dNt(i))))*costs(i)*(9.8*Vu*Hu/3600)*eta_T; end

final = sum (BAL);

Results_sim_dN(:,z)=dN; Results_sim_Final(:,z)=final; Results_sim_NU(:,z)=NU'; Results_sim_NL(:,z)=NL';

end

[M,I]=max(Results_sim_Final); Results_scenario_dN(:,n) = Results_sim_dN(:,I); Results_scenario_NU(:,n) = Results_sim_NU(:,I); Results_scenario_NL(:,n) = Results_sim_NL(:,I); Results_scenario_Final(:,n) = Results_sim_Final(:,I); N_FINAL_U(n) = Results_scenario_NU(24,n);

N_INIT_U_vector(:,n) = N_INIT_U; N_INIT_L_vector(:,n) = N_INIT_L;

end

Results_scenario_dN; Results_scenario_NU; Results_scenario_NL; Results_scenario_Final;

filename = 'Results.xlsx'; sheetResults = 'Results_Single_Penstock';

xlswrite(filename,Results_scenario_dN,sheetResults,'B2:K25'); xlswrite(filename,N_INIT_U_vector,sheetResults,'B29:K29'); xlswrite(filename,Results_scenario_NU,sheetResults,'B30:K53'); xlswrite(filename,N_INIT_L_vector,sheetResults,'B56:K56'); xlswrite(filename,Results_scenario_NL,sheetResults,'B57:K80');

106

B. Script code for Double Penstock Non-Linear Solver

%% _____________________________________________________________________|>| % Double Penstock Non Linear Programming Solver % ______________________________________________________________________

% Load values from excel file. % NOTE: make sure all numbers in the excel file are in number format % tt = xlsread(filename,sheet,'B3'); filename = 'single_penstock.xls'; sheet = 1; [status,sheets,xlFormat] = xlsfinfo(filename); % tt = xlsread(filename,sheet,'B3'); costs = xlsread(filename,sheet,'C3:C26'); % electricity tariff NQP = xlsread(filename,sheet,'C53'); % Maximum water level rise in upper

reservoir NQT = xlsread(filename,sheet,'H53'); % Maximum water level decrease in

upper reservoir eta_P = xlsread(filename,sheet,'C54'); % Pumping station efficiency eta_T = xlsread(filename,sheet,'H54'); % Generation station efficiency N_INIT_U_START = xlsread(filename,sheet,'C43'); % Initial level for the

upper reservoir on the first day of the simulation NMINU = xlsread(filename,sheet,'C42'); % Minimum water level in the upper

reservoir NMAXU = xlsread(filename,sheet,'C41'); % Maximum water level in the upper

reservoir NMINL = xlsread(filename,sheet,'H42'); % Minimum water level in the lower

reservoir NMAXL = xlsread(filename,sheet,'H41'); % Maximum water level in the lower

reservoir NCU = xlsread(filename,sheet,'E3:E26'); % Hourly water consumption in the

upper reservoir NIU = xlsread(filename,sheet,'D3:D26'); % Hourly water inlet in the upper

reservoir NCL = xlsread(filename,sheet,'G3:G26'); % Hourly water consumption in the

lower reservoir NIL = xlsread(filename,sheet,'F3:F26'); % Hourly water inlet in the lower

reservoir Vu = xlsread(filename,sheet,'C40'); % Volume per meter in height in the

reservoirs Hu = xlsread(filename,sheet,'L36'); % Head dNh_w = xlsread(filename,sheet,'Q3:Q26'); % Hourly water level variation in

the upper reservoir as a result of wind energy powered pumping

% Variables. num_variables = 48;

% Wind Curtailment for i=1:24 if dNh_w(i)>NQP dNh_w(i)=NQP; end end

% Convert input to 48 'hour' intervals % NCU NCU48=zeros(1,48); i=1;

107

for k=1:24 j=i+1; NCU48(i)=NCU(k)/2; NCU48(j)=NCU(k)/2; i=j+1; end NCU=NCU48';

% NIU NIU48=zeros(1,48); i=1; for k=1:24 j=i+1; NIU48(i)=NIU(k)/2; NIU48(j)=NIU(k)/2; i=j+1; end NIU=NIU48';

% NCL NCL48=zeros(1,48); i=1; for k=1:24 j=i+1; NCL48(i)=NCL(k)/2; NCL48(j)=NCL(k)/2; i=j+1; end NCL=NCL48';

% NIL NIL48=zeros(1,48); i=1; for k=1:24 j=i+1; NIL48(i)=NIL(k)/2; NIL48(j)=NIL(k)/2; i=j+1; end NIL=NIL48';

% dNh_w dNh_w_48=zeros(1,48); i=1; for k=1:24 j=i+1; dNh_w_48(i)=dNh_w(k); dNh_w_48(j)=0; i=j+1; end dNh_w=dNh_w_48';

%costs costs48=zeros(1,48); i=1; for k=1:24

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j=i+1; costs48(i)=costs(k); costs48(j)=costs(k); i=j+1; end costs=costs48';

% Number of scenarios with different initial levels for the upper % reservoir num_scenarios = (((NMAXU-NMINU-NMINL)/0.1)+1);

% Initial level for the upper reservoir for the different scenarios for n=1:10 N_INIT_U = NMINU+n*0.1-0.1; N_INIT_L = NMAXL - N_INIT_U;

% Inequality constraints. % Guarantee suply in the upper reservoir maintaining it's minimum required % level for i = 1:num_variables A1(i,:) = [-1*ones(1,i) zeros(1,num_variables-i)]; B1(i) = N_INIT_U-NMINU-sum(NCU(1:i))+sum(NIU(1:i)); end

% Guarantee that the upper reservoir doesn't spill over for i = 1:num_variables A2(i,:) = [1*ones(1,i) zeros(1,num_variables-i)]; B2(i) = NMAXU-N_INIT_U+sum(NCU(1:i))-sum(NIU(1:i)); end

% Guarantee supply in the lower reservoir while maintaining it's minimum % required level

for i = 1:num_variables A3(i,:)=[1*ones(1,i) zeros(1,num_variables-i)]; B3(i) = N_INIT_L-NMINL-sum(NCL(1:i))+sum(NIL(1:i)); end

% Guarantee that the lower reservoir doesn't spill over for i = 1:num_variables A4(i,:) = [-1*ones(1,i) zeros(1,num_variables-i)]; B4(i) = NMAXL-N_INIT_L+sum(NCL(1:i))-sum(NIL(1:i)); end

% Guarantee spinning reserve at 10 am A5 = [-1*ones(1,20) zeros(1,28)]; B5 = -1*(NMAXU-NMINU-N_INIT_U)+sum(NIU(1:22))-sum(NCU(1:22));

% Guarantee spinning reserve at 8 pm A6 = [-1*ones(1,40) zeros(1,8)]; B6 = -1*(NMAXU-NMINU-N_INIT_U)+sum(NIU(1:42))-sum(NCU(1:42));

109

% Separate penstocks for pump and turbine v1 = [-1 1]; v = [repmat(v1,1,24)]; A7 = diag(v); B7 = [zeros(1,48)];

A = [A1;A2;A3;A4;A5;A6;A7]; b = [B1.';B2.';B3.';B4.';B5.';B6.';B7.'].';

% Equality constraints. Aeq = []; beq = [];

% Bound constraints: lower and upper bounds of the variables. lb = [ones(1,num_variables)*NQT]; ub = [dNh_w'];

ResultsdN=zeros(48,100); ResultsFinal=zeros(1,100); ResultsNU=zeros(48,100); ResultsNL=zeros(48,100);

for z=1:100

% Initial point (initial approximation). x0 = (NQT + (NQP-NQT).*rand(48,1))';

% Objective function: param = [dNh_w; costs; eta_P; eta_T]; func = @(x)cost_function_double_penstock(x,param);

% Optimization solver options. options =

optimset('Algorithm','sqp','LargeScale','off','MaxFunEvals',10000, ... 'Tolcon',1e-10,'TolX',1e-10,'Tolfun',1e-10);

% Optimization solver. [x,fval,exitflag,output,lambda,grad,hessian]=

fmincon(func,x0,A,b,Aeq,beq,lb,ub,[],options); dN = x';

% RESERVOIR'S LEVELS %%%%%%%%%%%%%%%%%%%%%%%%%% % Lower Reservoir NL_aux(1) = N_INIT_L-dN(1)-NCL48(1)+NIL48(1); for i = 2:num_variables NL_aux(i) = NL_aux(i-1)-dN(i)-NCL48(i)+NIL48(i); end

110

% Upper Reservoir NU_aux(1) = N_INIT_U+dN(1)-NCU48(1)+NIU48(1); for i = 2:num_variables NU_aux(i) = NU_aux(i-1)+dN(i)-NCU48(i)+NIU48(i); end

% Convert to 24 'one hour' intervals % NL i=1; for k=1:24 j=i+1; NL(k)=NL_aux(j); i=j+1; end

% NU i=1; for k=1:24 j=i+1; NU(k)=NU_aux(j); i=j+1; end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Wind contribution to generation for i=1:num_variables dNw(i) = ((abs(dN(i))+dN(i))/(2*dN(i)))*dNh_w(i); end

for i=1:num_variables if dN(i)>= dNw(i) dNt(i) = dN(i) - dNw(i); else if dN(i)<0 dNt(i)=dN(i); else dNt (i) = 0; end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

for i = 1:num_variables BAL (i,:) = (0.5*(dNt(i) + abs(dNt(i))))*costs(i)*(-9.8*Vu*Hu/3600)/eta_P -

... (0.5*(dNt(i) - abs(dNt(i))))*costs(i)*(9.8*Vu*Hu/3600)*eta_T; end

final = sum (BAL);

Results_sim_dN(:,z)=dN; Results_sim_Final(:,z)=final; Results_sim_NU(:,z)=NU'; Results_sim_NL(:,z)=NL';

end

111

[M,I]=max(Results_sim_Final); Results_scenario_dN(:,n) = Results_sim_dN(:,I); Results_scenario_NU(:,n) = Results_sim_NU(:,I); Results_scenario_NL(:,n) = Results_sim_NL(:,I);

N_INIT_U_vector(:,n) = N_INIT_U; N_INIT_L_vector(:,n) = N_INIT_L;

end

filename = 'Results.xlsx'; sheetResults = 'Results_Double_Penstock';

xlswrite(filename,Results_scenario_dN,sheetResults,'B2:K49'); xlswrite(filename,N_INIT_U_vector,sheetResults,'B53:K53'); xlswrite(filename,Results_scenario_NU,sheetResults,'B54:K77'); xlswrite(filename,N_INIT_L_vector,sheetResults,'B80:K80'); xlswrite(filename,Results_scenario_NL,sheetResults,'B81:K104');

