ThesisPDF Available

Hybrid Wind, Solar and Storage Power Plant in Electricity Market

Authors:

Abstract

In this 15 ECTS master thesis belonging to the DTU Wind Energy master, a methodology is developed to bid in the day-ahead market for a wind-solar-storage based hybrid power plant with the objective to minimize variability. The input time series and forecast simulations are simulated in CorRES software for two selected regions, one in Denmark (DK2) and another in Sweden (SE2). The efficacy of the developed methodology is analysed through the assessment of hybrid power plant forecast error computation.
DTU Wind Energy
Master of Wind Energy
HybridWind,SolarandStoragePowerPlant
inElectricityMarket
Emilio Barrachina Gascó
DTU Wind Energy Master-0010
July 2020
DTU Wind Energy Master - 0010
August 2020
2nd version
Hybrid Wind, Solar and Storage
Power Plant in Electricity Market
DK2 and SE2 Hybrid Power Plants
Supervisors:
Professor Poul Ejnar Sørensen
Researcher Kaushik Das
External supervisor:
Professor Henrik Stiesdal
Student:
Emilio Barrachina Gascó
Fanzara, Spain
August 6th 2020
b
Preface
This master thesis was prepared at DTU Wind Energy Department at the Technical
University of Denmark in fulfillment of the requirements for acquiring the DTU Wind
Energy Master diploma.
The supervisors for this master thesis have been professor Poul Ejnar Sørensen and
researcher Kaushik Das, both from DTU Wind Energy Department.
The external supervisor for this master thesis has been professor Henrik Stiesdal from
Stiesdal A/S company.
The complete period of work for this master thesis development has been five months,
starting on February 2020 till the end of June 2020.
Fanzara, Spain
July 1st, 2020
Emilio Barrachina Gascó
MEng and MSc
emilio.barrachinagasco@iicv.es
Abstract
During the last two decades we have seen how the renewable energy sources have been
expanded all around the world evolving hand in hand because of the increase of envi-
ronmental conscious market acceptance. These renewable energy sources have a great
challenge which is the inherent variability as they have stochastic renewable power
generation.
The unreliability of wind and solar photovoltaic to generate the energy demanded
is the main reason for including energy storage technologies so that we gain dispatchabil-
ity of WPPs and PVPPs. Energy storage systems have a really special advantage in this
sense, as they can shift energy generation to later periods with higher electricity prices
and energy demand.
We are living really interesting times if we talk about hybrid wind and solar with
energy storage systems and I’m pretty sure they’re going to be crucial in the near future,
and so this can happen, integration of several energy storaging within the hybrid wind
and solar pv plants is key to boost penetration of these technologies into the energy
market.
Index terms
CorRES, time series, hybrid wind and solar pv power plant, battery energy storage sys-
tem, wind power, solar photovoltaic power, correlation coefficient, spot market prices
and RES negative correlation, power and energy surplus, bidding model methodol-
ogy, real time model methodology, forecast error minimization, reducing curtailment,
reducing penalties.
Future perspectives
Last summer when I was attending to the Wind Energy Master Graduation week event
at DTU Risø Campus many seminars were offered within its fantastic and complete
program prepared by Merete Badger and Nina Julh Madsen. Among them a Henrik
Stiesdal’s seminar aimed to last year finalist master students, Master of Wind Energy:
What now?.
After listening to Henrik I decided that in my master thesis he had to be included
due to his huge impact within the wind energy field of course, and for his impressive
enthusiasm communicating, vision of the future and extensive renewable knowledge in a
field as exciting as wind energy, that will undoubtedly mark the future in a significant
way for the next generations.
So we have had recently a phone call interview talking about many interesting and
relevant energy matters as follows. Needless to say that I am deeply grateful for the kind
attention that Henrik Stiesdal has always had with me in the course of this master thesis.
Henrik Stiesdal is going to place some thermal storage technology in the first world’s
energy artificial island which is going to be located at the Danish North Sea. It’s A
10 [
GW
]offshore wind and host electricity storage and power-to-X as well as housing, OM
facilities and HVDC converters for transmission and interconnectors. More information
can be consulted at Copenhagen Infrastructure Partners’s website.
This project is going to be developed in 3 stages in line with increasing Danish electricity
demand so Henrik Stiesdal’s participation will take place once the project has progressed
through the several phases planned but Henrik has already provided the project promoter
a pilot for phase one. Stiesdal Storage Technologies A/S has developed a thermal battery,
a grid-scale energy storage concept that can provide a backup to RES for a much longer
period than conventional batteries do.
iv Future perspectives
Talking to Henrik Stiesdal I asked him about HPP technologies and future perspectives
so he thinks that:
"HPP technology is going to be necessary in most places of the world. You can al-
ways introduce more load we could say that we solve things by avoiding having overflow
or wind and solar power production by having battery systems so then we can use the
excess power. But unless you accept very low efficiency of power rates then you’ll have
problems in regenerating when you don’t have enough wind and solar. So the half of the
problem is the overflow but we can’t avoid the other half of the problem that’s the under
supply of energy and for that we need storage. Storage of electrical energy promises to
make wind and solar power more viable by offering a solution to the fluctuations in the
energy supply they produce".
"At the present time there is no a direct energy market for storage but it wasn’t a
wind market when we started there it was all about the subsidies in the early years, there
were subsidies in California, subsidies in Denmark and then the market came, and the
same will happen with the storage, it has to be some kind of support mechanism".
"But of course you can also have good part of your revenue from capacity, in other
words you’re always ready to deliver power even though you might not need it now you
actually get paid per
kW month
basis rather than per
kW h
basis. And the capacity market
is quite huge in many parts of the world, at least in the US, so in a well defined capacity
market over there where you get a certain payment per
kW
and then we can do. So I do
think that can help in the distance case, so it’s not purely upping fast buying cheaper and
selling expensive".
Finally talking to Henrik about seasonal storaging and the variable demand that power
production has to face at every single moment he says: "normal ly say that we need three
type of storages: the short terms that batteries can do, that’s like half an hour or an hour
or so and then we need the mid-term that’s what we do with thermal storage as that can
do for a week, and then we need the seasonal storage which have to rely on chemistry so
it’s all about hybrid them and that can last of course. There is of course a limit on the
amount we can store but then we have ammonia instead, which is easy to keep so that
way for sure we’ll be able to solve it with these three types of storages"
Henrik Stiesdal
Wind power pioneer
CEO Stiesdal A/S
GWEC Ambassador
Taksigelser
Jeg vil gerne udtrykke min dybe og respektfulde tak til mine vejledere på hovedopgaven:
Professor Poul Ejnar Sørensen og Researcher Kaushik Das fra DTU Vindenergi, for deres
fantastiske vejledning, assistance, hjælp og støtte gennem hovedopgaven.Især i disse
måneder med COVID-19 med alt dette har forårsaget og konditioneret arbejdet med
universitetsundervisning og -forskning. Jeg værdsætter højt deres markante bidrag i form
af tid og ideer, hvilket har gjort, at dette interessante arbejde har været en stimulerende
og berigende oplevelse gennem 5 måneder.
Jeg vil også gerne udtrykke min dybtfølte tak til min eksterne vejleder: Henrik Stiesdal,
vindpioner fra Stiesdal A/S, for hans værdifulde samarbejde, venlig støtte og rådgivning
under dette arbejde.
Jeg vil også gerne udtrykke min tak til Researcher Matti Juhani Koivisto og Post-
doc Juan Pablo Murcia León fra DTU Vindenergi for deres venlige bidrag og støtte i
form af prognoser og målt energiproduktion til brug for denne hovedopgave.
Jeg vil gerne udtrykke min tak til Senior Scientist, Head of Master Studies, Merete Badger
hende altid fremragende effektiv opmærksomhed. Jeg vil gerne udtrykke min tak til
Sekretær og Master Programme Coordinator Nina Juhl Madsen hende altid fremragende
effektiv opmærksomhed.
Jeg vil gerne udtrykke min tak til alle undervisere involveret i DTU Master i Vin-
denergi for deres entusiasme, dedikation og undervisning igennem de 9 kurser.
Jeg vil gerne udtrykke min tak til mine medstuderende: Didde Okholm Kvorning,
Peter Fausbøll, Stephan Johannes Østergaard, José Alberto Navarro Martínez og Laín
Nieto Gómez. Det var virkelig en fornøjelse at være i masterprogrammet sammen med dig.
Jeg vil gerne udtrykke min tak til min ven, universitetskollega og forsker: Jaime Zabalza
Ostos fra Centre for Signal and Image Processing - University of Strathclyde(Glasgow,UK),
for hans gode råd i forbindelse med udarbejdelsen af denne hovedopgave.
Jeg vil gerne udtrykke min dybeste taknemmelighed til min moder, Juana Gascó Vivas,
til min fader, Emilio Barrachina Martí og til min tante Encarna Gascó Vivas, for al deres
indsats i form af at give mig min uddannelse.
Jeg vil gerne udtrykke min dybeste taknemmelighed til min onkel, Juan Carlos Gascó
Vivas, for hans super støtte og gode eksempel på kamp, som for os alle er med hans
daglige indsats i de vanskelige øjeblikke, som livet har sat ham igennem.
vi Taksigelser
Jeg vil gerne udtrykke min dybeste tak til min elskede kæreste, Sonia Marmaneu Vidal,
for al hendes forståelse og støtte under sådant et tidskrævende arbejde.
Sidst, men ikke mindst, tak til Audrey, min elskede hund, som har været sammen
med mig i 13 år, men som desværre gik bort i april måned.
Oversættelse foretaget af min ven og medlærer, Peter Fausbøll
Acknowledgements
I would like to express my most sincere and respectful gratitude to my master thesis supervisors:
Professor Poul Ejnar Sørensen and Researcher Kaushik Das from DTU Wind Energy department,
for their fantastic guidance, assistance, help and support throughout this master final project.
Especially during these months of COVID-19 with all that this has caused and conditioned the
work of university teaching and research. I really appreciate their notable contributions of time
and ideas provided, which have made this interesting work a very stimulating and enriching
experience during these 5 months period.
I would like also to express my sincere thanks to my external supervisor: Henrik Stiesdal, wind
industry pioneer from : Stiesdal A/S company, for their valuable cooperation, kind support
and advise during this work.
I would like like to express my gratitude to researcher Matti Juhani Koivisto and postdoc
Juan Pablo Murcia León from DTU Wind department for their kind contribution and support
providing forecast and measured power production data for this master thesis.
I would like to express my more sincere thanks to senior scientist and Head of Master Studies
Merete Badger her always excellent efficient attention.
I would like to express my more sincere thanks to secretary and Master Programme Co-
ordinator Nina Juhl Madsen her always excellent efficient attention.
I would like to express my sincere thanks to all the professors involved in the DTU Mas-
ter in Wind Energy for their enthusiasm, dedication and teaching all along the 9 courses.
I would like to express my gratitude to my master colleagues: Didde Okholm Kvorning,
Peter Fausbøll, Stephan Johannes Østergaard, José Alberto Navarro Martínez y Laín Nieto
Gómez, it has been a real pleasure sharing with them all this master time.
I would like to express my gratitude to my friend, university colleague and great researcher:
Jaime Zabalza Ostos from Centre for Signal and Image Processing - University of Strathclyde
(Glasgow,UK), for all his wise advise all along this master thesis work.
I would like to express my deepest gratitude to my mother, Juana Gascó Vivas, to my
father, Emilio Barrachina Martí and to my auntie Encarna Gascó Vivas, for all their efforts
having given me the education they gave me.
I want to express my deepest gratitude to my uncle, Juan Carlos Gascó Vivas, for his super
support and great example of struggle that for all of us is with his daily effort in the difficult
viii Acknowledgements
moments that life has put him through.
I would like to express my deepest gratitude to my beloved girlfriend, Sonia Marmaneu
Vidal, for all her understanding and support in such a time-demanding job.
Last but not least to Audrey, my beloved dog who has been together with me during these last
13 years that sadly passed away last April month.
Agradecimientos
Deseo expresar mi más sincera y respetuosa gratitud a mis supervisores de tesina: Catedrático
Poul Ejnar Sørensen y al Doctor Kaushik Das del departamento DTU Wind Energy por su
fantástica guía, asistencia, ayuda y apoyo durante esta tesina. Especialmente durante estos
meses de COVID-19 con todo lo que ello ha ocasionado y condicionado las labores de docencia
universitaria e investigación. Realmente aprecio sus notables contribuciones e ideas aportadas,
las cuales han hecho de este interesante trabajo una experiencia muy estimulante y enriquecedora
durante estos 5 meses.
Querría expresar mi más sincero agradecimiento a mi supervisor externo de tesina: Hen-
rik Stiesdal, pionero de la industria eólica de la compañía: Stiesdal A/S, por su valuosa
cooperación, apoyo y consejo durante este trabajo.
Me gustaría expresar mi gratitud al científico investigador Matti Juhani Koivisto y al post-
doctorando Juan Pablo Murcia León del departamento DTU Wind Energy por su amable
contribución y apoyo facilitando los datos de la previsión y medida de producción de potencia
utilizados en esta tesina.
Deseo expresar mi más sincero agradecimiento a la investigadora científica senior y Direc-
tora del Máster Merete Badger su siempre excelente atención.
Querría expresar mi más sincero agradecimiento a la secretaría y Coordinadora del Máster
Nina Juhl Madsen su siempre excelente atención.
Me gustaría trasladar mi más sincero agradecimiento a todos los profesores implicados en
el máster de energía eólica de la DTU, por su entusiasmo, dedicación y enseñanzas a lo largo
de los nueve cursos que comprende este máster.