112

C. Objective functions for Single and Double Penstock Non-Linear Solvers

function f = cost_function_single_penstock(x,param)

dN = x'; dNh_w = param(1:24); costs = param(25:48); eta_P = param(49); eta_T = param(50);

% _________________________________________________________________________ % Residual Function. F = (abs((dNh_w./dN)-1)).*(0.5*(dN + abs(dN))).*costs./eta_P + ... (0.5*(dN - abs(dN))).*costs.*eta_T;

% _________________________________________________________________________ % Objective Function. f = sum(F);

function f = cost_function_double_penstock(x,param) dN = x'; dNh_w = param(1:48); costs = param(49:96); eta_P = param(97); eta_T = param(98);

% _________________________________________________________________________ % Residual Function. F =(abs((dNh_w./dN)-1)).*(0.5*(dN + abs(dN))).*costs./eta_P + ... (0.5*(dN - abs(dN))).*costs.*eta_T; % _________________________________________________________________________ % Objective Function. f = sum(F);

113

D. Script code for calculating wasted wind energy and energy surplus from the grid

% ______________________________________________________________________|<|

% Load values from excel file. % NOTE: make sure all numbers in the excel file are in number format % tt = xlsread(filename,sheet,'B3'); filename = 'single_penstock.xls'; filename2 = 'Results.xlsx'; sheet = 'Input'; sheet2 = 'Results_Single_Penstock'; sheet3 = 'Results_Double_Penstock'; pump_single = xlsread(filename2,sheet2,'B2:K25'); pump_double = xlsread(filename2,sheet3,'B2:K49'); costs = xlsread(filename,sheet,'C3:C26'); % electricity tariff eta_P = xlsread(filename,sheet,'C54'); % Pumping station efficiency Vu = xlsread(filename,sheet,'C40'); % Volume per meter in height in the

reservoirs Hu = xlsread(filename,sheet,'L36'); % Head dNh_w = xlsread(filename,sheet,'Q3:Q26'); % Hourly water level variation in

the upper reservoir as a result of wind energy powered pumping in the

Summer

for i=1:24 for z=1:10 if pump_single(i,z)<0 pump_single(i,z)=0; end end end

for i=1:48 for z=1:10 if pump_double(i,z)<0 pump_double(i,z)=0; end end end

%_______Calculate wasted wind energy for adjustbale speed________%

% SINGLE PENSTOCK % Consider wind energy availabe during pumping hours exclusively

for i=1:24 for z=1:10 if pump_single(i,z)<=0 wind_single(i,z)=0; else wind_single(i,z)=dNh_w(i); end end

114

end

% Adjustable speed % Calculate time for which the pump is working in seconds in On/Off mode % (below 0.33 m3/s) for i=1:24 for z=1:10 if pump_single(i,z)<0.12 time_single_adj(i,z)=pump_single(i,z)*3600/0.12 ; else time_single_adj(i,z)=3600; end end end

% Synchronous speed % Calculate time for which the pump is working in seconds for i=1:24 for z=1:10 if pump_single(i,z)<0.24 time_single_synch(i,z)=pump_single(i,z)*3600/0.24; else if pump_single(i,z)<0.48 time_single_synch(i,z)=pump_single(i,z)*3600/0.48; else time_single_synch(i,z)=pump_single(i,z)*3600/0.72; end end end end

% Wasted wind energy % Adjustable Speed for i=1:24 for z=1:10 WW_single_adj(i,z) = (wind_single(i,z)-

pump_single(i,z))*time_single_adj(i,z)/3600+dNh_w(i)*(1-

time_single_adj(i,z)/3600); if WW_single_adj(i,z)<0 WW_single_adj(i,z)=0; end end end

% Synchronous Speed for i=1:24 for z=1:10 WW_single_synch(i,z) = (wind_single(i,z)-

pump_single(i,z))*time_single_synch(i,z)/3600+dNh_w(i)*(1-

time_single_synch(i,z)/3600); if WW_single_synch(i,z)<0 WW_single_synch(i,z)=0; end end end

115

% DOUBLE PENSTOCK

% Consider wind energy availabe during pumping hours exclusively % convert data to 48 intervals dNh_w_48=zeros(1,48); i=1; for k=1:24 j=i+1; dNh_w_48(i)=dNh_w(k); dNh_w_48(j)=0; i=j+1; end

for i=1:48 for z=1:10 if pump_double(i,z)<=0 wind_double(i,z)=0; else wind_double(i,z)=dNh_w_48(i); end end end

% Adjustable speed % Calculate time for which the pump is working in seconds in On/Off mode % (below 0.33 m3/s) for i=1:48 for z=1:10 if pump_double(i,z)<0.12 time_double_adj(i,z)=pump_double(i,z)*3600/0.24; else time_double_adj(i,z)=3600; end end end

% Synchronous speed % Calculate time for which the pump is working in seconds in On/Off mode

for i=1:48 for z=1:10 if pump_double(i,z)<0.24 time_double_synch(i,z)=pump_double(i,z)*3600/0.24; else if pump_double(i,z)<0.48 time_double_synch(i,z)=pump_double(i,z)*3600/0.48; else time_double_synch(i,z)=pump_double(i,z)*3600/0.72; end end end end

% Wasted wind energy % Adjustable Speed

116

for i=1:48 for z=1:10 WW_double_adj(i,z) = (wind_double(i,z)-

pump_double(i,z))*time_double_adj(i,z)/3600+dNh_w_48(i)*(1-

time_double_adj(i,z)/3600); if WW_double_adj(i,z)<0 WW_double_adj(i,z)=0; end end end

% Synch Speed for i=1:48 for z=1:10 WW_double_synch(i,z) = (wind_double(i,z)-

pump_double(i,z))*time_double_synch(i,z)/3600+dNh_w_48(i)*(1-

time_double_synch(i,z)/3600); if WW_double_synch(i,z)<0 WW_double_synch(i,z)=0; end end end

% Energy Surplus form grid % single penstock for i=1:24 for z=1:10 if pump_single(i,z)<0.24 surplus_single(i,z)=(time_single_synch(i,z)/3600)*(0.24-pump_single(i,z)); else if pump_single(i,z)<0.48 surplus_single(i,z)=(time_single_synch(i,z)/3600)*(0.48-

pump_single(i,z)); else surplus_single(i,z)=(time_single_synch(i,z)/3600)*(0.72-

pump_single(i,z)); end end end end

% double penstock for i=1:48 for z=1:10 if pump_double(i,z)<0.24 surplus_double(i,z)=(time_double_synch(i,z)/3600)*(0.24-pump_double(i,z)); else if pump_double(i,z)<0.48 surplus_double(i,z)=(time_double_synch(i,z)/3600)*(0.48-

pump_double(i,z)); else surplus_double(i,z)=(time_double_synch(i,z)/3600)*(0.72-

pump_double(i,z)); end end end end

117

filename = 'Results.xlsx'; sheetResults1 = 'WW_adj'; sheetResults2 = 'WW_synch'; sheetResults3 = 'surplus';

xlswrite(filename,WW_single_adj,sheetResults1,'B2:K25'); xlswrite(filename,WW_double_adj,sheetResults1,'B29:K76'); xlswrite(filename,WW_single_synch,sheetResults2,'B2:K25'); xlswrite(filename,WW_double_synch,sheetResults2,'B29:K76'); xlswrite(filename,surplus_single,sheetResults3,'B2:K25'); xlswrite(filename,surplus_double,sheetResults3,'B29:K76');

118

E. Results for Single Penstock ten scenarios simulations

Table A 1 – Hourly water level variations in upper reservoir for ten scenarios simulations for single penstock (m)

dN

00:00 0.02 0.45 0.45 -0.28 0.45 -0.48 0.45 0.45 -0.78 0.45

01:00 0.41 -0.12 0.41 0.41 0.41 0.41 -0.62 -0.72 0.41 -0.92

02:00 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44

03:00 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44

04:00 0.43 0.43 0.35 0.43 0.43 0.43 0.43 0.43 0.43 0.43

05:00 0.43 0.43 0.43 0.43 0.41 0.43 0.43 0.43 0.43 0.43

06:00 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41

07:00 0.26 0.26 0.26 0.26 -0.55 0.26 0.26 0.26 0.26 0.26

08:00 0.17 0.17 -0.38 0.17 0.17 0.17 0.17 0.17 0.17 0.17

09:00 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02

10:00 0.00 0.00 0.00 -0.58 0.00 -0.04 -0.08 0.00 -0.39 -0.34

11:00 -0.13 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

12:00 0.00 -0.01 -0.15 0.00 -0.61 0.00 0.00 -0.55 -0.03 -0.19

13:00 -0.55 -0.62 0.00 0.00 0.00 0.00 0.00 -0.10 -0.25 0.00

14:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

15:00 0.05 0.05 -0.48 0.05 0.05 0.05 -0.54 0.05 0.05 -0.09

16:00 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

17:00 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.14 0.16 0.16

18:00 0.18 0.18 0.18 0.08 0.18 -0.45 0.18 0.18 0.18 0.18

19:00 0.17 0.13 0.17 0.17 0.11 0.17 0.17 0.17 0.17 0.17

20:00 -1.25 -1.52 -1.14 -1.47 -0.83 -1.20 -1.41 -1.73 -0.89 -1.22

21:00 -1.79 -1.22 -1.85 -0.23 -1.04 -1.15 -1.39 -1.31 -1.78 -1.33

22:00 0.10 -0.33 0.12 -1.37 -1.20 -0.72 -0.27 0.03 -0.29 -0.30

23:00 0.17 0.17 -0.21 -0.01 -0.01 0.17 0.17 -0.07 -0.12 -0.24

Table A 2 – Hourly water level of the upper reservoir for ten scenarios simulations for single penstock (m)

NU

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

00:00 0.52 1.05 1.15 0.52 1.35 0.52 1.55 1.65 0.52 1.85

01:00 0.93 0.93 1.56 0.93 1.76 0.93 0.93 0.93 0.93 0.93

02:00 1.36 1.36 1.99 1.36 2.19 1.36 1.36 1.36 1.36 1.36

03:00 1.80 1.80 2.43 1.80 2.63 1.80 1.80 1.80 1.80 1.80

04:00 2.23 2.23 2.78 2.23 3.06 2.23 2.23 2.23 2.23 2.23

05:00 2.66 2.66 3.21 2.66 3.47 2.66 2.66 2.66 2.66 2.66

06:00 3.07 3.07 3.62 3.07 3.88 3.07 3.07 3.07 3.07 3.07

07:00 3.33 3.33 3.88 3.33 3.33 3.33 3.33 3.33 3.33 3.33

08:00 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50

09:00 3.51 3.51 3.51 3.51 3.51 3.51 3.51 3.51 3.51 3.51

10:00 3.50 3.50 3.50 2.92 3.50 3.46 3.42 3.50 3.11 3.16

11:00 3.39 3.52 3.52 2.94 3.52 3.48 3.43 3.52 3.12 3.18

119

12:00 3.41 3.53 3.39 2.96 2.92 3.50 3.45 2.99 3.11 3.00

13:00 2.85 2.90 3.38 2.95 2.91 3.49 3.44 2.87 2.85 2.99

14:00 2.83 2.87 3.36 2.93 2.89 3.47 3.42 2.85 2.83 2.97

15:00 2.86 2.91 2.86 2.96 2.92 3.50 2.86 2.88 2.86 2.86

16:00 2.98 3.03 2.98 3.08 3.04 3.62 2.98 3.01 2.98 2.98

17:00 3.14 3.18 3.14 3.24 3.20 3.77 3.14 3.14 3.14 3.14

18:00 3.32 3.36 3.32 3.32 3.38 3.32 3.32 3.32 3.32 3.32

19:00 3.49 3.49 3.49 3.49 3.49 3.49 3.49 3.49 3.49 3.49

20:00 2.25 1.98 2.36 2.03 2.67 2.30 2.09 1.77 2.61 2.28

21:00 0.50 0.80 0.55 1.84 1.67 1.19 0.74 0.50 0.87 0.99

22:00 0.63 0.50 0.70 0.50 0.50 0.50 0.50 0.56 0.61 0.73

23:00 0.81 0.68 0.50 0.50 0.50 0.68 0.68 0.50 0.50 0.50

Table A 3 - Hourly water level of the lower reservoir for ten scenarios simulations for single penstock (m)

NL

3.5 3.4 3.3 3.2 3.1 3 2.9 2.8 2.7 2.6

00:00 3.48 2.95 2.85 3.48 2.65 3.48 2.45 2.35 3.48 2.15

01:00 3.07 3.07 2.44 3.07 2.24 3.07 3.07 3.07 3.07 3.07

02:00 2.63 2.63 2.00 2.63 1.80 2.63 2.63 2.63 2.63 2.63

03:00 2.19 2.19 1.56 2.19 1.36 2.19 2.19 2.19 2.19 2.19

04:00 1.75 1.75 1.20 1.75 0.92 1.75 1.75 1.75 1.75 1.75

05:00 1.32 1.32 0.77 1.32 0.51 1.32 1.32 1.32 1.32 1.32

06:00 0.91 0.91 0.36 0.91 0.10 0.91 0.91 0.91 0.91 0.91

07:00 0.65 0.65 0.10 0.65 0.65 0.65 0.65 0.65 0.65 0.65

08:00 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48

09:00 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45

10:00 0.45 0.45 0.45 1.03 0.45 0.49 0.54 0.45 0.85 0.79

11:00 0.58 0.45 0.45 1.03 0.45 0.49 0.54 0.45 0.85 0.79

12:00 0.58 0.46 0.60 1.03 1.07 0.49 0.54 1.00 0.88 0.99

13:00 1.13 1.08 0.60 1.03 1.07 0.49 0.54 1.11 1.13 0.99

14:00 1.13 1.08 0.60 1.03 1.07 0.49 0.54 1.11 1.13 0.99

15:00 1.08 1.03 1.08 0.98 1.01 0.44 1.08 1.05 1.08 1.08

16:00 0.94 0.89 0.94 0.84 0.88 0.30 0.94 0.92 0.94 0.94

17:00 0.78 0.73 0.78 0.68 0.72 0.14 0.78 0.78 0.78 0.78

18:00 0.59 0.55 0.59 0.59 0.53 0.59 0.59 0.59 0.59 0.59

19:00 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42

20:00 1.67 1.94 1.56 1.89 1.25 1.62 1.83 2.15 1.31 1.64

21:00 3.46 3.16 3.41 2.12 2.29 2.77 3.22 3.46 3.09 2.97

22:00 3.36 3.49 3.29 3.49 3.49 3.49 3.49 3.43 3.38 3.26

23:00 3.19 3.32 3.50 3.50 3.50 3.32 3.32 3.50 3.50 3.50

120

F. Results for Double Penstock ten scenarios simulations

Table A 4 - Hourly water level variations in upper reservoir for ten scenarios simulations for double penstock (m)

dN

00:00 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45 0.45

00:00 -0.01 -0.03 -0.08 -0.09 -0.11 -0.13 -0.17 -0.38 -0.37 -0.26

01:00 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41

01:00 -0.03 -0.06 -0.09 -0.07 -0.11 -0.15 -0.16 -0.08 -0.18 -0.27

02:00 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44

02:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

03:00 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44 0.44

03:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

04:00 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43

04:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

05:00 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43 0.43

05:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

06:00 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41 0.41

06:00 0.00 -0.05 -0.08 -0.07 -0.11 -0.13 -0.17 -0.22 -0.17 -0.25

07:00 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26 0.26

07:00 -0.04 -0.02 -0.02 -0.13 -0.15 -0.16 -0.17 -0.08 -0.14 -0.19

08:00 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17

08:00 0.00 -0.02 0.00 -0.01 0.00 0.00 0.00 -0.02 0.00 0.00

09:00 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.00 0.02

09:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

10:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

10:00 -0.25 -0.27 -0.33 -0.35 -0.34 -0.35 -0.35 -0.57 -0.32 -0.27

11:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

11:00 -0.23 -0.28 -0.36 -0.34 -0.34 -0.33 -0.33 -0.23 -0.32 -0.24

12:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

12:00 -0.24 -0.28 -0.34 -0.34 -0.36 -0.35 -0.35 -0.23 -0.32 -0.44

13:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

13:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

14:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

14:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

15:00 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05

15:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

16:00 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14 0.14

16:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

17:00 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16

17:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

18:00 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18 0.18

18:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

19:00 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.17

19:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

20:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

121

20:00 -1.33 -1.57 -2.16 -1.12 -1.49 -1.77 -1.52 -1.76 -1.71 -2.12

21:00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

21:00 -2.03 -1.68 -0.88 -1.93 -1.55 -1.27 -1.52 -1.29 -1.40 -1.02

22:00 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12

22:00 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15 -0.15

23:00 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20

23:00 -0.21 -0.21 -0.21 -0.21 -0.21 -0.21 -0.21 -0.21 -0.21 -0.21

Table A 5 - Hourly water level of the upper reservoir for ten scenarios simulations for double penstock (m)

NU

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

00:00 0.94 1.02 1.06 1.16 1.24 1.32 1.38 1.27 1.38 1.59

01:00 1.32 1.37 1.38 1.50 1.54 1.57 1.62 1.60 1.61 1.73

02:00 1.76 1.81 1.82 1.93 1.98 2.01 2.06 2.04 2.05 2.17

03:00 2.20 2.25 2.25 2.37 2.41 2.45 2.50 2.48 2.49 2.60

04:00 2.63 2.68 2.68 2.80 2.84 2.88 2.93 2.91 2.92 3.03

05:00 3.05 3.11 3.11 3.23 3.27 3.31 3.36 3.34 3.35 3.46

06:00 3.46 3.46 3.44 3.57 3.57 3.59 3.59 3.53 3.58 3.61

07:00 3.68 3.70 3.69 3.70 3.68 3.68 3.69 3.70 3.71 3.68

08:00 3.85 3.85 3.85 3.85 3.85 3.85 3.85 3.85 3.88 3.85

09:00 3.86 3.86 3.86 3.86 3.86 3.86 3.87 3.86 3.87 3.86

10:00 3.61 3.58 3.52 3.50 3.52 3.50 3.50 3.29 3.53 3.59

11:00 3.40 3.32 3.18 3.18 3.20 3.19 3.19 3.07 3.23 3.37

12:00 3.18 3.06 2.86 2.86 2.86 2.86 2.86 2.86 2.93 2.95

13:00 3.17 3.06 2.85 2.85 2.85 2.85 2.85 2.85 2.92 2.94

14:00 3.15 3.04 2.83 2.83 2.83 2.83 2.83 2.83 2.90 2.92

15:00 3.18 3.07 2.86 2.86 2.86 2.86 2.86 2.86 2.93 2.95

16:00 3.30 3.19 2.98 2.98 2.98 2.98 2.98 2.98 3.05 3.07

17:00 3.46 3.34 3.14 3.14 3.14 3.14 3.14 3.14 3.20 3.23

18:00 3.64 3.53 3.32 3.32 3.32 3.32 3.32 3.32 3.39 3.41

19:00 3.81 3.70 3.49 3.49 3.49 3.49 3.49 3.49 3.56 3.58

20:00 2.49 2.14 1.34 2.38 2.01 1.73 1.98 1.74 1.86 1.47

21:00 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50

22:00 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50

23:00 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50

122

Table A 6 - Hourly water level of the lower reservoir for ten scenarios simulations for double penstock (m)

NL

3.5 3.4 3.3 3.2 3.1 3 2.9 2.8 2.7 2.6

00:00 3.06 2.98 2.94 2.84 2.77 2.68 2.62 2.73 2.62 2.41

01:00 2.68 2.62 2.62 2.50 2.46 2.42 2.37 2.39 2.38 2.27

02:00 2.23 2.18 2.18 2.06 2.02 1.98 1.93 1.95 1.94 1.83

03:00 1.79 1.74 1.73 1.62 1.58 1.54 1.49 1.51 1.50 1.38

04:00 1.36 1.30 1.30 1.18 1.14 1.10 1.05 1.07 1.06 0.95

05:00 0.93 0.87 0.87 0.75 0.71 0.67 0.62 0.64 0.63 0.52

06:00 0.52 0.51 0.53 0.41 0.41 0.39 0.39 0.45 0.39 0.36

07:00 0.29 0.27 0.29 0.28 0.29 0.29 0.29 0.27 0.27 0.29

08:00 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.10 0.12

09:00 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10

10:00 0.35 0.37 0.43 0.45 0.44 0.45 0.45 0.67 0.42 0.37

11:00 0.57 0.65 0.79 0.79 0.77 0.78 0.78 0.90 0.74 0.60

12:00 0.81 0.92 1.13 1.13 1.13 1.13 1.13 1.13 1.06 1.04

13:00 0.81 0.92 1.13 1.13 1.13 1.13 1.13 1.13 1.06 1.04

14:00 0.81 0.92 1.13 1.13 1.13 1.13 1.13 1.13 1.06 1.04

15:00 0.76 0.87 1.08 1.07 1.08 1.08 1.08 1.08 1.01 0.99

16:00 0.62 0.73 0.94 0.94 0.94 0.94 0.94 0.94 0.87 0.85

17:00 0.46 0.57 0.78 0.78 0.78 0.78 0.78 0.78 0.71 0.69

18:00 0.28 0.39 0.59 0.59 0.59 0.59 0.59 0.59 0.53 0.50

19:00 0.10 0.22 0.42 0.42 0.42 0.42 0.42 0.42 0.35 0.33

20:00 1.43 1.78 2.58 1.54 1.91 2.19 1.94 2.18 2.06 2.45

21:00 3.46 3.46 3.46 3.46 3.46 3.46 3.46 3.46 3.46 3.46

22:00 3.49 3.49 3.49 3.49 3.49 3.49 3.49 3.49 3.49 3.49

23:00 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50 3.50

123

G. Results for wasted wind energy for single and double penstock for ten scenarios

simulations

Table A 7 – Hourly wasted wind energy for adjustable speed and single penstock (kWh)