Quiero expresar mi gratitud a mis compañeros de clase: Didde Okholm Kvorning, Peter
Fausbøll, Stephan Johannes Østergaard, José Alberto Navarro Martínez y Laín Nieto Gómez,
ha sido un verdadero placer compartir con ellos todo este tiempo en el máster.
Querría expresar mi gratitud a mi gran amigo, compañero de carrera and gran científico
investigador: Jaime Zabalza Ostos del Centre for Signal and Image Processing - University
of Strathclyde (Glasgow,Reino Unido), por sus sabios consejos durante todo el trabajo de la
tesina.
Querría expresar mi más profunda gratitud y reconocimiento a mi madre, Juana Gascó
Vivas, a mi padre, Emilio Barrachina Martí y a mi tía Encarna Gascó Vivas, por todos sus
esfuerzos para ofrecerme toda la educacion que ellos me han dado.
xAgradecimientos
Deseo expresar mi más profunda gratitud a mi tío Juan Carlos Gascó Vivas, por su apoyo y
gran ejemplo de lucha que para todos nosotros és en su esfuerzo diario en los momentos difíciles
que la vida le ha hecho pasar.
Querría expresar mi más profunda gratitud a mi querida novia, Sonia Marmaneu Vidal,
por toda su comprensión y apoyo en un trabajo tan demandante de tiempo.
Por último pero no por ello menos importante a Audrey, mi querida perra quien ha estado
conmigo durante estos últimos trece años y que tristemente falleció el pasado mes de abril.
List of Figures
1.1 Hybrid power plant + battery energy storage system . . . . . . . . . . . . . . . . . 2
1.2 TopologyofconnectedHPP............................... 2
1.3 Types of HPPs: integration and operation of different generating modules . . . . . 3
1.4 World HPP and RES capacity share in 2024 . . . . . . . . . . . . . . . . . . . . . 3
2.1 Danish energy system - June 29th 2020 18:51 hrs . . . . . . . . . . . . . . . . . . . 5
3.1 Nordic area wind conditions - July 29th 2020 6.51 pm . . . . . . . . . . . . . . . . 8
3.2 DK2HPPlocation.................................... 9
3.3 DK2HPP......................................... 9
3.4 SE2HPPlocation .................................... 10
3.5 SE2HPP......................................... 10
3.6 CorRESblockdiagram ................................. 12
3.7 Scatter plot: Power generated per hour vs El. Spot market prices . . . . . . . . . 13
5.1 Bidding model algorithm flowchart . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.2 Bidding model algorithm flowchart - Charging detail . . . . . . . . . . . . . . . . . 21
5.3 Bidding model algorithm flowchart - Discharging detail . . . . . . . . . . . . . . . 22
5.4 Bidding model algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.5 DK2Bidding-Scenario9................................ 25
5.6 DK2Bidding-Scenario9................................ 25
5.7 DK2forecast-Scenario9................................ 26
5.8 DK2 forecast - Scenario 9 - P_LIMbatt = 50MW .................. 26
5.9 DK2forecast-Scenario9................................ 27
5.10 DK2 forecast - Scenario 9 - P_LIMbatt = 50MW .................. 27
5.11 DK2 forecast - Scenario 9 - P_LIMbatt = 100MW .................. 28
5.12 Real time model algorithm flowchart . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.13 DK2 measured - Scenario 9 - P_LIMbatt = 5MW .................. 32
5.14 DK2 measured - Scenario 9 - P_LIMbatt = 100MW ................. 32
5.15 DK2 measured - Scenario 9 - P_LIMbatt = 5MW and P_LIMbatt = 10MW . . . 33
5.16 DK2 measured - Scenario 9 - P_LIMbatt = 50MW ................. 33
5.17 Days with low Psurplus(t)Pbatt = 5 and 10 [M W ].................. 34
5.18 Days with low Psurplus(t)Pbatt = 50 and 100 [M W ]................. 34
5.19 Full model algorithm flowchart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
6.1 DK2 Forecast duration curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
6.2 DK2 Measured duration curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6.3 DK2 P_H P P _F(t)-P_LIMbatt = 5[M W ]Ebatt = 100[M W h].......... 40
6.4 DK2 P_H P P _F(t)-P_LIMbatt = 25[M W ]Ebatt = 100[M W h]......... 41
6.5 DK2 P_H P P _F(t)-P_LIMbatt = 50[M W ]Ebatt = 100[M W h]......... 41
xii List of Figures
6.6 DK2 P_H P P _F(t)-P_LIMbatt = 75[M W ]Ebatt = 100[M W h]......... 42
6.7 DK2 P_H P P (t)-P_LIMbatt = 5[M W ]Ebatt = 100[M W h]............ 43
6.8 DK2 P_H P P (t)-P_LIMbatt = 25[M W ]Ebatt = 100[M W h]........... 43
6.9 DK2 P_H P P (t)-P_LIMbatt = 50[M W ]Ebatt = 100[M W h]........... 44
6.10 DK2 P_H P P (t)-P_LIMbatt = 75[M W ]Ebatt = 100[M W h]........... 44
List of Tables
3.1 DK2 and SE2 RES scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2
DK2 HPP correlation coefficients - Power production per hour vs Spot market prices
13
3.3 SE2 HPP correlation coefficients - Power production per hour vs Spot market prices 14
3.4 Capacity factor and correlation of wind and solar power plant . . . . . . . . . . . 14
4.1 DK2 and SE2 RES E_RES_F - Scenario 9 - Forecast . . . . . . . . . . . . . . . . 16
4.2 DK2 and SE2 RES E_RES - Scenario 9 - Measured . . . . . . . . . . . . . . . . . 16
4.3 DK2 and SE2 RES CF and FWH - Scenario 9 - Forecast . . . . . . . . . . . . . . 16
4.4 DK2 and SE2 RES CF and FWH - Scenario 9 - Measured . . . . . . . . . . . . . . 16
4.5 DK2 and SE2 RES E_surplus_F - Scenario 9 - Forecast . . . . . . . . . . . . . . 17
4.6 DK2 and SE2 RES E_surplus - Scenario 9 - Measured . . . . . . . . . . . . . . . . 17
6.1 DK2 Ecurtailed_F(t) [GW h/year]............................ 46
6.2 SE2 Ecurtailed_F(t) [GW h/year]............................ 47
7.1
DK2 and SE2 Scenario 9
P_RES_F E
(
t
):
MAE_RES_F E
(
t
)and
RMSE_H P P _F E
(
t
)
49
7.2
DK2 Scenario 9
P_H P P _F E
(
t
):
MAE_H P P _F E
(
t
)and
RMSE_H P P _F E
(
t
)
50
7.3 SE2 Scenario 9 P_H P P _F E(t):MAE_H P P _F E(t)and RMSE_H P P _F E(t)50
7.4 DK2 and SE2 Scenario 9 P_H P P _F E(t)reduction[%] ............... 50
1 DK2 RES Scenarios comparison - Energy Produced and Surplused . . . . . . . . . 65
2
DK2 RES Scenarios comparison - Energy Produced Measured, Surplused and Curtailed
65
3
DK2 RES Scenarios comparison - Energy Produced Measured, Surplused and Curtailed
66
4 SE2 RES Scenarios comparison - Energy Produced and Surplused . . . . . . . . . 67
5 SE2 RES Scenarios comparison - Energy Produced and Surplused . . . . . . . . . 67
6 SE2 RES Scenarios comparison - Energy Produced and Surplused . . . . . . . . . 68
AEP Annual Energy Production [TWh/year]
BESS Battery Energy Storage System
CHP P Hybrid power plant cost[MW/Me]
CHP P _FHybrid power plant forecast cost [MW/Me]
Crate
Rate at which a battery is charged/discharged relative to its maxi-
mum capacity [hour]
CF Capacity Factor measured [%]
C F _FCapacity Factor forecast [%]
CorRES Correlations in Renewable Energy Sources
DA Day Ahead
Ebatt Battery Energy Capacity [MWh]
Ecurt Annual Energy Curtailed measured [GWh/year]
Ecurt_FAnnual Energy Curtailed forecast [GWh/year]
Ecurt_FAnnual Energy Surplus forecast [GWh/year]
Esurplus Annual Energy Surplus measured [GWh/year]
FWH Full work hours [hours/year]
GW EC Global Wind Energy Council
H P P Hybrid Power Plant
H P S Hybrid Power System
MAE Mean Absolut Error [MW]
M AF E Mean Absolut Forecast Error [MW]
P_H P P (t)Hybrid Power Produced [MW]
P_H P P _F(t)Hybrid Power Produced Forecast [MW]
P_H P P _F E(t)Hybrid Power Produced Forecast Error[MW]
Nomenclature
xvi Nomenclature
P_LIM batt Battery charging/discharging capacity [MW]
P_SOC headroom(t)State Of Charge Headroom Power [MW]
P_SOC headroom_F(t)State Of Charge Headroom Power Forecast [MW]
P RES(t)Wind and Solar Power Production Generated [MW]
P RES_F(t)Wind and Solar Power Production Forecast [MW]
Pcharge (t)Power Charged [MW]
Pcurt(t)Power Curtailed Generated [MW]
Pcurt_F(t)Power Curtailed Forecast [MW]
Pdischarge (t)Power Discharged [MW]
Pdischarge max(t)Maximum Power Discharge [MW]
Pgrid Power Grid Connection Constrain[MW]
Pgrid headroom(t)Grid Headroom Power[MW]
Pmissing(t)Power Missing Generated [MW]
Pshortage (t)Power shortage Generated [MW]
Psurp(t)Power Surplus Generated [MW]
Psurp_F(t)Power Surplus Forecast [MW]
P P Power Plant
P V P P Solar Photovoltaic Power Plant
RCorrelation coefficient
RES Renewable Energy Source
RMSE Root Mean Square Error [MW]
RM SF E Root Mean Square Forecast Error[MW]
SOC(t)State of Charge measured [p.u.]
SOC(t)_FState of Charge forecast [p.u.]
SOC0(t)Initial State of Charge measured [p.u.]
SOC0_F(t)Initial State of Charge forecast [p.u.]
T SO Transmission System Operator
V RE Variable Renewable Energy
WPP Wind Power Plant
Contents
Preface i
Abstract ii
Future perspectives iii
Taksigelser v
Acknowledgements vii
Agradecimientos ix
List of Figures xi
List of Tables xiii
Nomenclature xiv
Contents xvii
1Introduction 1
1.1 Aim and motivation of the study . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Objectiveofthestudy................................ 1
1.3 HPPwithBESSdesign ............................... 2
1.4 Advantages/values of hybrid power plants . . . . . . . . . . . . . . . . . . . . . 4
1.5 Scope of this master thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2Background 5
2.1 Introduction ..................................... 5
2.2 What services can energy batteries provide? . . . . . . . . . . . . . . . . . . . 7
3DK2 and SE2 HPP 8
3.1 Introduction ..................................... 8
3.2 DK2powerplantdetails .............................. 9
3.3 SE2powerplantdetails............................... 10
3.4 Hybrid power plant scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.5 REScorrelationstudy................................ 11
4HPP Case Scenario Study 16
4.1 Studycase:Scenario9 ............................... 16
xviii Contents
4.2 CorREStimeseries ................................. 17
5Bidding, Real and Full model Algorithms 19
5.1 Introduction ..................................... 19
5.2 Bidding model algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.3 Real time model algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.4 Fullmodelalgorithm ................................ 35
6Data Analysis 37
6.1 Durationcurves ................................... 37
6.2 Spot market bidding methodology . . . . . . . . . . . . . . . . . . . . . . . . . 40
6.3 Hybrid power production real time measured . . . . . . . . . . . . . . . . . . . 43
6.4 Energysurplusforecast ............................... 45
6.5 Energy curtailed forecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
6.6 Capacity factor forecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
7Forecast Error 48
7.1 Introduction ..................................... 48
7.2 Forecast error metrics: MAFE and RMSFE . . . . . . . . . . . . . . . . . . . . 49
8Conclusions and Future work 51
8.1 Main important aspects learnt . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
8.2 Contributions .................................... 51
8.3 Conclusion ...................................... 52
8.4 Futurework ..................................... 53
Bibliography 54
Appendix A: Matlab Code 57
Appendix B: Measured Scenarios Comparison 65
DK2HPP-Measured................................... 65
SE2HPP-Measured ................................... 67
CHAPTER 1
Introduction
1.1 Aim and motivation of the study
The aim of this master thesis is to develop an algorithm methodology to minimize the hybrid
power produced forecast error so it’s important to keep in mind that I’m not presenting an
optimization model in this work. I’ll show the dependency of the battery size used for this
purpose so using the forecast error we will reduce its variability. We will see what positive
effects adding a battery within a hybrid wind and solar power plant has, its sensitivity effect,
having as main advantages these:
reduction of the curtailment produced, bigger battery size less curtailment.
repair of the forecast error
For that purpose I’m using a 1 Day Ahead, 1DA, power production forecast for wind power
plant, WPP, and for solar photovoltaic power plant, PVPP, too. So we will see how much
storage system I’m including at the end.
This kind of forecasting is a medium term forecast type, being its key applications: scheduling,
reserve requirement, market trading and congestion management,
T. Tian and I. Chernyakhovskiy[16].
We have to take into account how every single scenario is affecting in the curtailment produced
by each one. We must also take into account that the amount of curtailed energy depends
on my algorithm design decision and the amount of energy generated, when more energy is
generated then you also curtail more.
1.2 Objective of the study
To develop a methodology model for the hybrid power plant, HPP, to bid in the spot market
and then minimize the forecast error in the real time model so we can reduce the applied
associated penalties due to this error produced.
When playing with different battery sizes we will see how it’s affecting to power curtailed
drawing the important conclusion that the bigger the battery size is the better in terms of
curtailment reduction.
It goes without saying that this increase in battery size will directly incur the consequent
increase in the price of energy storage system. It is important to keep in mind that the cost of
storage continues to fall We only have to look at the storage price evolution.