00:00 6579 0 0 6618 0 6618 0 0 6618 0

01:00 0 6071 0 0 0 0 6071 6071 0 6071

02:00 0 0 0 0 0 0 0 0 0 0

03:00 0 0 0 0 0 0 0 0 0 0

04:00 0 0 1179 0 0 0 0 0 0 0

05:00 0 0 0 0 255 0 0 0 0 0

06:00 0 0 0 0 0 0 0 0 0 0

07:00 0 0 0 0 3886 0 0 0 0 0

08:00 0 0 2550 0 0 0 0 0 0 0

09:00 271 271 271 271 271 271 271 271 271 271

10:00 12 12 12 12 12 12 12 12 12 12

11:00 10 10 10 10 10 10 10 10 10 10

12:00 9 9 9 9 9 9 9 9 9 9

13:00 9 9 9 9 9 9 9 9 9 9

14:00 10 10 10 10 10 10 10 10 10 10

15:00 437 437 777 437 437 437 777 437 437 777

16:00 0 0 0 0 0 0 0 0 0 0

17:00 0 0 0 0 0 0 0 344 0 0

18:00 0 0 0 1848 0 2732 0 0 0 0

19:00 0 660 0 0 1058 0 0 0 0 0

20:00 43 43 43 43 43 43 43 43 43 43

21:00 46 46 46 46 46 46 46 46 46 46

22:00 464 1761 16 1761 1761 1761 1761 1675 1761 1761

23:00 383 383 2914 2914 2914 383 383 2914 2914 2914

Table A 8 - Hourly wasted wind energy for synchronous speed and single penstock (kWh)

00:00 6599 457 457 6618 457 6618 457 457 6618 457

01:00 886 6071 886 886 886 886 6071 6071 886 6071

02:00 509 509 509 509 509 509 509 509 509 509

03:00 509 509 509 509 509 509 509 509 509 509

04:00 609 609 2548 609 609 609 609 609 609 609

05:00 658 658 658 658 1107 658 658 658 658 658

06:00 886 886 886 886 886 886 886 886 886 886

07:00 1762 1762 1762 1762 3886 1762 1762 1762 1762 1762

08:00 721 721 2550 721 721 721 721 721 721 721

09:00 303 303 303 303 303 303 303 303 303 303

10:00 12 12 12 12 12 12 12 12 12 12

11:00 10 10 10 10 10 10 10 10 10 10

12:00 9 9 9 9 9 9 9 9 9 9

13:00 9 9 9 9 9 9 9 9 9 9

124

14:00 10 10 10 10 10 10 10 10 10 10

15:00 607 607 777 607 607 607 777 607 607 777

16:00 869 869 869 869 869 869 869 869 869 869

17:00 790 790 790 790 790 790 790 1216 790 790

18:00 632 632 632 2290 632 2732 632 632 632 632

19:00 721 1545 721 721 1804 721 721 721 721 721

20:00 43 43 43 43 43 43 43 43 43 43

21:00 46 46 46 46 46 46 46 46 46 46

22:00 1112 1761 889 1761 1761 1761 1761 1718 1761 1761

23:00 1112 1112 2914 2914 2914 1112 1112 2914 2914 2914

Table A 9 - Hourly wasted wind energy for adjustable speed and double penstock (kWh)

00:00 0 0 0 0 0 0 0 0 0 0

01:00 0 0 0 0 0 0 0 0 0 0

02:00 0 0 0 0 0 0 0 0 0 0

03:00 0 0 0 0 0 0 0 0 0 0

04:00 0 0 0 0 0 0 0 0 0 0

05:00 0 0 0 0 0 0 0 0 0 0

06:00 0 0 0 0 0 0 0 0 0 0

07:00 0 0 0 0 0 0 0 0 0 0

08:00 0 0 0 0 0 0 0 0 0 0

09:00 303 303 303 303 303 303 303 303 334 303

10:00 11 11 11 11 11 11 12 11 12 11

11:00 10 10 10 10 10 10 10 10 10 10

12:00 9 9 9 9 9 9 9 9 9 9

13:00 9 9 9 9 9 9 9 9 9 9

14:00 10 10 10 10 10 10 10 10 10 10

15:00 607 607 607 607 607 607 607 607 607 607

17:00 0 0 0 0 0 0 0 0 0 0

18:00 0 0 0 0 0 0 0 0 0 0

19:00 0 0 0 0 0 0 0 0 0 0

20:00 42 42 42 42 42 42 42 42 42 42

21:00 45 45 45 45 46 45 45 45 46 45

22:00 889 889 889 889 889 889 889 889 889 889

23:00 0 0 0 0 0 0 0 0 0 0

Table A 10 - Hourly wasted wind energy for synchronous speed and double penstock (kWh)

00:00 457 457 457 457 457 457 457 457 457 457

01:00 886 886 886 886 886 886 886 886 886 886

02:00 509 509 509 509 509 509 509 509 509 509

03:00 509 509 509 509 509 509 509 509 509 509

125

04:00 609 609 609 609 609 609 609 609 609 609

05:00 658 658 658 658 658 658 658 658 658 658

06:00 886 886 886 886 886 886 886 886 886 886

07:00 1762 1762 1762 1762 1762 1762 1762 1762 1762 1762

08:00 721 721 721 721 721 721 721 721 721 721

09:00 303 303 303 303 303 303 303 303 334 303

10:00 11 11 11 11 11 11 12 11 12 11

11:00 10 10 10 10 10 10 10 10 10 10

12:00 9 9 9 9 9 9 9 9 9 9

13:00 9 9 9 9 9 9 9 9 9 9

14:00 10 10 10 10 10 10 10 10 10 10

15:00 607 607 607 607 607 607 607 607 607 607

16:00 869 869 869 869 869 869 869 869 869 869

17:00 790 790 790 790 790 790 790 790 790 790

18:00 632 632 632 632 632 632 632 632 632 632

19:00 721 721 721 721 721 721 721 721 721 721

20:00 42 42 42 42 42 42 42 42 42 42

21:00 45 45 45 45 46 45 45 45 46 45

22:00 889 889 889 889 889 889 889 889 889 889

23:00 525 525 525 525 525 525 525 525 525 525

126

H. Results for energy surplus from grid, for single and double penstock with synchronous

speed technology, for ten scenarios simulations

Table A 11 – Results for energy surplus from grid, for single penstock and synchronous speed, for ten scenarios simulations (kWh)

00:00 242 457 457 0 457 0 457 457 0 457

01:00 886 0 886 886 886 886 0 0 886 0

02:00 509 509 509 509 509 509 509 509 509 509

03:00 509 509 509 509 509 509 509 509 509 509

04:00 609 609 1370 609 609 609 609 609 609 609

05:00 658 658 658 658 851 658 658 658 658 658

06:00 886 886 886 886 886 886 886 886 886 886

07:00 1762 1762 1762 1762 0 1762 1762 1762 1762 1762

08:00 721 721 0 721 721 721 721 721 721 721

09:00 303 303 303 303 303 303 303 303 303 303

10:00 0 0 0 0 0 0 0 0 0 0

11:00 0 0 0 0 0 0 0 0 0 0

12:00 0 0 0 0 0 0 0 0 0 0

13:00 0 0 9 9 9 9 9 0 0 9

14:00 10 10 10 10 10 10 10 10 10 10

15:00 607 607 0 607 607 607 0 607 607 0

16:00 869 869 869 869 869 869 869 869 869 869

17:00 790 790 790 790 790 790 790 872 790 790

18:00 632 632 632 811 632 0 632 632 632 632

19:00 721 885 721 721 882 721 721 721 721 721

20:00 0 0 0 0 0 0 0 0 0 0

21:00 0 0 0 0 0 0 0 0 0 0

22:00 870 0 889 0 0 0 0 348 0 0

23:00 729 729 0 0 0 729 729 0 0 0

Table A 12 - Results for energy surplus from grid, for double penstock and synchronous speed, for ten scenarios simulations (kWh)

00:00 457 457 457 457 457 457 457 457 457 457

01:00 886 886 886 886 886 886 886 886 886 886

02:00 509 509 509 509 509 509 509 509 509 509

03:00 509 509 509 509 509 509 509 509 509 509

04:00 609 609 609 609 609 609 609 609 609 609

05:00 658 658 658 658 658 658 658 658 658 658

06:00 886 886 886 886 886 886 886 886 886 886

07:00 1762 1762 1762 1762 1762 1762 1762 1762 1762 1762

08:00 721 721 721 721 721 721 721 721 721 721

09:00 303 303 303 303 303 303 303 303 0 303

10:00 11 11 11 11 11 11 0 11 0 11

127

11:00 10 10 10 10 10 10 10 0 10 10

12:00 9 0 9 9 9 9 9 9 9 9

13:00 9 9 9 9 9 9 9 9 9 9

14:00 10 10 10 10 10 10 10 10 10 10

15:00 607 607 607 607 607 607 607 607 607 607

16:00 869 869 869 869 869 869 869 869 869 869

17:00 790 790 790 790 790 790 790 790 790 790

18:00 632 632 632 632 632 632 632 632 632 632

19:00 721 721 721 721 721 721 721 721 721 721

20:00 42 42 42 42 0 42 42 42 42 42

21:00 45 45 45 45 0 45 45 45 0 45

22:00 889 889 889 889 889 889 889 889 889 889

23:00 525 525 525 525 525 525 525 525 525 525

128

I. Flow histograms for single and double penstock over summer (dry) season

Table A 13 – Histogram for single penstock over summer (dry) season

Flow (m3/s) Hours

-6.00 0

-5.97 0

-5.94 0

-5.92 0

-5.89 0

-5.86 0

-5.83 0

-5.81 0

-5.78 0

-5.75 0

-5.72 0

-5.69 0

-5.67 0

-5.64 0

-5.61 0

-5.58 0

-5.56 0

-5.53 0

-5.50 0

-5.47 0

-5.44 0

-5.42 0

-5.39 0

-5.36 0

-5.33 0

-5.31 0

-5.28 0

-5.25 0

-5.22 0

-5.19 0

-5.17 0

-5.14 0

-5.11 18.3

-5.08 0

-5.06 0

-5.03 0

-5.00 0

-4.97 0

-4.94 18.3

-4.92 18.3

Flow (m3/s) Hours

-4.89 0

-4.86 0

-4.83 0

-4.81 0

-4.78 18.3

-4.75 0

-4.72 0

-4.69 0

-4.67 0

-4.64 0

-4.61 0

-4.58 0

-4.56 0

-4.53 0

-4.50 0

-4.47 0

-4.44 0

-4.42 0

-4.39 0

-4.36 0

-4.33 0

-4.31 0

-4.28 0

-4.25 0

-4.22 0

-4.19 18.3

-4.17 0

-4.14 0

-4.11 0

-4.08 0

-4.06 18.3

-4.03 0

-4.00 0

-3.97 0

-3.94 0

-3.92 0

-3.89 18.3

-3.86 0

-3.83 18.3

-3.81 0

Flow (m3/s) Hours

-3.78 18.3

-3.75 0

-3.72 0

-3.69 0

-3.67 18.3

-3.64 0

-3.61 18.3

-3.58 0

-3.56 0

-3.53 0

-3.50 0

-3.47 0

-3.44 18.3

-3.42 0

-3.39 0

-3.36 36.6

-3.33 0

-3.31 36.6

-3.28 0

-3.25 0

-3.22 0

-3.19 0

-3.17 18.3

-3.14 18.3

-3.11 0

-3.08 0

-3.06 0

-3.03 0

-3.00 0

-2.97 0

-2.94 0

-2.92 0

-2.89 0

-2.86 18.3

-2.83 0

-2.81 0

-2.78 0

-2.75 0

-2.72 0

-2.69 0

Flow (m3/s) Hours

-2.67 0

-2.64 0

-2.61 0

-2.58 0

-2.56 0

-2.53 18.3

-2.50 0

-2.47 0

-2.44 18.3

-2.42 0

-2.39 0

-2.36 0

-2.33 0

-2.31 0

-2.28 18.3

-2.25 0

-2.22 0

-2.19 0

-2.17 0

-2.14 18.3

-2.11 0

-2.08 0

-2.06 0

-2.03 0

-2.00 0

-1.97 36.6

-1.94 0

-1.92 0

-1.89 0

-1.86 0

-1.83 0

-1.81 0

-1.78 0

-1.75 0

-1.72 0

-1.69 36.6

-1.67 18.3

-1.64 0

-1.61 0

-1.58 18.3

129

Flow (m3/s) Hours

-1.56 0

-1.53 0

-1.50 54.9

-1.47 18.3

-1.44 0

-1.42 0

-1.39 0

-1.36 0

-1.33 0

-1.31 36.6

-1.28 0

-1.25 0

-1.22 18.3

-1.19 0

-1.17 0

-1.14 0

-1.11 0

-1.08 0

-1.06 18.3

-1.03 18.3

-1.00 0

-0.97 0

-0.94 0

-0.92 18.3

-0.89 18.3

-0.86 0

-0.83 0

-0.81 18.3

-0.78 18.3

-0.75 18.3

-0.72 18.3

-0.69 0

-0.67 18.3

-0.64 18.3

-0.61 18.3

-0.58 0

-0.56 18.3

-0.53 0

-0.50 18.3

-0.47 0

Flow (m3/s) Hours

-0.44 0

-0.42 18.3

-0.39 0

-0.36 18.3

-0.33 36.6

-0.31 0

-0.28 18.3

-0.25 18.3

-0.22 18.3

-0.19 18.3

-0.17 0

-0.14 0

-0.11 18.3

-0.08 18.3

-0.06 0

-0.03 54.9

0.00 0

0.03 0

0.06 0

0.08 201.3

0.11 18.3

0.14 0

0.17 128.1

0.19 0

0.22 0

0.25 18.3

0.28 0

0.31 18.3

0.33 18.3

0.36 18.3

0.39 18.3

0.42 201.3

0.44 0

0.47 164.7

0.50 384.3

0.53 146.4

0.56 0

0.58 0

0.61 0

0.64 0

Flow (m3/s) Hours

0.67 0

0.69 0

0.72 0

0.75 164.7

0.78 0

0.81 0

0.83 0

0.86 0

0.89 0

0.92 0

0.94 0

0.97 0

1.00 18.3

1.03 0

1.06 0

1.08 0

1.11 0

1.14 0

1.17 311.1

1.19 0

1.22 329.4

1.25 366

1.28 109.8

1.31 0

1.33 0

1.36 0

1.39 0

1.42 0

1.44 0

1.47 0

1.50 0

1.53 0

1.56 0

1.58 0

1.61 0

1.64 0

1.67 0

1.69 0

1.72 0

1.75 0

Flow (m3/s) Hours

1.78 0

1.81 0

1.83 0

1.86 0

1.89 0

1.92 0

1.94 0

1.97 0

2.00 0

130

Table A 14 – Histogram for double penstock over summer (dry) season

Flow (m3/s) Hours

-6.00 18.3

-5.97 0

-5.94 0

-5.92 0

-5.89 18.3

-5.86 0

-5.83 0

-5.81 0

-5.78 0

-5.75 0

-5.72 0

-5.69 0

-5.67 0

-5.64 0

-5.61 18.3

-5.58 0

-5.56 0

-5.53 0

-5.50 0

-5.47 0

-5.44 0

-5.42 0

-5.39 0

-5.36 0

-5.33 18.3

-5.31 0

-5.28 0

-5.25 0

-5.22 0

-5.19 0

-5.17 0

-5.14 0

-5.11 0

-5.08 0

-5.06 0

-5.03 0

-5.00 0

-4.97 0

-4.94 0

-4.92 0

Flow (m3/s) Hours

-4.89 18.3

-4.86 18.3

-4.83 0

-4.81 0

-4.78 0

-4.75 0

-4.72 18.3

-4.69 0

-4.67 0

-4.64 18.3

-4.61 0

-4.58 0

-4.56 0

-4.53 0

-4.50 0

-4.47 0

-4.44 0

-4.42 0

-4.39 0

-4.36 0

-4.33 18.3

-4.31 0

-4.28 18.3

-4.25 0

-4.22 0

-4.19 36.6

-4.17 0

-4.14 0

-4.11 18.3

-4.08 0

-4.06 0

-4.03 0

-4.00 0

-3.97 0

-3.94 0

-3.92 0

-3.89 0

-3.86 18.3

-3.83 0

-3.81 0

Flow (m3/s) Hours

-3.78 0

-3.75 0

-3.72 0

-3.69 0

-3.67 18.3

-3.64 0

-3.61 0

-3.58 0

-3.56 18.3

-3.53 0

-3.50 18.3

-3.47 0

-3.44 0

-3.42 0

-3.39 0

-3.36 0

-3.33 0

-3.31 0

-3.28 0

-3.25 0

-3.22 0

-3.19 0

-3.17 0

-3.14 0

-3.11 0

-3.08 18.3

-3.06 0

-3.03 0

-3.00 0

-2.97 0

-2.94 0

-2.92 0

-2.89 0

-2.86 0

-2.83 0

-2.81 18.3

-2.78 0

-2.75 0

-2.72 0

-2.69 0

Flow (m3/s) Hours

-2.67 0

-2.64 0

-2.61 0

-2.58 0

-2.56 0

-2.53 0

-2.50 0

-2.47 0

-2.44 0

-2.42 18.3

-2.39 0

-2.36 0

-2.33 0

-2.31 0

-2.28 0

-2.25 0

-2.22 0

-2.19 0

-2.17 0

-2.14 0

-2.11 0

-2.08 0

-2.06 0

-2.03 0

-2.00 0

-1.97 0

-1.94 0

-1.92 0

-1.89 0

-1.86 0

-1.83 0

-1.81 0

-1.78 0

-1.75 0

-1.72 0

-1.69 0

-1.67 0

-1.64 0

-1.61 0

-1.58 0

131

Flow (m3/s) Hours

-1.56 18.3

-1.53 0

-1.50 0

-1.47 0

-1.44 0

-1.42 0

-1.39 0

-1.36 0

-1.33 0

-1.31 0

-1.28 0

-1.25 0

-1.22 0

-1.19 18.3

-1.17 0

-1.14 0

-1.11 0

-1.08 0

-1.06 0

-1.03 18.3

-1.00 18.3

-0.97 36.6

-0.94 91.5

-0.92 91.5

-0.89 54.9

-0.86 54.9

-0.83 0

-0.81 0

-0.78 0

-0.75 36.6

-0.72 54.9

-0.69 18.3

-0.67 36.6

-0.64 36.6

-0.61 54.9

-0.58 18.3

-0.56 183

-0.53 0

-0.50 18.3

-0.47 91.5

Flow (m3/s) Hours

-0.44 36.6

-0.42 219.6

-0.39 18.3

-0.36 54.9

-0.33 0

-0.31 54.9

-0.28 0

-0.25 36.6

-0.22 73.2

-0.19 36.6

-0.17 0

-0.14 36.6

-0.11 18.3

-0.08 36.6

-0.06 73.2

-0.03 36.6

0.00 0

0.03 0

0.06 0

0.08 164.7

0.11 0

0.14 0

0.17 183

0.19 0

0.22 0

0.25 0

0.28 0

0.31 0

0.33 0

0.36 183

0.39 0

0.42 183

0.44 0

0.47 183

0.50 366

0.53 183

0.56 0

0.58 183

0.61 0

0.64 0

Flow (m3/s) Hours

0.67 0

0.69 0

0.72 0

0.75 183

0.78 0

0.81 0

0.83 0

0.86 0

0.89 0

0.92 0

0.94 0

0.97 0

1.00 0

1.03 0

1.06 0

1.08 0

1.11 0

1.14 0

1.17 366

1.19 0

1.22 366

1.25 366

1.28 183

1.31 0

1.33 0

1.36 0

1.39 0

1.42 0

1.44 0

1.47 0

1.50 0

1.53 0

1.56 0

1.58 0

1.61 0

1.64 0

1.67 0

1.69 0

1.72 0

1.75 0

Flow (m3/s) Hours

1.78 0

1.81 0

1.83 0

1.86 0

1.89 0

1.92 0

1.94 0

1.97 0

2.00 0

132

J. Pump station efficiency for adjustable speed

Table A 15 – Pump station efficiency for adjustable speed

Flow Efficiency

m3/s

1 p

um

p

0.33 0.72

0.36 0.74

0.39 0.76

0.42 0.79

0.44 0.81

0.47 0.83

0.5 0.84

0.53 0.83

0.56 0.81

0.58 0.79

0.61 0.76

0.64 0.74

0.67 0.72

2 p

um

ps

0.69 0.73

0.72 0.74

0.75 0.75

0.78 0.76

0.81 0.78

0.83 0.79

0.86 0.8

0.89 0.81

0.92 0.82

0.94 0.83

0.97 0.84

1 0.84

1.03 0.84

1.06 0.83

1.08 0.82

1.11 0.81

1.14 0.8

1.17 0.79

1.19 0.77

Flow Efficiency

m3/s

3 p

um

ps

1.22 0.78

1.25 0.79

1.28 0.8

1.31 0.8

1.33 0.81

1.36 0.81

1.39 0.82

1.42 0.83

1.44 0.83

1.47 0.83

1.5 0.84

1.53 0.83

1.56 0.83

1.58 0.83

1.61 0.82

1.64 0.81

1.67 0.81

1.69 0.8

1.72 0.8

1.75 0.79

1.78 0.78

1.81 0.77

1.83 0.76

1.86 0.75

1.89 0.75

1.92 0.74

1.94 0.73

1.97 0.73

2 0.72

133

K. Results for consumed/generated energy for double penstock

Table A 16 – Results for specific energy and total energy consumed over summer season for single penstock