2 1 Introduction
1.3 HPP with BESS design
Here in Figure 1.1 we can see how the hybrid power plant, HPP, is designed including the
battery energy storage system, BESS:
Figure 1.1: Hybrid power plant + battery energy storage system
Here in Figure 1.2 we can see the AC and DC coupled HPP with BESS designs. Being the
main advantage from AC connected HPP its ease of expansion as it enables more systems to
be added in parallel to either increase the storage power or the overall HPP capacity. Those
designs are out of this master thesis scope but if interested further relevant content can be
found at Kaushik Das et al.[6].
(a) AC connected HPP (b) DC connected HPP
Figure 1.2: Topology of connected HPP
There are mainly two HPP configurations which are is the mostly developed right one, while
the left one is an alternative version where solar converters can be removed in some situations.
1.3 HPP with BESS design 3
Figure 1.3: Types of HPPs: integration and operation of different generating modules
(a) Global map with HPP locations and types
(b) Capacity share of wind, solar and storage tech-
nologies in 2024
Figure 1.4: World HPP and RES capacity share in 2024
All this information presented in Figures 1.3 and 1.4 has been extracted from Wind Europe
report, Renewable Hybrid Power Plants - Exploring the Benefits and Market Opportunities -
July 2019 elaborated by Wind Europe.
4 1 Introduction
1.4 Advantages/values of hybrid power plants
The main advantages are cost reduction and revenue increase.
Reduction in land cost
Optical use of electric infrastructure and other infrastructure saves costs.
Joint permitting process reduces risks and costs
Shared resources reduce internal costs
Joint site development reduces costs
Less fluctuating production increases electrical infrastructure utilization
Storage increases flexibility and number of accessible markets (Energy market, ancillary
services market)
Reduction of Forecast Error using storage
1.5 Scope of this master thesis
This report is divided in the following chapters:
Chapter 1 presents introduction
Chapter 2 includes background
Chapter 3 presents DK2 and SE2 HPP locations
Chapter 4 presents scenario 9 study
Chapter 5 includes Spot Market Bidding and Operational methodologies
Chapter 6 includes data analysis scenario 9 study
Chapter 7 presents forecast error P_H P P _F E(t)
Chapter 8 are drawn the main master thesis conclusions
CHAPTER 2
Background
2.1 Introduction
Figure 2.1: Danish energy system - June 29th 2020 18:51 hrs
Energinet.dk website
I’ve decided to start with this fantastic picture above, where the Danish Energy System can be
perfectly understood. It was indeed one of the first figures commented at the very beginning
of this master thesis work in our supervisory meeting. Show us the importance of the energy
connections between neighbouring countries and their energy tradings, with import and export
energy.
Penetration rates of renewable energy sources, RES, expanded during the last years due
to increased environmental conscience and market acceptance. Another benefit of combining
wind and solar photovoltaic power from the TSO’s point of view is a better utilization of grid
infrastructure and reduced congestion: improving security of energy supply and system stability
Kaushik Das et. al.[8].
The main challenge with RES is their inherent variability due to the stochastic nature of
the RES causing some difficulties as severe power ramps, up and down, and increased volatility
in the power generation in general. In future WPPs and PVPPs need to participate more in
the energy markets. Adding energy storage we will increase the dispatchability of RES. Wind
6 2 Background
and solar photovoltaic power don’t reliably produce power on demand, so including energy
storage system is a mitigation strategy.
Negative impact associated to stochastic nature of RES can be reduced by coupling WPPs
and PVPPs with BESS. Energy storage will be more relevant even where power prizes are
correlated negatively with renewable power production.
Battery storage is one of several technology options that can enhance power system flexi-
bility and enable high levels of renewable energy integration. Studies and real-world experience
have demonstrated that interconnected power systems can safely and reliably integrate high lev-
els of renewable energy from VRE sources without new energy storage resources
Thomas Bowen
;
Ilya Chernyakhovskiy;Paul Denholm[6].
Energy storage allows RES to increase their revenue providing flexibility and time shift-
ing of the power production. We have to take into account that increasing the integration of
RES also increases energy curtailment situations due to power overproduction compared to
grid connection constrain.
If we store surplus power,
Psurplus
(
t
), at times of high output we can improve the RES
production stabilization.
In order to participate in energy market, VRE sources need to reduce the uncertainty of
forecast errors. Inclusion of storage can be a viable option not only to minimize the penalties
due to forecast uncertainties but also to maximize the revenue generation
Kaushik Das et. al.
[4].
Wind and solar photovoltaic power are used in convex optimisation algorithm for making
day ahead decisions on battery operation. One day ahead optimized results are used as input
for the operating model.
Adding BESS in the WPP and PVPP we have several advantages as:
minimize the penalties due to forecast uncertainties.
minimize the excess energy spilt.
maximize the revenue generation.
Including BESS we will reduce the impact of the forecast error associated to wind and solar
photovoltaic power production forecasts so it’ll reduce balancing penalty too.
It’s important to say that this master thesis study is covering the HPP but not the hy-
brid power system, HPS, as I’m not taking into account
Pdemand
(
t
)neither
Edemand
(
t
)in the
methodology development scope of this master thesis work.
2.2 What services can energy batteries provide? 7
2.2 What services can energy batteries provide?
To answer these questions there is an excellent NREL document called "Grid-Scale Battery Stor-
age Frequently Asked Questions" by Thomas Bowen;Ilya Chernyakhovskiy;Paul Denholm[5].
Including this paragraph extracted from this cited document:
["...Arbitrage: Arbitrage involves charging the battery when energy prices are low and dis-
charging during more expensive peak hours. For the BESS operator, this practice can provide a
source of income by taking advantage of electricity prices that may vary throughout the day.
One extension of the energy arbitrage service is reducing renewable energy curtailment. System
operators and project developers have an interest in using as much low-cost, emissions-free
renewable energy generation as possible; however, in systems with a growing share of VRE,
limited flexibility of conventional generators and temporal mismatches between renewable energy
supply and electricity demand (e.g., excess wind generation in the middle of the night) may
require renewable generators to curtail their output. By charging the battery with low-cost
energy during periods of excess renewable generation and discharging during periods of high
demand, BESS can both reduce renewable energy curtailment and maximize the value of the
energy developers can sell to the market..."]
As we’re going to see all along this master thesis work all this is going to be fully stud-
ied and explained completely in detail. We could summarize it saying that using a really big
battery size we’re making sure that we’re reducing power curtailed but as we’ll find included
within the models methodology development presented, it’s not that simple, and many aspects
must be taken into account to get a complete picture of it.
CHAPTER 3
DK2 and SE2 HPP
3.1 Introduction
DK2 and SE2 HPP distance is: 877.06 [Km].
Figure 3.1: Nordic area wind conditions - July 29th 2020 6.51 pm
Source: Windy.com
3.2 DK2 power plant details 9
3.2 DK2 power plant details
DK2 HPP location:
Ringsted, Ringsted Municipality, Region Zealand, 4100, Denmark. The geographic coordinates
for DK2 hybrid power plant are:
Latitude: 55o27’ 8.256" North and Longitude: 11o49’ 25.429" East
Figure 3.2: DK2 HPP location
Source: Global Wind Atlas
(a) Mean power density (b) Wind speed rose (c) Mean wind speed
Figure 3.3: DK2 HPP
Source: Global Wind Atlas
10 3 DK2 and SE2 HPP
3.3 SE2 power plant details
SE2 HPP location:
Storsjön, Östersunds kommun, Jämtland County, Region Norrland, Sweden
The geographic coordinates for SE2 hybrid power plant are:
Latitude: 63o13’ 15.594" North Longitude: 14o20’ 33.474" East
Figure 3.4: SE2 HPP location
Source: Global Wind Atlas
(a) Mean power density (b) Wind speed rose (c) Mean wind speed
Figure 3.5: SE2 HPP
Source: Global Wind Atlas
3.4 Hybrid power plant scenarios 11
3.4 Hybrid power plant scenarios
WPP+PVPP Scenario DK2 and SE2 RES Pgrid [M W ]
Scenario 1 0 WPP+100 PVPP 100
Scenario 2 25 WPP+75 PVPP 100
Scenario 3 50 WPP+50 PVPP 100
Scenario 4 75 WPP+25 PVPP 100
Scenario 5 100 WPP+0 PVPP 100
Scenario 6: Overplanting case 80 WPP+60 PVPP 100
Scenario 7: Overplanting case 100 WPP+40 PVPP 100
Scenario 8: Overplanting case 105 WPP+35 PVPP 100
Scenario 9: Overplanting case 120 WPP+20 PVPP 100
Table 3.1: DK2 and SE2 RES scenarios
The hybrid wind and solar pv power plant scenarios studied for DK2 and SE2 power plant
locations can be seen in Table 3.1 above. Where 4 overplanting scenarios have been also taken
into account for DK2 and SE2 power plant Nordic locations. We can see how in every single
scenario there is a power grid connection constraint,
Pgrid
= 100 [
MW
]which is going to be
one of the input parameters for the bidding model algorithm later presented in Chapter 5.
From all the nine scenarios studied and work all along this master thesis development I’m
presenting mainly scenario 9 in this document as I found it more interesting than the other
eight. I have also seen the effect of increasing the wind ans solar pv installed capacity in every
single one of them and as I’ve been working with two Nordic power plant locations, DK2 and
SE2 the effect of the solar photovoltaic has less effect than it would in other locations like, for
example in Spain or France, where capacity factors for PVPP are higher than in Denmark
or Sweden. It goes without saying that the weight and generation behaviour of wind energy
production is completely different from solar pv.
To understand the enhanced value of HPP different studies in terms of capacity factors, vari-
ability, curtailment, value of storage etc. It should be noted that the value of HPP is enhanced
when the evacuation capacity to the grid is limited. It can be interpreted that for limited grid
connection, maximum weather resources should be used to generate maximum power close to
the evacuation capacity to maximize revenue.Kaushik Das et. al.[8]
3.5 RES correlation study
I’m presenting here a correlation study between RES power production and spot market prices.
Spot market prices have been obtained from Nordpool website:
https://www.nordpoolgroup.
com/historical-market-data/
, It can be read a complete and detailed correlation study here
Matti Koivisto et. al.[10].
12 3 DK2 and SE2 HPP
This is the block diagram of the main parts of CorRES. Simulated available power gener-
ation means the generation before, for example, curtailment:
Figure 3.6: CorRES block diagram
Matti Koivisto et. al.[10]
CorRES have provided the following time series:
Wind power production forecast WPP_F(t) [p.u.]
Solar pv power production forecast P V P P _F(t) [p.u.]
Wind power production measured WPP(t) [p.u.]
Solar pv power production measured P V P P (t) [p.u.]
These power production time series will be used as inputs for the bidding and real time models
later in
Chapter 5
. It will be then when I take into account the wind and solar capacity to get
P_RES_F(t)and P_RES(t).
3.5 RES correlation study 13
I’m presenting the study correlation from the time series obtained using
CorRES
software
for year 2016 for DK2 and SE2 wind and solar pv power plants. In this figure we can see
forecast and measured correlation studies between power production per hour vs spot market
prices. Storage is specially relevant for market where power prices are negatively correlated, as
we are going to see that happens with this two Nordic hybrid power plants.
Figure 3.7: Scatter plot: Power generated per hour vs El. Spot market prices
Here in Table 3.2 I’m including the correlation factor results for DK2 and SE2 for all the 9
scenarios:
HPP correlation coefficient Forecast Measured
Scenario 1 R: 0.1155 0.1153
Scenario 2 R: 0.0217 0.0156
Scenario 3 R: -0.0945 -0.1149
Scenario 4 R: -0.1588 -0.1878
Scenario 5 R: -0.1844 -0.2142
Scenario 6 R: -0.1188 -0.1429
Scenario 7 R: -0.1528 -0.1813
Scenario 8 R: -0.1588 -0.1878
Scenario 9 R: -0.1727 -0.2025
Table 3.2: DK2 HPP correlation coefficients - Power production per hour vs Spot market
prices
14 3 DK2 and SE2 HPP
HPP correlation coefficient Forecast Measured
Scenario 1 R: 0.0746 0.0719
Scenario 2 R: 0.0177 0.0207
Scenario 3 R: -0.0594 -0.0579
Scenario 4 R: -0.1087 -0.1163
Scenario 5 R: -0.1288 -0.1392
Scenario 6 R: -0.0775 -0.0788
Scenario 7 R: -0.1039 -0.1106
Scenario 8 R: -0.1087 -0.1163
Scenario 9 R: -0.1196 -0.1292
Table 3.3: SE2 HPP correlation coefficients - Power production per hour vs Spot market
prices
Reviewing these Tables 3.2 and 3.3 firstly we can easily see the impact of WPPs installed
capacity when is gaining more participation in the different scenarios presented. Secondly there
is another important conclusion we can draw from these tables, and is that PVPPs participation
is relevant too, that can be seen if we compare scenario 5 with 8 and 9, where correlation
coefficients, R, in absolute value are lower than correlation coefficient for scenario 5.
One could say, then why we just pick scenario 3 if is having a lower
R
value? The an-
swer for that is the power generation, that is lower than in scenarios 8 and 9. And this is
precisely why I think is a good idea choosing for this study just Scenario 9.
So taking into account scenario 9 now, if we analyze scenario correlation coefficient result
firstly we can observe that the correlation is negative, the electric prices are higher when the
renewable generation is lower and upside down, when the power produced is reaching a higher
value then the prices are lower, the law of supply and demand. Secondly the higher the cor-
relation factor R value is the better, in terms of R absolute value, the smaller the value the better.
Here is when the BESS becomes more relevant, in terms of improving its revenue being
able to sell the energy when prices are higher. As it allows us to move the power in time
transferring to the grid at later times when the price is higher Jose L. Crespo-Vazquez.[14].