Flow (m3/s)

Hours

adjustable speed synchronous speed

Es (kWh/m3) E

(kWh) Es (kWh/m3)

seconds per hour

E (kWh)

0.00 0 0 0 0 0 0

0.03 0 1.48 0 150 1.48 0

0.06 0 1.48 0 300 1.48 0

0.08 201.3 1.48 89439 450 1.48 89439

0.11 18.3 1.48 10841 600 1.48 10841

0.14 0 1.48 0 750 1.48 0

0.17 128.1 1.48 113831 900 1.48 113831

0.19 0 1.48 0 1050 1.48 0

0.22 0 1.48 0 1200 1.48 0

0.25 18.3 1.48 24392 1350 1.48 24392

0.28 0 1.48 0 1500 1.48 0

0.31 18.3 1.48 29813 1650 1.48 29813

0.33 18.3 1.73 38002 1800 1.48 32523

0.36 18.3 1.69 40212 1950 1.48 35233

0.39 18.3 1.63 41795 2100 1.48 37944

0.42 201.3 1.58 475738 2250 1.48 447194

0.44 0 1.54 0 2400 1.48 0

0.47 164.7 1.51 421903 2550 1.48 414670

0.50 384.3 1.47 1019745 2700 1.48 1024480

0.53 146.4 1.51 419145 2850 1.48 411960

0.56 0 1.54 0 3000 1.48 0

0.58 0 1.58 0 3150 1.48 0

0.61 0 1.63 0 3300 1.48 0

0.64 0 1.69 0 3450 1.48 0

0.67 0 1.73 0 3600 1.48 0

0.69 0 1.70 0 1875 1.48 0

0.72 0 1.68 0 1950 1.48 0

0.75 164.7 1.66 737625 2025 1.48 658594

0.78 0 1.64 0 2100 1.48 0

0.81 0 1.59 0 2175 1.48 0

0.83 0 1.57 0 2250 1.48 0

0.86 0 1.56 0 2325 1.48 0

0.89 0 1.54 0 2400 1.48 0

0.92 0 1.52 0 2475 1.48 0

0.94 0 1.50 0 2550 1.48 0

0.97 0 1.48 0 2625 1.48 0

1.00 18.3 1.48 97569 2700 1.48 97569

1.03 0 1.48 0 2775 1.48 0

1.06 0 1.50 0 2850 1.48 0

134

1.08 0 1.52 0 2925 1.48 0

1.11 0 1.54 0 3000 1.48 0

1.14 0 1.56 0 3075 1.48 0

1.17 311.1 1.57 2057605 3150 1.48 1935128

1.19 0 1.62 0 3225 1.48 0

1.22 329.4 1.59 2311647 3300 1.48 2146529

1.25 366 1.57 2593620 3375 1.48 2439238

1.28 109.8 1.56 785434 3450 1.48 748033

1.31 0 1.56 0 3525 1.48 0

1.33 0 1.54 0 3600 1.48 0

1.36 0 1.54 0 2450 1.48 0

1.39 0 1.52 0 2500 1.48 0

1.42 0 1.50 0 2550 1.48 0

1.44 0 1.50 0 2600 1.48 0

1.47 0 1.50 0 2650 1.48 0

1.50 0 1.48 0 2700 1.48 0

1.53 0 1.50 0 2750 1.48 0

1.56 0 1.50 0 2800 1.48 0

1.58 0 1.50 0 2850 1.48 0

1.61 0 1.52 0 2900 1.48 0

1.64 0 1.54 0 2950 1.48 0

1.67 0 1.54 0 3000 1.48 0

1.69 0 1.56 0 3050 1.48 0

1.72 0 1.56 0 3100 1.48 0

1.75 0 1.57 0 3150 1.48 0

1.78 0 1.59 0 3200 1.48 0

1.81 0 1.62 0 3250 1.48 0

1.83 0 1.64 0 3300 1.48 0

1.86 0 1.66 0 3350 1.48 0

1.89 0 1.66 0 3400 1.48 0

1.92 0 1.68 0 3450 1.48 0

1.94 0 1.70 0 3500 1.48 0

1.97 0 1.70 0 3550 1.48 0

2.00 0 1.73 0 3600 1.48 0

135

Table A 17 – Results for specific energy and total energy produced over summer season for single penstock

Flow (m3/s) Hours Efficiency Es (kW/m3) E (kWh)

-6.00 0 0.91 1.13 0.00

-5.97 0 0.91 1.13 0.00

-5.94 0 0.91 1.13 0.00

-5.92 0 0.91 1.13 0.00

-5.89 0 0.91 1.13 0.00

-5.86 0 0.91 1.13 0.00

-5.83 0 0.91 1.13 0.00

-5.81 0 0.91 1.13 0.00

-5.78 0 0.91 1.13 0.00

-5.75 0 0.91 1.13 0.00

-5.72 0 0.91 1.13 0.00

-5.69 0 0.91 1.13 0.00

-5.67 0 0.91 1.13 0.00

-5.64 0 0.91 1.13 0.00

-5.61 0 0.91 1.13 0.00

-5.58 0 0.91 1.13 0.00

-5.56 0 0.91 1.13 0.00

-5.53 0 0.91 1.13 0.00

-5.50 0 0.91 1.13 0.00

-5.47 0 0.91 1.13 0.00

-5.44 0 0.91 1.13 0.00

-5.42 0 0.91 1.13 0.00

-5.39 0 0.91 1.13 0.00

-5.36 0 0.91 1.13 0.00

-5.33 0 0.91 1.13 0.00

-5.31 0 0.91 1.13 0.00

-5.28 0 0.91 1.13 0.00

-5.25 0 0.91 1.13 0.00

-5.22 0 0.91 1.13 0.00

-5.19 0 0.91 1.13 0.00

-5.17 0 0.91 1.13 0.00

-5.14 0 0.91 1.13 0.00

-5.11 18.3 0.91 1.13 -381197.53

-5.08 0 0.91 1.13 0.00

-5.06 0 0.91 1.13 0.00

-5.03 0 0.91 1.13 0.00

-5.00 0 0.91 1.13 0.00

-4.97 0 0.91 1.13 0.00

-4.94 18.3 0.91 1.13 -368767.18

-4.92 18.3 0.91 1.13 -366695.45

-4.89 0 0.91 1.13 0.00

-4.86 0 0.91 1.13 0.00

-4.83 0 0.91 1.13 0.00

-4.81 0 0.91 1.13 0.00

136

-4.78 18.3 0.91 1.13 -356336.82

-4.75 0 0.91 1.13 0.00

-4.72 0 0.91 1.13 0.00

-4.69 0 0.91 1.13 0.00

-4.67 0 0.91 1.13 0.00

-4.64 0 0.91 1.13 0.00

-4.61 0 0.91 1.13 0.00

-4.58 0 0.91 1.13 0.00

-4.56 0 0.91 1.13 0.00

-4.53 0 0.91 1.13 0.00

-4.50 0 0.91 1.13 0.00

-4.47 0 0.91 1.13 0.00

-4.44 0 0.91 1.13 0.00

-4.42 0 0.91 1.13 0.00

-4.39 0 0.91 1.13 0.00

-4.36 0 0.91 1.13 0.00

-4.33 0 0.91 1.13 0.00

-4.31 0 0.91 1.13 0.00

-4.28 0 0.91 1.13 0.00

-4.25 0 0.91 1.13 0.00

-4.22 0 0.91 1.13 0.00

-4.19 18.3 0.91 1.13 -312830.58

-4.17 0 0.91 1.13 0.00

-4.14 0 0.91 1.13 0.00

-4.11 0 0.91 1.13 0.00

-4.08 0 0.91 1.13 0.00

-4.06 18.3 0.91 1.13 -302471.95

-4.03 0 0.91 1.13 0.00

-4.00 0 0.91 1.13 0.00

-3.97 0 0.91 1.13 0.00

-3.94 0 0.91 1.13 0.00

-3.92 0 0.91 1.13 0.00

-3.89 18.3 0.91 1.13 -290041.60

-3.86 0 0.91 1.13 0.00

-3.83 18.3 0.91 1.13 -285898.15

-3.81 0 0.91 1.13 0.00

-3.78 18.3 0.91 1.13 -281754.70

-3.75 0 0.91 1.13 0.00

-3.72 0 0.91 1.13 0.00

-3.69 0 0.91 1.13 0.00

-3.67 18.3 0.91 1.13 -273467.79

-3.64 0 0.91 1.13 0.00

-3.61 18.3 0.91 1.13 -269324.34

-3.58 0 0.91 1.13 0.00

-3.56 0 0.91 1.13 0.00

-3.53 0 0.91 1.13 0.00

137

-3.50 0 0.91 1.13 0.00

-3.47 0 0.91 1.13 0.00

-3.44 18.3 0.91 1.13 -256893.99

-3.42 0 0.91 1.13 0.00

-3.39 0 0.91 1.13 0.00

-3.36 36.6 0.91 1.13 -501357.62

-3.33 0 0.91 1.13 0.00

-3.31 36.6 0.91 1.13 -493070.72

-3.28 0 0.91 1.13 0.00

-3.25 0 0.91 1.13 0.00

-3.22 0 0.91 1.13 0.00

-3.19 0 0.91 1.13 0.00

-3.17 18.3 0.91 1.13 -236176.73

-3.14 18.3 0.91 1.13 -234105.01

-3.11 0 0.91 1.13 0.00

-3.08 0 0.91 1.13 0.00

-3.06 0 0.91 1.13 0.00

-3.03 0 0.91 1.13 0.00

-3.00 0 0.91 1.13 0.00

-2.97 0 0.91 1.13 0.00

-2.94 0 0.91 1.13 0.00

-2.92 0 0.91 1.13 0.00

-2.89 0 0.91 1.13 0.00

-2.86 18.3 0.91 1.13 -213387.75

-2.83 0 0.91 1.13 0.00

-2.81 0 0.91 1.13 0.00

-2.78 0 0.91 1.13 0.00

-2.75 0 0.91 1.13 0.00

-2.72 0 0.91 1.13 0.00

-2.69 0 0.91 1.13 0.00

-2.67 0 0.91 1.13 0.00

-2.64 0 0.91 1.13 0.00

-2.61 0 0.91 1.13 0.00

-2.58 0 0.91 1.13 0.00

-2.56 0 0.91 1.13 0.00

-2.53 18.3 0.91 1.13 -188527.04

-2.50 0 0.91 1.13 0.00

-2.47 0 0.91 1.13 0.00

-2.44 18.3 0.91 1.13 -182311.86

-2.42 0 0.91 1.13 0.00

-2.39 0 0.91 1.13 0.00

-2.36 0 0.91 1.13 0.00

-2.33 0 0.91 1.13 0.00

-2.31 0 0.91 1.13 0.00

-2.28 18.3 0.91 1.13 -169881.51

-2.25 0 0.91 1.13 0.00

138

-2.22 0 0.91 1.13 0.00

-2.19 0 0.91 1.13 0.00

-2.17 0 0.91 1.13 0.00

-2.14 18.3 0.91 1.13 -159522.88

-2.11 0 0.91 1.13 0.00

-2.08 0 0.91 1.13 0.00

-2.06 0 0.91 1.13 0.00

-2.03 0 0.91 1.13 0.00

-2.00 0 0.91 1.13 0.00

-1.97 36.6 0.91 1.13 -294185.05

-1.94 0 0.91 1.13 0.00

-1.92 0 0.91 1.13 0.00

-1.89 0 0.91 1.13 0.00

-1.86 0 0.91 1.13 0.00

-1.83 0 0.91 1.13 0.00

-1.81 0 0.91 1.13 0.00

-1.78 0 0.91 1.13 0.00

-1.75 0 0.91 1.13 0.00

-1.72 0 0.91 1.13 0.00

-1.69 36.6 0.91 1.13 -252750.54

-1.67 18.3 0.91 1.13 -124303.54

-1.64 0 0.91 1.13 0.00

-1.61 0 0.91 1.13 0.00

-1.58 18.3 0.91 1.13 -118088.37

-1.56 0 0.91 1.13 0.00

-1.53 0 0.91 1.13 0.00

-1.50 54.9 0.91 1.13 -335619.57

-1.47 18.3 0.91 1.13 -109801.46

-1.44 0 0.91 1.13 0.00

-1.42 0 0.91 1.13 0.00

-1.39 0 0.91 1.13 0.00

-1.36 0 0.91 1.13 0.00

-1.33 0 0.91 1.13 0.00

-1.31 36.6 0.91 1.13 -194742.22

-1.28 0 0.91 1.13 0.00

-1.25 0 0.91 1.13 0.00

-1.22 18.3 0.91 1.13 -91155.93

-1.19 0 0.91 1.13 0.00

-1.17 0 0.91 1.13 0.00

-1.14 0 0.91 1.13 0.00

-1.11 0 0.91 1.13 0.00

-1.08 0 0.91 1.13 0.00

-1.06 18.3 0.91 1.13 -78725.58

-1.03 18.3 0.91 1.13 -76653.85

-1.00 0 0.91 1.13 0.00

-0.97 0 0.91 1.13 0.00

139

-0.94 0 0.91 1.13 0.00

-0.92 18.3 0.91 1.13 -68366.95

-0.89 18.3 0.91 1.13 -66295.22

-0.86 0 0.91 1.13 0.00

-0.83 0 0.91 1.13 0.00

-0.81 18.3 0.85 1.06 -56118.72

-0.78 18.3 0.85 1.06 -54183.60

-0.75 18.3 0.85 1.06 -52248.47

-0.72 18.3 0.85 1.06 -50313.34

-0.69 0 0.85 1.06 0.00

-0.67 18.3 0.85 1.06 -46443.08

-0.64 18.3 0.85 1.06 -44507.95

-0.61 18.3 0.85 1.06 -42572.83

-0.58 0 0.85 1.06 0.00

-0.56 18.3 0.85 1.06 -38702.57

-0.53 0 0.85 1.06 0.00

-0.50 18.3 0.85 1.06 -34832.31

-0.47 0 0.85 1.06 0.00

-0.44 0 0.85 1.06 0.00

-0.42 18.3 0.85 1.06 -29026.93

-0.39 0 0.75 0.93 0.00

-0.36 18.3 0.75 0.93 -22197.06

-0.33 36.6 0.75 0.93 -40979.19

-0.31 0 0.75 0.93 0.00

-0.28 18.3 0.75 0.93 -17074.66

-0.25 18.3 0.75 0.93 -15367.20

-0.22 18.3 0.75 0.93 -13659.73

-0.19 18.3 0.65 0.81 -10358.63

-0.17 0 0.55 0.68 0.00

-0.14 0 0.4 0.50 0.00

-0.11 18.3 0.3 0.37 -2731.95

-0.08 18.3 0.2 0.25 -1365.97

-0.06 0 0.1 0.12 0.00

-0.03 54.9 0 0.00 0.00

0.00 0 0 0.00 0.00

140

L. Results for consumed/generated energy for double penstock

Table A 18 – Results for specific energy and total energy consumed over summer season for double penstock

Flow (m3/s)

Hours adjustable speed synchronous speed

Es (kWh/m3) E

(kWh) Es

(kWh/m3) seconds per

hour E

(kWh)

0.00 0 0 0 0 0 0

0.03 0 1.48 0 1.48 150 0

0.06 0 1.48 0 1.48 300 0

0.08 164.7 1.48 73177 1.48 450 73177

0.11 0 1.48 0 1.48 600 0

0.14 0 1.48 0 1.48 750 0

0.17 183 1.48 162616 1.48 900 162616

0.19 0 1.48 0 1.48 1050 0

0.22 0 1.48 0 1.48 1200 0

0.25 0 1.48 0 1.48 1350 0

0.28 0 1.48 0 1.48 1500 0

0.31 0 1.48 0 1.48 1650 0

0.33 0 1.73 0 1.48 1800 0

0.36 183 1.69 402121 1.48 1950 352334

0.39 0 1.63 0 1.48 2100 0

0.42 183 1.58 432489 1.48 2250 406540

0.44 0 1.54 0 1.48 2400 0

0.47 183 1.51 468781 1.48 2550 460745

0.50 366 1.47 971186 1.48 2700 975695

0.53 183 1.51 523932 1.48 2850 514950

0.56 0 1.54 0 1.48 3000 0

0.58 183 1.58 605484 1.48 3150 569155

0.61 0 1.63 0 1.48 3300 0

0.64 0 1.69 0 1.48 3450 0

0.67 0 1.73 0 1.48 3600 0

0.69 0 1.70 0 1.48 1875 0

0.72 0 1.68 0 1.48 1950 0

0.75 183 1.66 819584 1.48 2025 731771

0.78 0 1.64 0 1.48 2100 0

0.81 0 1.59 0 1.48 2175 0

0.83 0 1.57 0 1.48 2250 0

0.86 0 1.56 0 1.48 2325 0

0.89 0 1.54 0 1.48 2400 0

0.92 0 1.52 0 1.48 2475 0

0.94 0 1.50 0 1.48 2550 0

0.97 0 1.48 0 1.48 2625 0

1.00 0 1.48 0 1.48 2700 0

1.03 0 1.48 0 1.48 2775 0

1.06 0 1.50 0 1.48 2850 0

141

1.08 0 1.52 0 1.48 2925 0

1.11 0 1.54 0 1.48 3000 0

1.14 0 1.56 0 1.48 3075 0

1.17 366 1.57 2420712 1.48 3150 2276622

1.19 0 1.62 0 1.48 3225 0

1.22 366 1.59 2568496 1.48 3300 2385032

1.25 366 1.57 2593620 1.48 3375 2439238

1.28 183 1.56 1309057 1.48 3450 1246721

1.31 0 1.56 0 1.48 3525 0

1.33 0 1.54 0 1.48 3600 0

1.36 0 1.54 0 1.48 2450 0

1.39 0 1.52 0 1.48 2500 0

1.42 0 1.50 0 1.48 2550 0

1.44 0 1.50 0 1.48 2600 0

1.47 0 1.50 0 1.48 2650 0

1.50 0 1.48 0 1.48 2700 0

1.53 0 1.50 0 1.48 2750 0

1.56 0 1.50 0 1.48 2800 0

1.58 0 1.50 0 1.48 2850 0

1.61 0 1.52 0 1.48 2900 0

1.64 0 1.54 0 1.48 2950 0

1.67 0 1.54 0 1.48 3000 0

1.69 0 1.56 0 1.48 3050 0

1.72 0 1.56 0 1.48 3100 0

1.75 0 1.57 0 1.48 3150 0

1.78 0 1.59 0 1.48 3200 0

1.81 0 1.62 0 1.48 3250 0

1.83 0 1.64 0 1.48 3300 0

1.86 0 1.66 0 1.48 3350 0

1.89 0 1.66 0 1.48 3400 0

1.92 0 1.68 0 1.48 3450 0

1.94 0 1.70 0 1.48 3500 0

1.97 0 1.70 0 1.48 3550 0

2.00 0 1.73 0 1.48 3600 0

142

Table A 19 – Results for specific energy and total energy produced over summer season for double penstock

Flow (m3/s) Hours Efficiency Es (kW/m3) E (kWh)