Another correlation study between DK2 and SE2 wind and solar power plants and capacity
factors can be also found at:
Table.1 Kaushik Das et. al.
[8], where the following results are
presented in Table 3.4:
PP Location Wind Power CF [%] Solar PV Power CF [%] R
DK2 PP: 42 12 -0.1574
SE2 PP: 24 10 -0.1206
Table 3.4: Capacity factor and correlation of wind and solar power plant
3.5 RES correlation study 15
The stronger the negative correlation the better regarding e.g. utilization of the grid
connection and balanced energy output.
CHAPTER 4
HPP Case Scenario Study
4.1 Study case: Scenario 9
As commented previously in
Chapter 3
, I’m focusing my study on scenario 9, as I’ve found
it more interesting, so all the results and analysis that I’m presenting belong to the study of
this scenario. For all calculations power grid connection constraint
Pgrid
= 100 [
MW
]has been
taken into account. Here in the following Tables 4.1, 4.2, 4.3, 4.4, 4.5 and 4.6 I’m presenting
some relevant scenario 9 main figures:
Scenario 9 DK2 E_RES_F[T W h/y ear]SE2 E_RES_F[T W h/year ]
120 WPP+20 PVPP 0.471 0.303
Table 4.1: DK2 and SE2 RES E_RES_F - Scenario 9 - Forecast
Scenario 9 DK2 E_RES_F[T W h/y ear]SE2 E_RES_F[T W h/year ]
120 WPP+20 PVPP 0.468 0.281
Table 4.2: DK2 and SE2 RES E_RES - Scenario 9 - Measured
Scenario 9 DK2 CF [%] DK2 FWH [h] SE2 [%] SE2 FWH [h]
120 WPP+20 PVPP 53.75 4708.5 34.63 3033.6
Table 4.3: DK2 and SE2 RES CF and FWH - Scenario 9 - Forecast
Scenario 9 DK2 CF [%] DK2 FWH [h] SE2 [%] SE2 FWH [h]
120 WPP+20 PVPP 53.46 4683.1 32.09 2811.1
Table 4.4: DK2 and SE2 RES CF and FWH - Scenario 9 - Measured
4.2 CorRES time series 17
Scenario 9 DK2 Esurplus_F[GW h/year]SE2 Esurplus_F[GW h/y ear]
120 WPP+20 PVPP 30.403 13.273
Table 4.5: DK2 and SE2 RES E_surplus_F - Scenario 9 - Forecast
Scenario 9 DK2 Esurplus [GW h/year]SE2 Esurplus [GW h/y ear]
120 WPP+20 PVPP 25.509 8.997
Table 4.6: DK2 and SE2 RES E_surplus - Scenario 9 - Measured
4.2 CorRES time series
CorRES, Correlations in Renewable Energy Sources, is a simulation tool developed by DTU
Wind Energy department. It’s capable of simulating both wind and solar power generation.
Correlations in Renewable Energy Sources (CorRES) is a simulation tool developed at Technical
University of Denmark, Department of Wind Energy capable of simulating both wind and
solar generation. It uses a unique combination of meteorological time series and stochastic
simulations to provide consistent VRE generation and forecast error time series with temporal
resolution in the minute scale.
Such simulated VRE time series can be used in addressing the challenges posed by the
increasing share of VRE generation. These capabilities will be demonstrated through three
case studies: one about the use of large-scale VRE generation simulations in energy system
analysis, and two about the use of the simulations in power system operation, planning, and
analysis Matti Koivisto et. al.[10].
Application of VRE generation simulation tools can be used:
in the estimation of adequacy of reserves in power systems
in stability analysis
long-term transmission system planning
electricity market studies
There are different approaches for VRE generation simulation:
meteorological reanalysis models for generating the underlying meteorological fields
stochastic time series models for simulating the time series of interest
18 4 HPP Case Scenario Study
To assess the value of storage for revenue maximization of a wind power plant. The results
show that proposed algorithms can increase the revenue by more than
10[%]
compared to the
operation of WPP without BESS.
CorRES outputs are:
Forecast RES power production
Measured RES power production
In this study case, RES are wind and solar photolvotaic.
Forecast and measured wind and solar power production time series obtained with DTU
CorRES tool are the starting point of this master thesis work. These power production time
series belong to years 2015 and 2016 for DK2 and SE2 wind and solar photovoltaic power plant
specified locations. So I’ve worked with hourly power production data for these two mentioned
years. As I’m not presenting a variability study I’m combining both years in order to work
with only one data for each scenario getting more weightage to the obtained results. I have to
say that in a very beginning stage of this work I used persistent PVPP forecast before using
CorRES forecast. Persistent forecast is a poor forecast which consist of assuming for the next
period that the power will be the same that it was in the last past one. The challenge of using
a bad forecast, as persistent is, battery will be used quite a lot, so a really big battery will be
needed.
We can read more about time series in this really interesting article: "Simulation of transconti-
nental wind and solar PV generation time series" Edgar Nuño et. al.[12].
CHAPTER 5
Bidding, Real and Full model
Algorithms
5.1 Introduction
The criteria for designing the HPP is to minimize the forecast error,
P_H P P _F E
(
t
), not
to have stable power production over the day. So reducing the forecast error means that you
will be penalized less for it, then this is the main improvement of this methodology here presented.
The purpose of including within this hybrid power plant a
BESS
is precisely to reduce
the forecast error
P_H P P _F E
(
t
)as well as to reduce curtailment including an appropiate
battery energy storage system size.
Another important factor is the amount of energy than can be charged and discharged to/from
the battery in one hour time. This is because it is not possible to get more that a limited amount
of energy supply from the battery as well as is not possible to charge the battery all the amount
we would like to charge it. This is where
P_LIMbatt
parameter becomes important as it is
the power battery limitation for charging and discharging operation. In this chapter I am pre-
senting how it is taken into account as a parameter for the bidding and real time modes analyzed.
Power surplus,
Psurplus
(
t
), is used to charge the battery too, so it will reduce forecast er-
ror too. Every single time we have
Psurplus
(
t
)then we take the opportunity to charge the
battery and when we don’t then we just bid what we have, P_HP P _F(t).
And finally when it is not possible to include all this
Psurplus
(
t
)produced within the bat-
tery then we spill this power, commonly known as
Pcurtailed
(
t
). Curtailment is spilling the
energy, letting it go as we are not able to storage it within BESS. This situation is going to
happen every single time that battery is full charged and from RES we are producing more
power than
Pgrid
then battery won’t be able to accommodate that power produced, then
Pcurtailed
(
t
)will be spilt. Just like I am showing, in this master thesis, increasing the battery
capacity, Ebatt we’ll reduce Pcurtailed (t)value.
One of the main battery parameters is the rate at which a battery is charged/discharged
relative to its maximum capacity, known as Crate.
From this study we can see and understand how important is to have a really good power
production forecast for the hybrid power plant. It will reduce the forecast error and of course
the battery size needed too. In order to participate in energy market, VRE need to reduce the
uncertainty of forecast errors. So this is why storage is a viable option: to minimize penal-
20 5 Bidding, Real and Full model Algorithms
ties due to forecast uncertainties and to maximize the revenue generation
Kaushik Das et. al.
[4].
The hybrid power production forecast
P_H P P _F
(
t
)is going to be our 1DA bid for real
time model, that is going to be one of the inputs for it. This is the main reason for the
bidding model design, as we are trading with this hybrid power production forecast not with
the P_RES_F(t)or with SOC_F(t).
5.2 Bidding model algorithm
In this model I’m working with the actual power production values provided by CorRES, that
is to say:
P_WPP_F(t) + P_P V P P _F(t) = P_RES_F(t) [M W ](5.1)
Bidding model inputs:
Wind and solar power forecast: P_RES_F(t) [M W ]
Power grid connection constrain: Pg rid = 100 [M W ]
Battery capacity: Ebatt [M W h]
Initial state of charge: SOC0_F= 0.5 [p.u.]
Parameters:
Power battery limitation for charging and discharging P_LIMbatt [M W ]
Rate measure at which a battery is charged/discharged relative to its maximum capacity:
Crate [h]
Assumption:
Sampling time resolution: 1 [hour]
Bidding model outputs:
State of charge forecast: SOC_F(t) [p.u.]
Hybrid power produced forecast: P_H P P _F(t) [M W ]
Power curtailed forecast: Pcur tailed_F(t) [M W ]
5.2 Bidding model algorithm 21
5.2.1 Bidding model flowchart
Here I’m presenting how bidding model works, where complete methodology can be seen in
the next three figures. First one, Figure 5.1 is a complete overview showing how it works,
meanwhile Figure 5.2 and Figure 5.3 are showing in detail charging and discharging procedures.
Figure 5.1: Bidding model algorithm flowchart
Figure 5.2: Bidding model algorithm flowchart - Charging detail
22 5 Bidding, Real and Full model Algorithms
Figure 5.3: Bidding model algorithm flowchart - Discharging detail
The dispatch SOC_F(t) for this preliminary bidding model the following equations have
been taken into account:
P_SOC headroom_F(t) = (1 SOC _F(t1)) ·Ebatt [M W ](5.2)
Pcharge _F(t) = minimum(Psurplus _F(t), P _SOC headroom_F(t), P _LIMbatt) [M W ]
(5.3)
Pdischarge max_F(t)=(SOC_F(t1) 0.5) ·Ebatt [M W ](5.4)
SOC_F(t) = SOC_F(t1) + (Pcharge_F(t)Pdischar ge_F(t))/Ebatt [M W ](5.5)
Pgrid headroom(t) = minimum(Pgrid P_RES_F(t),0) [M W ](5.6)
Pdischarge _F(t) = minimum(Pdischarge max_F(t), Pgrid headroom_F(t), P _LIMbatt) [M W ]
(5.7)
It has helped myself to clearly better understand how the bidding model is working and how it
is providing the P_HP P _F(t).
In order to provide more consistency between bidding and real time models this is the definitive
bidding model implemented, it has already checked and is providing the same results as previous
bidding model version too. And finally here in Figure 5.4 is the bidding model algorithm which
has also been included within the Matlab code attached in Appendix A:
5.2 Bidding model algorithm 23
Figure 5.4: Bidding model algorithm
We can see here how the SOC_F(t) dispatch is working properly, I’ve included two dynamic
limiters that rules the battery operation completely, letting the power produced getting in when
it’s possible to meet the model design conditions for battery charging and discharging.
To get that battery capacity will always be above the 50 [%] of its capacity is crucial to
set the SOC_F(t)limits have been set correctly, that is to say, between: [0.5 : 1] [p.u.]
Another important thing done is to check in every single moment that we are working with the
same units and not mixing them, which of course, needless to say would affect badly to the
model methodology designed and completely to the results obtained. As it’s commonly said
being sure that we’re not mixing apples with bananas is extremely important here.
5.2.2 Bidding Model Study Cases
I’ve distinguished 2 different cases to be studied and included within the bidding algorithm and
Matlab code presented in Appendix A, which are:
1st operational condition:
P_RES_F(t)> Pgr id [M W ](5.8)
then we have:
Psurplus_F(t) [M W ](5.9)
2nd operational condition:
P_RES_F(t)<=Pgr id [M W ](5.10)
then we have:
Psurplus_F(t) = 0 [M W ](5.11)
In Table 4.5 have been already presented
E_RES_F
and
Esurplus_F
values for scenario 9 in
DK2 and SE2 hybrid power plants.
24 5 Bidding, Real and Full model Algorithms
5.2.3 Bidding model algorithm behaviour
It’s really important to be aware that battery charging and discharging can not happen at the
same time, so if you charge then you don’t charge and vice versa. Basically we will charge
when we will have available
Psurplus_F
(
t
)due to RES overproduction and will discharge when
we won’t have it, of course we’ll be able to do it having energy stored previously taking into
account SOCF(t)limitation that must always be [0.5 [p.u.] : 1 [p.u.]].
When do I charge the battery?
Every single time I have
Psurplus_F
(
t
)and it’s room in the battery for it, otherwise power
produced will be curtailed partially or entirely depending on the available room for energy
storing. It is important to take into account that
P_LIMbatt
will limit the charge and discharge
operation. Taking a look to Figure 5.4 we can see that we’ll charge when we’re not discharging,
in other words, when
Pbatt
is negative then is meeting the limiter with down limit zero, so it’s
not discharging.
When do I discharge the battery?
Pdischarge _F
(
t
)is calculated as we want to discharge what it takes to get. As we have
just seen it’s important to take into account +
/Pbatt_max_F
limit values that will limit the
charge and discharge operation. Eventually I’m taking the minimum value just to really know
what power is discharged and supplied to grid. Ultimately in the next adder
Pdischarge _F
(
t
)
is compared to
Pdischarge _F_req
(
t
), fruit of both is
P_missing_F
(
t
)that is aggregated to
Pgrid , then we have obtained our bid for real time model, P_H P P _F(t).
What is Pcurtailment_F_total(t)?
Power curtailment is the power spilt because there is no room for it within the battery,
this power produced is not going into the grid. It could be used for selling it later. We have to
take into account a really important aspect, curtailment power is can come from two places
within the Figure 5.4, which are both limiters, when signal is overlimits. So to calculate
Pcurtailment_F_total(t)we have to apply the following formula:
Pcurtailment_F_total(t) = Pcurtailment _F(t) + P0
curtailment_F(t) [M W ](5.12)
5.2 Bidding model algorithm 25
5.2.4 Bidding model results
Bidding model results are widely presented in Chapter 6, but here we can see a quick plotting
comparison for all the forecast time series taking into account 2015 and 2016 years, for several
P_LIMbatt parameter values: 5, 10, 50 and 100 [MW].
(a) P_LIMbatt = 5MW (b) P_LIMbatt = 10MW
Figure 5.5: DK2 Bidding - Scenario 9
(a) P_LIMbatt = 50MW (b) P_LIMbatt = 100MW
Figure 5.6: DK2 Bidding - Scenario 9
To facilitate its better understanding what I’m going to present now is only two days
detailed study so we’ll be able to fully understand the forecast results provided. Firstly we will
see a clear case of charging operation as we have plenty of Psurplus_F(t).
I have chosen two consecutive days, June 17
th
and 18
th
from the power production time
series provided by CorRES, where is a clear example of Psurplus(t)existence.
I’m presenting a complete study including different
P_LIMbatt
values: 5, 10, and 50 [MW]
and Crate = 1 [hour].
26 5 Bidding, Real and Full model Algorithms
(a) P_LIMbatt = 5MW (b) P_LIMbatt = 10MW
Figure 5.7: DK2 forecast - Scenario 9
Figure 5.8: DK2 forecast - Scenario 9 - P_LIMbatt = 50MW
Reviewing Figures 5.7 and 5.8 we can check how
Pcurtailed_F
(
t
),
SOC_F
(
t
)and
Pdischarge _F
(
t
)
is varying according to the
P_LIMbatt
parameter value taken in every single case. I’m present-
ing here in this work specifically in Chapter 6 a complete data analysis using the duration curves.
Secondly now we will see a clear case of discharging operation providing its energy to the grid
as we don’t have much of
Psurplus_F
(
t
)produced this time. I have chosen for showing this two
consecutive days in June 2015, June 8th and 9th for DK2 HPP.
5.2 Bidding model algorithm 27
(a) P_LIMbatt = 5MW (b) P_LIMbatt = 10MW
Figure 5.9: DK2 forecast - Scenario 9
Figure 5.10: DK2 forecast - Scenario 9 - P_LIMbatt = 50MW
28 5 Bidding, Real and Full model Algorithms
Figure 5.11: DK2 forecast - Scenario 9 - P_LIMbatt = 100MW
In these Figures 5.9, 5.10 and 5.11 we can check how
Pcurtailed_F
(
t
),
SOC_F
(
t
)and
Pdischarge _F
(
t
)is varying according to the
P_LIMbatt
value taken in every single case. In this
second case as advanced can be clearly seen how low is
Psurplus_F
(
t
)compare to the first case
above presented. It can be also seen clearly the power generation intermittency of RES.
5.3 Real time model algorithm 29
5.3 Real time model algorithm
In this model I’m working with the actual power production values provided by CorRES, that
is to say:
P_WPP(t) + P_P V P P (t) = P_RES(t) [M W ](5.13)
taking into account the WPP and PVPP capacity installed, as CorRES is providing time series
in per units, so for scenario 9. Another input for this real time model will be hybrid power
production forecast,
P_H P P _F
(
t
), output from the previous model algorithm, bidding model.
Real time model output is the
P_H P P
(
t
), so after obtaining this value we are able to calcu-
late the
P_H P P _F E
(
t
)and quantify how good our hybrid power production forecast has been.
As we have also seen within the bidding model that the battery charging and discharging
operation can not happen both at the same time. So if you charge then you don’t charge and
vice versa. So basically we will charge when we’ll have
Psurplus
(
t
)and will discharge when we
won’t and, of course, having stored energy previously within the BESS to be provided to the grid.
It’s really important to take into account that our bid is:
P_H P P _F
(
t
), 1 DA, so it means
that we are saying that our forecast obtained the previous day, is what is going to happen in
the actual day, that could be fully understood checking the real time model flowchart presented
in this fifth chapter, point 5.3.2.
Once we have run both models, bidding and real time model, then hybrid power produced
forecast error, P_H P P _F E(t), can be calculated as:
P_H P P _F E(t) = P_H P P (t)P_HP P _F(t) [M W ](5.14)
5.3.1 Inputs, outputs, parameters and assumptions
Real time model inputs:
Wind and solar power production measured: PRES (t) [M W ]
Power grid connection constrain: Pg rid = 100 [M W ]
Hybrid power production forecast: PH P P _F[M W ]
Battery capacity: Ebatt [M W h]
Initial state of charge: SOC0[p.u.]
Parameters:
P_LIMbatt [M W ]
Crate [h]
30 5 Bidding, Real and Full model Algorithms
Assumption:
Sampling time resolution: 1 [hour]
Real time model outputs:
State of charge: SOC(t) [p.u]
Hybrid power produced measured: P_H P P (t) [M W ]
Power curtailed: Pcur tailed_total(t) [M W ]
5.3.2 Real time model flowchart
Figure 5.12: Real time model algorithm flowchart
5.3.3 Real Time Model Study cases
I’ve distinguished 3 different cases to be studied and included within the real time algorithm
and Matlab code, which are:
1st operational condition:
P_RES(t)> P _H P P _F(t) [M W ](5.15)
then we have:
Pbatt(t)_req < 0 [M W ](5.16)
2nd operational condition:
P_RES(t)< P _H P P _F(t) [M W ](5.17)
then we have:
Pbatt(t)_req > 0 [M W ](5.18)
5.3 Real time model algorithm 31
3rd operational condition:
P_RES(t) = P_H P P _F(t) [M W ](5.19)
then we have:
Pbatt(t)_req = 0 [M W ](5.20)
So we are calculating Pbatt(t)_req as:
Pbatt(t)_req =P_HP P _F(t)P_RES(t) [M W ](5.21)
and taking into account that the corresponding operational condition
Pbatt
(
t
)
_req
will be
positive, negative or zero.
Our priority is to minimize the hybrid power plant forecast error,
P_H P P _F E
(
t
). So
this time we are not keeping the 50 [%] of the battery capacity all the time as I have presented
in bidding model algorithm. As soon as we get power we will try to provide it to the grid if it’s
possible. I’m remarking again that it is not possible to charge and discharge at the same time,
this has been also taken into account in the real time model algorithm.
5.3.4 Real time model algorithm behaviour
It is really important to be aware that battery charging and discharging can not happen at the
same time, as happened with previous model presented, bidding model. So if you charges then
you can’t charge and vice versa.
When do I charge the battery?
Every single time I have
Psurplus
(
t
)and it’s room in the battery for it, otherwise it will be
curtailed. It is important to take into account
P_LIMbatt
that will limit the charge and
discharge operation. Taking a look to Figure 5.12 we can see that we’ll charge when we are not
discharging, in other words, when
Pbatt
is negative then is meeting the limiter with down limit
with zero value, so it’s not discharging.
When do I discharge the battery?
Pdischarge
(
t
)is calculated as we want to discharge what it takes to get. As we have just seen it’s
important to take into account +
/Pbatt_max
limits that will limit the charge and discharge
operation. I’m taking the minimum value just to really know what power is discharged and
supplied to grid. Finally in the next adder
Pdischarge
(
t
)is compared to
Pdischarge _req
(
t
), fruit
of both is
P_missing
(
t
)that is aggregated to
P_H P P _F
(
t
), our bid from bidding model,
then we have obtained our bid for real time model, P_H P P (t).
What is Pcurtailment_total(t)?
It’s the power spilt because there is no room for it within the battery, this power produced is
not going into the grid. It could be used for selling it later. We have to take into account a
really important aspect, curtailment power is can come from two places within the Figure 5.12,
which are both limiters, when signal is overlimits. So to calculate
Pcurtailment_total
(
t
)we have
to apply the following formula:
Pcurtailment_total(t) = Pcurtailment (t) + P0
curtailment(t) [M W ](5.22)
32 5 Bidding, Real and Full model Algorithms
5.3.5 Real time model results
Measured results are widely presented in Chapter 6, but here we can see a quick comparison
plotting for all the forecast time series taking into account 2015 and 2016 years, for several
P_LIMbatt values.
Figure 5.13: DK2 measured - Scenario 9 - P_LIMbatt = 5MW
Figure 5.14: DK2 measured - Scenario 9 - P_LIMbatt = 100MW
5.3 Real time model algorithm 33
To facilitate its understanding what we are going to do now is only a two days detailed
study so we’ll be able to fully understand the forecast results provided.
I have chosen two consecutive days, June 17
th
and 18
th
2016 from the time series provided,
where is a clear example of Psurplus(t)existence.
I’m presenting a complete study including different
P_LIMbatt
values: 5, 10, 50 and 100
[MW] and Crate = 1 [hour].
(a) P_LIMbatt = 5MW (b) P_LIMbatt = 10MW
Figure 5.15: DK2 measured - Scenario 9 -
P_LIMbatt
= 5
MW
and
P_LIMbatt
= 10
MW
Figure 5.16: DK2 measured - Scenario 9 - P_LIMbatt = 50MW
In these figures above we can check how
Pcurtailed
(
t
),
SOC
(
t
)and
Pdischarge
(
t
)are varying
according to the
P_LIMbatt
value taken in every single case. I’m presenting here in this work
34 5 Bidding, Real and Full model Algorithms
specifically in Chapter 6 a complete data analysis using the duration curves.
Secondly we will see a clear case of discharging operation providing its energy to the grid as we
don’t have much of
Psurplus
(
t
)power produced this time. I have chosen for showing this two
consecutive days in June 2015, June 8th and 9th for DK2 HPP.
(a) P_LIMbatt = 5MW (b) P_LIMbatt = 10MW
Figure 5.17: Days with low Psurplus(t)Pbatt = 5 and 10 [M W ]
(a) P_LIMbatt = 50MW (b) P_LIMbatt = 100MW
Figure 5.18: Days with low Psurplus(t)Pbatt = 50 and 100 [M W ]
Finally in these Figures 5.17 and 5.18 we can see how
Pcurtailed
(
t
),
SOC
(
t
)and
Pdischarge
(
t
)
are varying according to the
P_LIMbatt
value taken in every single case. In this second case as
advanced can be clearly seen how low is
Psurplus
(
t
)compare to the first case above presented.
It can be seen also clearly the intermittency of RES power generation again, as it has already
happen with the forecast too.
5.4 Full model algorithm 35
5.4 Full model algorithm
Here full model algorithm is presented, where forecast and real time models are integrated
together, taking into account the time execution sequence for both.
Full model inputs:
Wind and solar time series: WPP_F(t),P V P P _F(t),WPP(t)and P V P P (t) [p.u.]
Wind and solar capacities
P_WPP_F
,
P_P V P P _F
,
P_WPP
and
P_P V P P
[
MW
]
Parameters:
Wind power capacity P_WPP [MW ]
Solar pv power capacity P_P V P P [M W ]
Assumption:
Time resolution: 1 [hour]
Full model outputs:
HPP power produced: P_H P P (t) [M W ]
Hybrid power plant forecast error: P_H P P _F E(t) [M W ]
5.4.1 Full model flowchart
Figure 5.19: Full model algorithm flowchart
36 5 Bidding, Real and Full model Algorithms
5.4.2 Full model algorithm behaviour
CorRES software is providing us the wind and solar production time series, for bidding and for
real time models, in [p.u.]. As we’re having different wind and solar capacities for every single
one of the scenarios, e.g. for scenario 9, having as results the following:
P_RES_F(t)=(WPP_F(t)) ·P_WPP + (P V P P _F(t)) ·P_P V P P [M W ](5.23)
P_RES(t)=(WPP(t)) ·P_WPP + (P V P P (t)) ·P_P V P P [M W ](5.24)
Then, firstly
P_RES_F
(
t
)is taken into account within the bidding algorithm meanwhile
P_RES(t)will be entering within the real time model.
Secondly once we have already obtained
P_H P P _F
(
t
), as bidding model output, that will be
one of the inputs for the real time model together with the previously mentioned
P_RES
(
t
).
Finally we’re obtaining the full model outputs, which are:
P_H P P
(
t
)supplied to the grid and
P_H P P _F E
(
t
). As we have seen during this master thesis hybrid power plant forecast error
will tell us how good the forecast, which was our 1 day ahead bid. All the hybrid power plant
forecast error metrics calculated are provided in detail in Chapter 7
CHAPTER 6
Data Analysis
6.1 Duration curves
Duration curves is another way of plotting the ramp rates, which haven’t been used here,
but this time the results are plotted in a sorted manner, e.g. based on its value and not
chronologically. Then we are able to check for a certain number of hours how much the power
variation is. The maximum and minimum values are exactly the same as in the time series
plotting as I haven’t changed anything about how I’m calculating from time series plotting
method to this one. What the duration curve is telling us is for how long we can expect what
kind of changes, so we can see the power variability.
Cumulative distribution function:
A cumulative frequency distribution is the sum of the
class and all classes below it in a frequency distribution which means that is the sum of the
events when the signal has a certain value. So in cumulative distribution function we are
counting how many times the signal has every single value. It can be also done for different
bins or changes in the power production.
What I’m including here in the first 2 figures, Figures 6.1a and 6.1b, following below is
the main relevant aspects for the forecast as:
P_RES_F(t)
Psurplus_F(t)
Pcurtailed_F(t)
Pcharge _F(t)
Pdischarge _F(t)
SOC_F(t)·Ebatt
P_H P P _F(t)
I’ve changed the values of
P_LIMbatt
parameter taking: 5, and 50 [
MW
]values maintaining
E_batt size to 100 [
M W h
], these figures have been plotted using the bidding model presented
in Chapter 5, which are:
38 6 Data Analysis
(a) P_LIMbatt = 5MW (b) P_LIMbatt = 50MW
Figure 6.1: DK2 Forecast duration curves
Some of the observation that I can get from these figures reviewing is how is reduced
Pcurtailed_F
(
t
)when
P_LIMbatt
is increased from 5 [
MW
]to 50 [
MW
]. As it was expected
and have been explained in this master thesis work one of the two main advantages of using
energy storage is minimizing the curtailment, the bigger the better in terms of reducing power
curtailed.