-6.00 18.3 0.91 1.13 -447492.75

-5.97 0 0.91 1.13 0.00

-5.94 0 0.91 1.13 0.00

-5.92 0 0.91 1.13 0.00

-5.89 18.3 0.91 1.13 -439205.85

-5.86 0 0.91 1.13 0.00

-5.83 0 0.91 1.13 0.00

-5.81 0 0.91 1.13 0.00

-5.78 0 0.91 1.13 0.00

-5.75 0 0.91 1.13 0.00

-5.72 0 0.91 1.13 0.00

-5.69 0 0.91 1.13 0.00

-5.67 0 0.91 1.13 0.00

-5.64 0 0.91 1.13 0.00

-5.61 18.3 0.91 1.13 -418488.59

-5.58 0 0.91 1.13 0.00

-5.56 0 0.91 1.13 0.00

-5.53 0 0.91 1.13 0.00

-5.50 0 0.91 1.13 0.00

-5.47 0 0.91 1.13 0.00

-5.44 0 0.91 1.13 0.00

-5.42 0 0.91 1.13 0.00

-5.39 0 0.91 1.13 0.00

-5.36 0 0.91 1.13 0.00

-5.33 18.3 0.91 1.13 -397771.34

-5.31 0 0.91 1.13 0.00

-5.28 0 0.91 1.13 0.00

-5.25 0 0.91 1.13 0.00

-5.22 0 0.91 1.13 0.00

-5.19 0 0.91 1.13 0.00

-5.17 0 0.91 1.13 0.00

-5.14 0 0.91 1.13 0.00

-5.11 0 0.91 1.13 0.00

-5.08 0 0.91 1.13 0.00

-5.06 0 0.91 1.13 0.00

-5.03 0 0.91 1.13 0.00

-5.00 0 0.91 1.13 0.00

-4.97 0 0.91 1.13 0.00

-4.94 0 0.91 1.13 0.00

-4.92 0 0.91 1.13 0.00

-4.89 18.3 0.91 1.13 -364623.73

-4.86 18.3 0.91 1.13 -362552.00

-4.83 0 0.91 1.13 0.00

-4.81 0 0.91 1.13 0.00

143

-4.78 0 0.91 1.13 0.00

-4.75 0 0.91 1.13 0.00

-4.72 18.3 0.91 1.13 -352193.37

-4.69 0 0.91 1.13 0.00

-4.67 0 0.91 1.13 0.00

-4.64 18.3 0.91 1.13 -345978.19

-4.61 0 0.91 1.13 0.00

-4.58 0 0.91 1.13 0.00

-4.56 0 0.91 1.13 0.00

-4.53 0 0.91 1.13 0.00

-4.50 0 0.91 1.13 0.00

-4.47 0 0.91 1.13 0.00

-4.44 0 0.91 1.13 0.00

-4.42 0 0.91 1.13 0.00

-4.39 0 0.91 1.13 0.00

-4.36 0 0.91 1.13 0.00

-4.33 18.3 0.91 1.13 -323189.21

-4.31 0 0.91 1.13 0.00

-4.28 18.3 0.91 1.13 -319045.76

-4.25 0 0.91 1.13 0.00

-4.22 0 0.91 1.13 0.00

-4.19 36.6 0.91 1.13 -625661.17

-4.17 0 0.91 1.13 0.00

-4.14 0 0.91 1.13 0.00

-4.11 18.3 0.91 1.13 -306615.41

-4.08 0 0.91 1.13 0.00

-4.06 0 0.91 1.13 0.00

-4.03 0 0.91 1.13 0.00

-4.00 0 0.91 1.13 0.00

-3.97 0 0.91 1.13 0.00

-3.94 0 0.91 1.13 0.00

-3.92 0 0.91 1.13 0.00

-3.89 0 0.91 1.13 0.00

-3.86 18.3 0.91 1.13 -287969.87

-3.83 0 0.91 1.13 0.00

-3.81 0 0.91 1.13 0.00

-3.78 0 0.91 1.13 0.00

-3.75 0 0.91 1.13 0.00

-3.72 0 0.91 1.13 0.00

-3.69 0 0.91 1.13 0.00

-3.67 18.3 0.91 1.13 -273467.79

-3.64 0 0.91 1.13 0.00

-3.61 0 0.91 1.13 0.00

-3.58 0 0.91 1.13 0.00

-3.56 18.3 0.91 1.13 -265180.89

-3.53 0 0.91 1.13 0.00

144

-3.50 18.3 0.91 1.13 -261037.44

-3.47 0 0.91 1.13 0.00

-3.44 0 0.91 1.13 0.00

-3.42 0 0.91 1.13 0.00

-3.39 0 0.91 1.13 0.00

-3.36 0 0.91 1.13 0.00

-3.33 0 0.91 1.13 0.00

-3.31 0 0.91 1.13 0.00

-3.28 0 0.91 1.13 0.00

-3.25 0 0.91 1.13 0.00

-3.22 0 0.91 1.13 0.00

-3.19 0 0.91 1.13 0.00

-3.17 0 0.91 1.13 0.00

-3.14 0 0.91 1.13 0.00

-3.11 0 0.91 1.13 0.00

-3.08 18.3 0.91 1.13 -229961.55

-3.06 0 0.91 1.13 0.00

-3.03 0 0.91 1.13 0.00

-3.00 0 0.91 1.13 0.00

-2.97 0 0.91 1.13 0.00

-2.94 0 0.91 1.13 0.00

-2.92 0 0.91 1.13 0.00

-2.89 0 0.91 1.13 0.00

-2.86 0 0.91 1.13 0.00

-2.83 0 0.91 1.13 0.00

-2.81 18.3 0.91 1.13 -209244.30

-2.78 0 0.91 1.13 0.00

-2.75 0 0.91 1.13 0.00

-2.72 0 0.91 1.13 0.00

-2.69 0 0.91 1.13 0.00

-2.67 0 0.91 1.13 0.00

-2.64 0 0.91 1.13 0.00

-2.61 0 0.91 1.13 0.00

-2.58 0 0.91 1.13 0.00

-2.56 0 0.91 1.13 0.00

-2.53 0 0.91 1.13 0.00

-2.50 0 0.91 1.13 0.00

-2.47 0 0.91 1.13 0.00

-2.44 0 0.91 1.13 0.00

-2.42 18.3 0.91 1.13 -180240.14

-2.39 0 0.91 1.13 0.00

-2.36 0 0.91 1.13 0.00

-2.33 0 0.91 1.13 0.00

-2.31 0 0.91 1.13 0.00

-2.28 0 0.91 1.13 0.00

-2.25 0 0.91 1.13 0.00

145

-2.22 0 0.91 1.13 0.00

-2.19 0 0.91 1.13 0.00

-2.17 0 0.91 1.13 0.00

-2.14 0 0.91 1.13 0.00

-2.11 0 0.91 1.13 0.00

-2.08 0 0.91 1.13 0.00

-2.06 0 0.91 1.13 0.00

-2.03 0 0.91 1.13 0.00

-2.00 0 0.91 1.13 0.00

-1.97 0 0.91 1.13 0.00

-1.94 0 0.91 1.13 0.00

-1.92 0 0.91 1.13 0.00

-1.89 0 0.91 1.13 0.00

-1.86 0 0.91 1.13 0.00

-1.83 0 0.91 1.13 0.00

-1.81 0 0.91 1.13 0.00

-1.78 0 0.91 1.13 0.00

-1.75 0 0.91 1.13 0.00

-1.72 0 0.91 1.13 0.00

-1.69 0 0.91 1.13 0.00

-1.67 0 0.91 1.13 0.00

-1.64 0 0.91 1.13 0.00

-1.61 0 0.91 1.13 0.00

-1.58 0 0.91 1.13 0.00

-1.56 18.3 0.91 1.13 -116016.64

-1.53 0 0.91 1.13 0.00

-1.50 0 0.91 1.13 0.00

-1.47 0 0.91 1.13 0.00

-1.44 0 0.91 1.13 0.00

-1.42 0 0.91 1.13 0.00

-1.39 0 0.91 1.13 0.00

-1.36 0 0.91 1.13 0.00

-1.33 0 0.91 1.13 0.00

-1.31 0 0.91 1.13 0.00

-1.28 0 0.91 1.13 0.00

-1.25 0 0.91 1.13 0.00

-1.22 0 0.91 1.13 0.00

-1.19 18.3 0.91 1.13 -89084.21

-1.17 0 0.91 1.13 0.00

-1.14 0 0.91 1.13 0.00

-1.11 0 0.91 1.13 0.00

-1.08 0 0.91 1.13 0.00

-1.06 0 0.91 1.13 0.00

-1.03 18.3 0.91 1.13 -76653.85

-1.00 18.3 0.91 1.13 -74582.13

-0.97 36.6 0.91 1.13 -145020.80

146

-0.94 91.5 0.91 1.13 -352193.37

-0.92 91.5 0.91 1.13 -341834.74

-0.89 54.9 0.91 1.13 -198885.67

-0.86 54.9 0.91 1.13 -192670.49

-0.83 0 0.91 1.13 0.00

-0.81 0 0.85 1.06 0.00

-0.78 0 0.85 1.06 0.00

-0.75 36.6 0.85 1.06 -104496.93

-0.72 54.9 0.85 1.06 -150940.02

-0.69 18.3 0.85 1.06 -48378.21

-0.67 36.6 0.85 1.06 -92886.16

-0.64 36.6 0.85 1.06 -89015.91

-0.61 54.9 0.85 1.06 -127718.48

-0.58 18.3 0.85 1.06 -40637.70

-0.56 183 0.85 1.06 -387025.68

-0.53 0 0.85 1.06 0.00

-0.50 18.3 0.85 1.06 -34832.31

-0.47 91.5 0.85 1.06 -164485.92

-0.44 36.6 0.85 1.06 -61924.11

-0.42 219.6 0.85 1.06 -348323.12

-0.39 18.3 0.75 0.93 -23904.53

-0.36 54.9 0.75 0.93 -66591.18

-0.33 0 0.75 0.93 0.00

-0.31 54.9 0.75 0.93 -56346.39

-0.28 0 0.75 0.93 0.00

-0.25 36.6 0.75 0.93 -30734.39

-0.22 73.2 0.75 0.93 -54638.92

-0.19 36.6 0.65 0.81 -20717.26

-0.17 0 0.55 0.68 0.00

-0.14 36.6 0.4 0.50 -9106.49

-0.11 18.3 0.3 0.37 -2731.95

-0.08 36.6 0.2 0.25 -2731.95

-0.06 73.2 0.1 0.12 -1821.30

-0.03 36.6 0 0.00 0.00

0.00 0 0 0 0

147

M. Records from July of 2014 of the Socorridos System: Consumed/generated energy and

water level for the upper and lower reservoirs

-12-606

121824

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 0 1 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

% Upper Reservoir - 01/07/2014

0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

m Lower Reservoir - 01/07/2014

-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 0 2 / 0 7 / 2 0 1 4

0255075

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


148

-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 0 3 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 0 4 / 0 7 / 2 0 1 4

0255075

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


149

-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 0 5 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


-12-606

121824

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 0 6 / 0 7 / 2 0 1 4

0255075

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


150

-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 0 7 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


-12-606

121824

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 0 8 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


151

-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 0 9 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 1 0 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


152

-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 1 1 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


01234

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 1 2 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


153

-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 1 3 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 1 4 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


154

-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 1 5 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 1 6 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


155

-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 1 7 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 1 8 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

%Upper Reservoir - 18/07/2014

0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


156

-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 1 9 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 2 0 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


157

-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 2 1 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

%Upper Reservoir - 21/07/2014

0

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00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 2 2 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


158

-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 2 3 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 2 4 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


159

-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 2 5 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 2 6 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


160

-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 2 7 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 2 8 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


161

-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 2 9 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 3 0 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


162

-12

-6

0

6

12

18

24

0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00

MW 3 1 / 0 7 / 2 0 1 4

0

25

50

75

100

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


0

1

2

3

4

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


Documents

Contribution of Pumped-Hydro Storage to Electrical Grids · Contribution of Pumped-Hydro Storage to Electrical Grids and Improvement Measures José Gonçalo Faria de Sousa Thesis