Secondly, another important aspect of plotting these duration curves is to check
SOC_F
(
t
),
then we can see that takes a little more time to get the 100 [%] of its capacity when
P_LIMbatt
value is 50 [
MW
]. It is understandable as battery size will be bigger too. Also it can be seen how
the
SOC_F
(
t
)is behaving as expected in this bidding model due to the design methodology,
maintaining 50 [%] as minimum value of its capacity all the time.
Finally we can see what happens to
P_H P P _F
(
t
)in both cases, where for a higher
P_LIMbatt
value and a bigger battery size we can provide during more time the power grid connection
constrain value,
Pgrid
= 100 [
MW
]. This would be the main conclusion, the bigger the better,
in terms of battery size, as we can provide and comply with
Pgrid
during more time and this
exactly one of the actions we want to obtain from this model. It is important to remark that
bidding model presented is not the optimized model. I’m sure that can be presented other
model versions which better optimize their results, but what it’s for sure is that the bidding
model presented is working with consistency and reliability providing good results as we can
see.
Now I’m doing the same for the real time model, the next two figures are plotted using it
and the main relevant aspects are:
P_RES(t)
Psurplus(t)
Pcurtailed(t)
Pcharge (t)
Pdischarge (t)
6.1 Duration curves 39
SOC(t)·Ebatt
P_H P P (t)
(a) P_LIMbatt = 5MW (b) P_LIMbatt = 50MW
Figure 6.2: DK2 Measured duration curves
Some of the observations that I can get from these figures reviewing is how is reduced
Pcurtailed_F
(
t
)when
P_LIMbatt
is increased from 5 [
MW
]to 10 [
MW
]. Here we can also
see another great difference compared to bidding model, which is that for lower
P_LIMbatt
values curtailment is really high, increasing dramatically 20 [%] of the time. It’ seen also that
curtailment is happening approximately 50 [%] of the time.
If we increase
P_LIMbatt
for a same
Ebatt
value we can easily see how the direct conse-
quences of doing it are. There are mainly two: we’ll reduce dramatically curtailment till just
having less than 5 [%] of the time and these curtailment values will be really high. Here we
can see another big difference compared to bidding model, and this is due to our main model
strategy which is minimizing the forecast error, P_HP P _F E (t).
Again as expected one of the two main advantages of using energy storage is minimizing
the curtailment, the bigger the better but for real time model we can see that this also affects
to the high value of it when we increase P_LIMbatt values.
Here, in the real time model, it’s important to say that the design methodology for the
SOC_F
(
t
)is different to the previous model, it can be easily seen when checking the limits
of the dynamic limiters included within the real time model in the SOC dispatch. Secondly,
another important aspect of plotting these duration curves is to check
SOC_F
(
t
), then we can
see that takes more time to get the 100 [%] of its storing capacity when
P_LIMbatt
= 50 [
MW
],
more than it does with bidding model too. Thirdly, battery is remaining completely empty more
than 35 [%] of the time for lower
P_LIMbatt
values, 25[%] of the time for higher
P_LIMbatt
values as it happens with P_LIMbatt = 50 [M W ].
Again we can see what happens to
P_H P P
(
t
)in both cases, for a higher
P_LIMbatt
value,
we can provide during more time the power grid connection constrain value,
Pgrid
= 100 [
MW
].
This would be the main conclusion, the bigger the better as we can provide and comply with
the
Pgrid
during more time and this exactly one of the actions we want to obtain from this
40 6 Data Analysis
model. It is important to remark that real time model presented is not the optimized model
neither. I’m sure that can be presented other model versions which better optimize the results,
but what it’s for sure is that this real time model presented is working with consistency and
reliability providing good results, as we can see.
Finally if we take into account bidding and real time model figures we can conclude that
we are reducing the forecast error of the hybrid power plant,
P_H P P _F E
(
t
). This is going
to be studied in detail in the next chapter, Chapter 7 where I’m presenting the forecast error
metric calculated and their results.
6.2 Spot market bidding methodology
I have taken into account several different battery limits,
P_LIMbatt
[
MW
]in both HPP loca-
tions for this scenario 9 detailed study. I have also taken into account that
Ebatt
= 100 [
M W h
]
and Crate = 1 [hour].
Changing
P_LIMbatt
because this parameter will affect to the forecast
Pcharge _F
(
t
),
Pdischarge _F
(
t
),
Pcurtailed_F(t), and of course P_H P P _F(t)too.
6.2.1 Hybrid power production forecast
Figure 6.3: DK2 P_H P P _F(t)-P_LIMbatt = 5[M W ]Ebatt = 100[M W h]
6.2 Spot market bidding methodology 41
Figure 6.4: DK2 P_H P P _F(t)-P_LIMbatt = 25[M W ]Ebatt = 100[M W h]
Figure 6.5: DK2 P_H P P _F(t)-P_LIMbatt = 50[M W ]Ebatt = 100[M W h]
42 6 Data Analysis
Figure 6.6: DK2 P_H P P _F(t)-P_LIMbatt = 75[M W ]Ebatt = 100[M W h]
In these four Figures above, 6.3, 6.4, 6.5 and 6.6, we can clearly observe two main things: Firstly
SOC_F
(
t
)
·Ebatt
which is reaching full charge just 15 [%] of the time for
P_LIMbatt
= 5 [
MW
]
which is only 12
.
5 [%] approximately, here we can see that in terms of battery full capacity
charged we need to increase
P_LIMbatt
values otherwise most of the time we’ll be below full
charge situation.
Secondly, how
Pcurtailed
(
t
)is behaving when I’m increasing
P_LIMbatt
from 5 [
MW
]till
75 [
MW
], also it can be seen that there is no change detected from 50 to 75 [
MW
], having the
same
Pcurtailed
(
t
)value. In this case I would say that there is no justified reason for increasing
P_LIMbatt
parameter value, but we have to take into account that the other main reason of
including BESS is minimizing forecast error. So we’ll need to check first about it and after to
make the right decision looking at the whole picture.
Finally we can see how is
P_H P P _F
(
t
)just reaching
Pgrid
between the: [25% : 27
.
5%]
of the time depending on the
P_LIMbatt
value taken. Here you can see another difference with
the real time model where
P_H P P
(
t
)can’t manage to reach
Pgrid
during as much time as
bidding model does.
6.3 Hybrid power production real time measured 43
6.3 Hybrid power production real time measured
Figure 6.7: DK2 P_H P P (t)-P_LIMbatt = 5[M W ]Ebatt = 100[M W h]
Figure 6.8: DK2 P_H P P (t)-P_LIMbatt = 25[M W ]Ebatt = 100[M W h]
44 6 Data Analysis
Figure 6.9: DK2 P_H P P (t)-P_LIMbatt = 50[M W ]Ebatt = 100[M W h]
Figure 6.10: DK2 P_H P P (t)-P_LIMbatt = 75[M W ]Ebatt = 100[M W h]
As it has happened in the last point these four Figures above, 6.7, 6.8, 6.9 and 6.10, are showing
mainly two aspects: Firstly
SOC
(
t
)
·Ebatt
which is reaching full charge just [57
.
5%] of the time
less for
P_LIMbatt
= 5 [
MW
]which is only [67
.
5%] approximately, here we can see that in
6.4 Energy surplus forecast 45
terms of battery full capacity charged we need to increase
P_LIMbatt
values otherwise most of
the time we’ll be below full charge situation. If we compare to forecast figures from last point
there is another aspect, the behaviour of
SOC_F
(
t
)and
SOC
(
t
)is different, and this because
bidding and real time model have different limits within the second limiter placed in SOC
dispatch. Bidding model is keeping all the time this established range between: [0
.
5 : 1] [
p.u.
]
meanwhile real time model isn’t.
Secondly, how
Pcurtailed
(
t
)is behaving when increasing
P_LIMbatt
from 5 [
MW
]till 75 [
MW
].
But here it is a great difference with last point as I have detected a different behaviour
Pcurtailed
(
t
). This is due to the real time methodology algorithm design which is slightly
different as it can be seen in Chapter 5.
Finally we can see how is
P_H P P
(
t
)just reaching
Pgrid
between the: [17
.
5% : 21%] of
the time depending on the
P_LIMbatt
value taken. Here you can see another difference with
the bidding model where P_H P P _F(t)manage to reach Pgrid during a little more time.
6.4 Energy surplus forecast
Pgrid connection constrain is constant, its power value is: 100[M W ].
Psurplus(t)_Fis defined as:
P_RES_FPgr id [M W ](6.1)
when:
P_RES_F > Pgrid [M W ](6.2)
So you can obtain Esurplus(t)_Fjust summing up its Psurplus(t)_Ffor all the time series.
DK2 Esurplus_F(t)
Esurplus_F(t) = 30.404 [GW h/year](6.3)
SE2 Esurplus_F(t)
Esurplus_F(t) = 13.273 [GW h/year](6.4)
6.5 Energy curtailed forecast
Pcurtailed
(
t
), measured and forecasted, is defined as the power spilt that you can storage within
the battery because it’s fully loaded. As I have said before one of the main effects of including a
BESS is reducing
Pcurtailed
(
t
), storaging all the energy we can within the battery and supplying
it later to the grid.
So you can obtain
Ecurtailed
(
t
)
_F
just summing up its
Pcurtailed
(
t
)
_F
for all the time se-
ries. This is one of the outputs of the spot market bidding model algorithm.
46 6 Data Analysis
6.5.1 DK2 Ecurtailed_F(t)
Ecurtailed_F
(
t
)will vary from one battery size chosen to other, also as we can see here in the
table below, will be
Crate
dependent. Concluding the much bigger battery size we include
within HPP the better as we will reduce
Pcurtailed
(
t
)and
Ecurtailed
(
t
)so hybrid power plant
forecast error, P_H P P _F E(t).
We are going to see here some results obtained with the bidding model presented in
Chapter 7
using Matlab code included in the
Appendix A
. It has been taken into account
Ebatt
= 100 [
MW
]
and Crate = 1 [hour].
P_LIMbatt [MW] Ecurtailed(t) [GW h/year]
10 46.797
20 6.685
30 0.236
40 0.236
50 0.236
Table 6.1: DK2 Ecurtailed _F(t) [GW h/year]
So we can see how increasing 5 times P_LIMbatt we can highly reduce Ecurtailed_F(t).
6.6 Capacity factor forecast 47
6.5.2 SE2 Ecurtailed_F(t)
P_LIMbatt [MWh] Ecurtailed(t) [GW h/year]
10 20.102
20 5.834
30 0.095
40 0.095
50 0.095
Table 6.2: SE2 Ecurtailed _F(t) [GW h/year]
So we can see how increasing 5 times P_LIMbatt we can highly reduce Ecurtailed_F(t).
6.6 Capacity factor forecast
DK2 C F _F(t)Capacity factor forecast for DK2 HPP is:
DK2C F _F= 53.75 [%]
and full work hours forecast for DK2 HPP is:
DK2FWH_F= 4708.50 [hours]
SE2 C F _F(t)
Capacity factor forecast for SE2 HPP is:
SE2C F _F= 34.62 [%]
and full work hours forecast for SE2 HPP is:
SE2FWH_F= 3032.12 [hours]
CHAPTER 7
Forecast Error
7.1 Introduction
We have to say that when we’re talking about minimizing the forecast error, as it’s our main
criteria and strategy followed in the presented methodology included in
Chapter 5
, we have to
take into account the two dimensions of it, the power and the energy.
If we’re talking about power dimension, using the duration curves then what we can see
is having one determined battery size how much power I’ll be able to minimize in terms of the
time, in [MW] units.
On the other side if we take into account the developed algorithm then we can talk about the
energy side, the state of charge, SOC (t)in [MWh] units.
It’s already known that a storage unit consists in two parts:
electrical infrastructure mainly with the converter, [MW ]
battery bank, which is placed behind, [M W h]
The battery bank, energy side, is the most critical, which means how much battery and how
many battery hours we have. Both, power and energy side are duable, but second is more
costly. In this master thesis I’m not going through a cost study of the battery as it is out of
the scope but it is important to know that it has changed dramatically during the last ten
years, nowadays it’s about
P ricebattery bank
= 230 [$
/M W h
]. What we have seen during the last
decade is that this battery energy price for battery bank has been decreasing dramatically and
it’s expected that this will happen even more. It should not be forgotten in cost calculations
the battery converters price either.
So it will be a compromise between reducing the hybrid power plant forecast error,
P_H P P _F E
(
t
)
and the overcost added buying more battery.
We don’t have to forget, as commented previously in this master thesis, we’re using this
battery to utilize the curtailed power, that would also mean we have a little value of reduction
of cost of energy, CHP P [e/M W h].
In this master thesis a complete study taking into account different energy capacities is
presented.
7.2 Forecast error metrics: MAFE and RMSFE 49
7.2 Forecast error metrics: MAFE and RMSFE
With the forecast error metrics we can see easily how relevant the effects of including an
BESS
within the wind and solar photovoltaic power plant are.
Forecast error metrics formulas:
Mean Absolute Forecast Error:
M AF E =1
n·
n
X
n=1
|(yjˆyj)|(7.1)
Root Mean Square Forecast Error:
RM SF E =v
u
u
t
1
n·
n
X
n=1
(yjˆyj)2(7.2)
and this equation must always be fulfilled:
RM SF E M AF E (7.3)
where:
yiis measured hybrid power production P_HP P (t) [M W ]
ˆyjis forecast hybrid power production P_HP P _F(t) [M W ]
being the hybrid power plant forecast error, P_HP P _F E (t), which can be calculated:
P_H P P _F E(t) = P_H P P (t)P_HP P _F(t)(7.4)
being:
Pgrid
= 100 [
MW
],
Ebatt
= 100 [
M W h
]and
Crate
= 1 [
hour
]. Previously using the time
series provided by CorRES and taking into account the wind and solar capacity installed for
scenario 9, I’ve calculated MAE and RMSE for P_RES_F E(t), where this is:
P_RES_F E (t) = P_RES(t)P_RES_F(t)(7.5)
having the following results for DK2 and SE2 RES locations:
RES MAE_H P P _RES(t)[M W ]RMSE_RES_F E(t)[M W ]
DK2 18.1 26.5
SE2 14.9 22.9
Table 7.1: DK2 and SE2 Scenario 9
P_RES_F E
(
t
):
MAE_RES_F E
(
t
)and
RMSE_HP P _F E(t)
Knowing this two forecast error metrics then now I’m presenting how the inclusion of a
BESS affects to the reduction of the P_H P P _F E(t)for DK2 HPP:
50 7 Forecast Error
P_LIMbatt [M W ]MAE_H P P _F E(t)[M W ]RM SE_H P P _F E(t)[M W ]
5 7.0 16.3
25 6.7 16.6
50 6.7 16.8
75 6.7 16.8
Table 7.2: DK2 Scenario 9
P_H P P _F E
(
t
):
MAE_H P P _F E
(
t
)and
RMSE_HP P _F E(t)
And for SE2 HPP:
P_LIMbatt [M W ]MAE_H P P _F E(t)[M W ]RM SE_H P P _F E(t)[M W ]
5 7.0 16.0
25 6.7 16.3
50 6.7 16.5
75 6.7 16.5
Table 7.3: SE2 Scenario 9
P_H P P _F E
(
t
):
MAE_H P P _F E
(
t
)and
RMSE_HP P _F E(t)
We can easily observe that including BESS has a real effect on the reduction of the forecast
error, between: [2
.
5 : 2
.
7] times for DK2 HPP and [2
.
1 : 2
.
21] times for SE2 HPP. Another
interesting conclusion that we can draw from these results is that we will have more success
when we have better power production. With the figures I’ve calculated it can be seen that we
can reach 0.5 points of difference if we look at the reduction range.
Another important conclusion can be drawn from the results and is that as much bigger
value of
P_LIMbatt
the better for reducing forecast error. Please remember that I have used
for this calculation an Ebatt = 100 [M W ].
Finally answering to the question How much can we reduce forecast error adding BESS
in Scen. 9? here it’s the answer and results:
P_LIMbatt [M W ]DK2P_HP P _F E(t)reduction[%] SE2P_H P P _F E(t)reduction[%]
5 61.28 53.11
50 63.12 54.82
Table 7.4: DK2 and SE2 Scenario 9 P_H P P _F E(t)reduction[%]
CHAPTER 8
Conclusions and Future work
8.1 Main important aspects learnt
During the master thesis work all along this five months period I’ve learnt the following aspects:
Relevance of battery energy storage system inclusion in wind and solar power plants.
Study of the proper strategy to be applied to get a forecast error reduction.
Developing of model methodology: bidding and real time algorithms.
The importance of the optimization of both algorithms if we want to have success reducing
penalties.
To work with forecast and real time data provided by CorRES.
The effect of choosing a good forecast to be taken into account 1 Day Ahead as our bid.
Relevance and impact of battery energy storage size in the forecast error reduction.
8.2 Contributions
Reviewing the most relevant results obtained during this master thesis work I’ve have clearly
presented the following aspects:
Bidding model algorithm development and methodology
Real time model algorithm development and methodology
Forecast error metric calculations where can be checked the effectiveness of the models
A complete data analysis of the SOC(t),Pcurtailed(t)and P_H P P (t)
52 8 Conclusions and Future work
8.3 Conclusion
As RES are totally weather dependent so are intermittent and stochastic resources and there
is an essential need of incorporate battery energy storage systems. It is known that if we
want to complete and allow them to be fully integrated within the energy market then BESS
participation is absolutely necessary. RES are very valuable and adding energy storage systems
to the hybrid wind and solar plants if integrated in large scale. Including BESS we’re boosting
and allowing them to provided system services and congestion reduction for power systems.
During this master thesis work reviewing all the data analysis provided I can conclude the high
impact that battery energy storage has on two main aspects, which are:
minimizing the forecast error, P_H P P _F E(t)
minimizing the power curtailment, Pcurtailed(t)
Another important aspect to be taken into account is the relevance of
P_LIMbatt
parameter
value, it has been fully reviewed the effect of its increase and how it affects to curtailment and
forecast error reduction too. To have success with both aspects battery size is decisive, being
a rule of thumb, the bigger the better in terms of forecast error and curtailment reduction.
Of course, needless to say that the model methodology algorithm design is crucial to achieve
excellent results. For that purpose it is necessary to establish correctly which is going to be
your strategy and priority. In this work it has been to minimize the forecast error.
Then BESS becomes more relevant, in terms of improving its revenue being able to sell
the energy when prices are higher. As it allows us to move the power in time transferring to
the grid at later times when the price is higher.
8.4 Future work 53
8.4 Future work
Further research aim to cover the following aspects:
To Develop model methodology algorithm to reach the optimal forecast error reduction.
RES power generation forecasting using ensemble approach based on deep learning and
statistical methods.
To include within the model methodology development the spot market prices as one of
the inputs.
To include new energy storage system combinations: electric + thermal and chemical
storage to be added to the hybrid wind and solar pv plant.
Integration of Power-to-X technologies storage in energy islands.
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Appendix A: Matlab Code
This Matlab code presented has not been optimized but implemented following a clarity criteria,
although I have already verified that the code is correct and the contribution of this master
thesis is valid, this code must be used for reference purposes only, without any warranty or
liability for my part.
1
2% === = = = = = = ====== = = = = = = == ===== = = = = = = = ====== = = = = = = ====== = = = = = = ====== = = = = %
3% Emilio Barrachina Gasco %
4% s1 8 2 80 4 @ s tu d e n t . d tu . d k %
5% Master thesis %
6% Wind Energy Master %
7% Te c h n i c a l U n i v e r s i t y o f D e n m a r k %
8% J u ly 1 s t 2 0 20 %
9% === = = = = = = ====== = = = = = = == ===== = = = = = = = ====== = = = = = = ====== = = = = = = ====== = = = = %
10
11 c le a r a ll ;c l os e a l l ;cl c ;
12
13 %% CorRES TIME SERIES INPUTS
14
15 %% INPUTS
16
17 P_RES_F = xlsread(’ DK 2 R ES _F ’ ,’ S ce n a ri o 9 ’ ,’ B 2 : B 17 5 4 5 ’ );
18 f re q u en c y = x ls r e ad ( ’ DK 2 R ES _F ’ ,’ S ce n a ri o 9 ’ ,’ C2 : C 1 7 54 5 ’ ) ;
19 P _R E S = x l sr e a d ( ’ DK 2 R ES ’ ,’ S ce n a ri o 9 ’ ,’ A 2 : A 17 5 4 5 ’ );
20
21 % Zo o m s t u dy for on l y t wo days
22 %{
23 P_RES_F = xlsread(’ DK 2 R ES _F ’ ,’ S ce n a ri o 9 ’ ,’ B 2 : B4 8 ’ ) ;
24 f re q u en c y = x ls r e ad ( ’ DK 2 R ES _F ’ ,’ S ce n a ri o 9 ’ ,’ D2 : D 49 );
25 P _R E S = x l sr e a d ( ’ DK 2 R ES ’ ,’ S ce n a ri o 9 ’ ,’ C 2 : C4 9 ’ ) ;
26 %}
27 t_range = 1:1 7 5 4 4 ;
28 tim e = 1 : length(t_range);
29
30
31 SOC_pre_F = 0.5; % [ p . u . ]
32 SOC_pre = 0. 5 ; % [ p . u .]
33 P_grid = 100; % [ MW ] , g r i d c o nn e c t io n p o we r c on s t ra i n
34
35 C_rate = 1; % [ h o u rs ] , we can c h a n g e it to 2, 4 , 6 , 8 h o u r s
36 P_LIM_batt = 50; % [ MW ] , w e c an c h oo s e a h i gh e r v al u e , 2 5 , 50 , 7 5 ,. . .
37 % P _b a tt _ ma x _F = P _ LI M_ b at t / C _r at e ;
58 Appendix A: Matlab Code
38 % P _b a tt _ ma x = P_ L IM _ ba t t / C_ ra t e ;
39 P _b a tt _ ma x _F = P _L I M_ b at t ;
40 P _b a tt _ ma x = P_ L IM _ ba t t ;
41
42 E_batt = 10 0; % [ M Wh ]
43
44 %% YE A R L Y R ES ENERGY GENERATED AND C A P A C I T Y F A C T O R : FO R E C A S T A ND MEASURED
45
46 for t = ti m e
47 P _R E S_ F ( t) = P _R ES _ F (t ) ;
48 E_RES_F=su m (P_RES_F );
49 E _R E S_ F _y e ar = E _ RE S _F / 2 ;
50
51 P _R ES ( t ) = P_ R ES ( t );
52 E _R E S = su m ( P _R ES ) ;
53 E _R E S_ y ea r = E _R E S /2 ;
54 end
55
56 E_RES_F_year = E_RES_F_year /1000000 % [ TW h / y ea r ]
57 E_RES_year = E_RES_year / 1 0 0 0 0 0 0 % [ TW h / y ea r ]
58
59 C F_ F = (( E _ RE S _F _ ye a r ) /( 8 76 0 ) ) *1 00 0 00 0 % [%]
60 CF = ( ( E_ R ES _ ye a r ) /( 8 76 0 ) ) *1 00 0 00 0 % [ %]
61
62 % FU L L WORK HOU R S : FO R E C A S T A N D MEASURED
63 FWH_ F = ( CF _F * 87 60 ) /1 00 % [ h ou r s /y e ar ]
64 F WH = ( C F * 8 76 0 ) / 1 00 % [ h ou rs / y e ar ]
65
66
67 %% BIDDING M ODEL
68 for t = ti m e
69
70 P _d i sc h ar g e _r e q_ F ( t) = - P_ R ES _ F (t ) + P_ g ri d ;
71
72 if P _ RE S _F ( t ) > P _g ri d
73 P _s u rp _ F (t ) = P _ RE S _F ( t ) - P _g ri d ;
74
75 elseif P _R E S_ F ( t) <= P _g ri d
76 P _s u rp _F ( t ) = 0;
77 end
78
79 if P_discharge_req_F (t)<0
80 P_discharge_req_F(t)=0;
81 end
82 P _b a tt _ re q _F ( t )= - P _R E S_ F ( t) + P _g r id ;
83 if P_batt_req_F (t)>P_batt_max_F
84 D el t a_ S OC _ re q _F ( t )= P _ ba t t_ ma x _F * ( -1 / E_ b at t );
85 P _c u r ta i l me n t _F ( t ) =0 ;
86 elseif P_batt_req_F(t)<-P_batt_max_F
87 D el t a_ S OC _ re q _F ( t )= - P _b a tt _ ma x_ F * ( -1 / E_ b at t );
88 P _c u rt a il m e nt _ F (t ) = P_ b at t _m a x_ F - P _ ba t t _r e q_ F ( t) ;
89 else
Appendix A: Matlab Code 59
90 D el t a_ S OC _ re q _F ( t )= P _ ba t t_ re q _F ( t ) *( - 1/ E _b a tt ) ;
91 P _c u r ta i l me n t _F ( t ) =0 ;
92 end
93 if D e l ta _ SO C _ re q _F ( t ) + SO C _p re _ F > 1
94 S OC _ F (t ) = 1;
95 P _c u rt a il m en t _F _ ( t) = D el t a_ SO C _r e q_ F ( t) + S OC _p re _ F - 1;
96 elseif D el t a_ S O C_ r eq _ F ( t) + S OC _ pr e _F <0 . 5
97 S OC _F ( t ) = 0. 5;
98 P_curtailment_F_(t)=0;
99 else
100 S OC _F ( t )= D e lt a _ SO C _r e q_ F ( t) + S OC _ pr e _F ;
101 P_curtailment_F_(t)=0;
102 end
103 D el t a_ S OC _ F ( t) = S OC _ F (t ) - S OC _ pr e _F ;
104 S OC _ pr e _F = S O C_ F ( t) ;
105 P _b a t t _F ( t ) = D e l ta _ S O C_ F ( t ) *( - E _b a t t / 1 ) ;
106 if P _ ba t t_ F ( t) > =0
107 P _d i sc h ar g e_ F ( t) = P _b a tt _ F (t ) ;
108 P _c h a rg e _F ( t ) =0 ;
109 else
110 P _d i s ch a r ge _ F ( t ) =0 ;
111 P _c h ar g e_ F ( t) = - P_ b at t _F ( t );
112 end
113 P _m i ss in g _F ( t )= - P _d i sc h ar g e_ r eq _ F (t ) + P_ d is c ha r ge _F ( t ) ;
114 P _H PP _ F (t ) = P_ g ri d + P_ m is s in g _F ( t );
115 P _c u rt a il m en t _t o ta l _F ( t )= P _ cu r ta i lm e nt _ F (t ) + P_ c ur t ai lm e nt _ F_ ( t );
116 end
117
118 %% REAL T I ME M O D E L
119 for t = ti m e
120
121 P _d i sc h a rg e _r e q ( t) = - P _R ES ( t ) + P_ H PP _ F (t ) ;
122 if P _ RE S ( t) > P _g r id
123 P _s ur p ( t ) = P _ RE S ( t) - P _ gr i d ;
124 elseif P _R ES ( t ) < = P _g ri d
125 P _s ur p ( t ) = 0 ;
126 end
127
128 if P _ di s ch a rg e _r e q (t ) <0
129 P _d i s ch a r ge _ r eq ( t ) =0 ;
130 end
131 P _b a tt _ re q ( t )= - P _R E S (t ) + P _H P P_ F ( t) ;
132 if P _ b a tt _ r eq ( t ) > P _b a t t_ m a x
133 D el t a_ S OC _r e q (t ) = P _b at t _m a x *( - 1/ E _ ba tt ) ;
134 P _c u r ta i l me n t ( t ) =0 ;
135 elseif P _b a tt _ r eq ( t ) <- P _ b at t _m a x
136 D el t a_ S OC _r e q (t ) = - P_ ba t t_ m ax * ( -1 / E _b at t ) ;
137 P _c u rt a il m en t ( t) = P _b at t _m ax - P _ ba t t_ r eq ( t );
138 else
139 D el t a_ S OC _ re q ( t) = P _b a tt _ re q ( t) * ( -1 / E_ b at t );
140 P _c u r ta i l me n t ( t ) =0 ;
141 end
60 Appendix A: Matlab Code
142 if D e l ta _ S OC _ re q ( t ) + SO C_ p re >1
143 S OC ( t ) =1 ;
144 P _c u rt a il m en t_ ( t ) = De l ta _S O C_ r eq ( t )+ S OC _ pr e - 1;
145 elseif D el t a _S O C_ r e q ( t) + S OC _ pr e < 0
146 S OC ( t ) =0 ;
147 P_curtailment_(t)=0;
148 else
149 S OC ( t) = D e lt a _S O C_ r eq ( t ) + SO C_ p re ;
150 P_curtailment_(t)=0;
151 end
152 D el t a _S O C ( t) = S OC ( t ) - S OC _ pr e ;
153 S OC _ pr e = S OC ( t ) ;
154 P _b at t ( t) = D el t a_ S OC ( t ) *( - E_ b at t / 1) ;
155 if P _ ba t t (t ) > =0
156 P _d i sc h ar g e ( t) = P _b a tt ( t );
157 P _c h ar g e ( t ) =0 ;
158 else
159 P _d i s ch a rg e ( t ) = 0;
160 P _c h ar g e (t ) = - P_ ba t t (t ) ;
161 end
162 P _m i ss in g ( t) = - P_ d is c ha r ge _ re q ( t) + P _d i sc ha r ge ( t );
163 P _H PP ( t ) = P_ HP P _F ( t ) + P_ m is s in g ( t) ;
164 P _c u rt a il m en t _t o ta l ( t) = P _c u rt a il m en t ( t) + P _c u rt a il m en t_ ( t ) ;
165 end
166
167 %% FULL M O D EL
168
169 for t = ti m e
170 P _H P P_ F E (t ) = P _H PP ( t ) - P_ H PP _ F (t ) ;
171 G RI D (t ) = P _H PP ( t ) ;
172 P _c u rt ai l ed ( t )= P _ cu r ta i lm en t _t o ta l ( t) ;
173 P _R ES ( t ) = P_ R ES ( t ) -P _ RE S _F ( t ) ;
174 end
175
176 % % E RR OR M E TR IC S : P _ HP P _F E ( t) M AF E a nd R SM FE
177
178 fprintf(’ P _ H PP _ F E E R RO R M ET R I CS % s \ n ’) ;
179
180 MAE_P_HPP_FE = mean(abs ( P _H P P_ F E ))
181 RMSE_P_H P P _ F E = sqrt(mean( ( P _ HP P _F E ) . ^2 ) )
182
183 % % E RR OR M E TR IC S : P _ RE S _F E ( t) M A E an d R S ME
184 fprintf(’ P _ R ES _ F E E R RO R M ET R I CS % s \ n ’) ;
185
186 MAE_P_RES_FE = mean(abs ( P _R E S ))
187 RMSE_P_R E S _ F E = sqrt(mean( ( P _R E S ) .^ 2 ) )
188
189 % % PL O TT I NG S
190
191 figure
192 plot( t im e , P _R E S_ F )
193 t it le (’ D K 2 H PP S c en a r io 9 - T i me s e ri e s - P \ _ RE S \ _ F ( t) ’ )
Appendix A: Matlab Code 61
194 xli m ([ 1 1 75 4 4] )
195 xlabel(’ T im e [ h ou r s ] ’)
196 ylabel(’ P \ _ RE S \ _ F [ MW ] ’ )
197 grid on
198
199 figure
200 plot( t im e , P _R E S )
201 t it le (’ D K 2 H PP S c en a r io 9 - T i me s e ri e s - P \ _ RE S ( t ) ’ )
202 xli m ([ 1 1 75 4 4] )
203 xlabel(’ T im e [ h ou r s ] ’)
204 ylabel(’ P \ _ RE S [ M W ] ’ )
205 grid on
206
207
208 figure
209 plot( t im e , P _s ur p _F )
210 t it le (’ D K 2 H PP S c en a r i o 9 - T im e s er i e s - P _ { su r p } \ _F ( t ) ’ )
211 xli m ([ 1 1 75 4 4] )
212 xlabel(’ T im e [ h ou r s ] ’)
213 ylabel(’ P _ { s ur p l us } \ _F [ M W ] ’ )
214 grid on
215
216 figure
217 plot( t im e , P _ su r p )
218 t it le (’ D K 2 H PP S c en a r i o 9 - T im e s er i e s - P _ { su r p } ( t) ’ )
219 xli m ([ 1 1 75 4 4] )
220 xlabel(’ T im e [ h ou r s ] ’)
221 ylabel(’ P _ { s ur p l us } [ MW ] ’ )
222 grid on
223
224 figure
225 plot(time,P_curtailment_total_F)
226 t it le (’ D K 2 H PP S c en a r i o 9 - T im e s er i e s - P _ { cu r t a il e d } \ _ F (t ) ’ )
227 xli m ([ 1 1 75 4 4] )
228 xlabel(’ T im e [ h ou r s ] ’)
229 ylabel(’ P _ { c ur t a i le d } \ _ F [ MW ] ’ )
230 grid on
231
232 figure
233 plot(time,P_curtailment_total)
234 t it le (’ D K 2 H PP S c en a r i o 9 - T im e s er i e s - P _ { cu r t a il e d } ( t ) - J un e 8 t h a nd
9 th 2 01 5 ’ )
235 xli m ([ 1 1 75 4 4] )
236 xlabel(’ T im e [ h ou r s ] ’)
237 ylabel(’ P _ { c ur t a i le d } [ M W ] ’)
238 grid on
239
240 figure
241 plot( t im e ,( S OC _ F * P_ LI M _b a tt ) )
242 t it le (’ D K 2 H PP S c en a r i o 9 - T im e s er i e s - S OC \ _ F ( t ) - J un e 8 t h a nd 9 t h
2015’)
243 xli m ([ 1 1 75 4 4] )
62 Appendix A: Matlab Code
244 xlabel(’ T im e [ h ou r s ] ’)
245 ylabel(’ S O C \ _F * P _ L I M_ b a tt [ M W ] ’)
246 grid on
247
248 figure
249 plot( t im e ,( S O C* P _ LI M _b a tt ) )
250 t it le (’ D K 2 H PP S c en a r io 9 - T i me s e ri e s - S OC ( t ) - J un e 8 t h a nd 9 t h 2 0 15
)
251 xlim([1 48])
252 xlabel(’ T im e [ h ou r s ] ’)
253 ylabel(’ S O C * P _L I M _b a t t [ M W ] ’)
254 grid on
255
256
257 figure
258 plot( t im e , P _c ha r ge _ F )
259 t it le (’ D K 2 H PP S c en a r i o 9 - T im e s er i e s - P _ { ch a r ge d }\ _ F (t ) - J u n e 8 th
a nd 9 t h 2 0 15 )
260 xlim([1 48])
261 xlabel(’ T im e [ h ou r s ] ’)
262 ylabel(’ P o we r C h ar g e d [ MW ] ’ )
263 grid on
264
265 figure
266 plot( t im e , P _c ha r ge )
267 t it le (’ D K 2 H PP S c en a r i o 9 - T im e s er i e s - P _ { ch a r ge d }( t ) - J un e 8 t h a nd 9
th 2 01 5 ’)
268 xlim([1 48])
269 xlabel(’ T im e [ h ou r s ] ’)
270 ylabel(’ P o we r C h ar g e d [ MW ] ’ )
271 grid on
272
273 figure
274 plot( t im e , P _d is c ha r ge _ F )
275 t it le (’ D K 2 H PP S c en a r i o 9 - T im e s er i e s - P _ { d is c h ar g e d } \ _F ( t ) - J u ne 8 th
a nd 9 t h 2 0 15 )
276 xlim([1 48])
277 xlabel(’ T im e [ h ou r s ] ’)
278 ylabel(’ P o we r d i sc h a r ge d [ M W ] ’ )
279 grid on
280
281 figure
282 plot( t im e , P _d is c ha r ge )
283 t it le (’ D K 2 H PP S c en a r i o 9 - T im e s er i e s - P _ { d is c h ar g e d } ( t ) - J un e 8 t h
a nd 9 t h 2 0 15 )
284 xlim([1 48])
285 xlabel(’ T im e [ h ou r s ] ’)
286 ylabel(’ P o we r d i sc h a r ge d [ M W ] ’ )
287 grid on
288
289 figure
290 plot( frequency ,sort( P _ su r p_ F ) )
Appendix A: Matlab Code 63
291 t it le (’ D K 2 H PP S c en a r i o 9 - D u ra t i on C u rv e - P_ { s ur p } \ _ F (t ) - J u ne 1 7 th
a nd 1 8 th 2 01 6 ’ )
292 xli m ([ 0 1 ])
293 xlabel(’ C u m ul a te d f r eq u en c y ’ )
294 ylabel(’ P _ { s ur p l us } \ _F [ M W ] ’ )
295 grid on
296
297 figure
298 plot( frequency ,sort( P_surp))
299 t it le (’ D K 2 H PP S c en a r i o 9 - D u ra t i on C u rv e - P_ { s ur p } ( t ) - J un e 1 7 t h a nd
18 t h 2 01 6 ’ )
300 xli m ([ 0 1 ])
301 xlabel(’ C u m ul a te d f r eq u en c y ’ )
302 ylabel(’ P _ { s ur p l us } [ MW ] ’ )
303 grid on
304
305 figure
306 plot( frequency ,sort( P_curtailment_total_F))
307 t it le (’ D K 2 H PP S c en a r i o 9 - D u ra t i on C u rv e - P_ { c u rt a i le d }\ _ t ot a l \ _ F (t ) -
J un e 1 7 th a nd 1 8 th 2 0 16 ’ )
308 xli m ([ 0 1 ])
309 xlabel(’ C u m ul a te d f r eq u en c y ’ )
310 ylabel(’ P _ { c ur t a i le d } \ _ F [ MW ] ’ )
311 grid on
312
313 figure
314 plot( frequency ,sort( P_curtailment_total))
315 t it le (’ D K 2 H PP S c en a r i o 9 - D u ra t i on C u rv e - P_ { c u rt a i le d }\ _ t ot a l ( t ) -
J un e 1 7 th a nd 1 8 th 2 0 16 ’ )
316 xli m ([ 0 1 ])
317 xlabel(’ C u m ul a te d f r eq u en c y ’ )
318 ylabel(’ P _ { c ur t a i le d } [ M W ] ’)
319 grid on
320
321 figure
322 plot( frequency ,sort( S O C_ F ) )
323 t it le ( DK 2 HPP S c e n a r i o 9 - D u r a t i o n C u r ve - S OC \ _ F ( t) - Ju n e 17 th and 18
th 2 01 6 ’)
324 xli m ([ 0 1 ])
325 yli m ([ 0 1 .2 ])
326 xlabel(’ C u m ul a te d f r eq u en c y ’ )
327 ylabel(’ S O C \ _F [ p . u .] )
328 grid on
329
330 figure
331 plot( frequency ,sort( S O C ))
332 t it le (’ D K2 H PP S ce n ar i o 9 - D u ra t io n C u rv e - S OC ( t ) - J un e 1 7 th a nd 1 8 th
2016’)
333 xli m ([ 0 1 ])
334 yli m ([ 0 1 .2 ])
335 xlabel(’ C u m ul a te d f r eq u en c y ’ )
336 ylabel(’ S O C [ p . u . ] ’)
64 Appendix A: Matlab Code
337 grid on
338
339 figure
340 plot( frequency ,sort( P _ di s ch a rg e _F ) )
341 t it le (’ D K 2 H PP S c en a r i o 9 - D u ra t i on C u rv e - P_ { d i sc h a rg e d } \ _ F ( t) - J un e
17 t h a nd 1 8 th 2 0 16 ’ )
342 xli m ([ 0 1 ])
343 yli m ([ 0 3 ])
344 xlabel(’ C u m ul a te d f r eq u e nc y ’ )
345 ylabel(’ P o we r d i sc h a r ge d [ M W ] ’ )
346 grid on
347
348 figure
349 plot( frequency ,sort( P_discharge))
350 t it le ( DK 2 HPP S c e n a r i o 9 - D u r a t i o n C u r ve - _ { di s c h a r g e d }( t ) - J u ne 17 t h
a nd 1 8 th 2 01 6 ’ )
351 xli m ([ 0 1 ])
352 xlabel(’ C u m ul a te d f r eq u e nc y ’ )
353 ylabel(’ P o we r d i sc h a r ge d [ M W ] ’ )
354 grid on
Appendix B: Measured
Scenarios Comparison
DK2 HPP - Measured
DK2 Energy surplused measured for hybrid power plant
scenarios comparison
RES Scenarios ERE S (t)[T W h/y]Esurplused (t)[GW h/y]Ecur tailed(t)[GW h/y ]
Sc.1: 0WPP+100PVPP 0.129 0.000 0.000
Sc.2: 25WPP+75PVPP 0.189 0.000 0.000
Sc.3: 50WPP+50PVPP 0.249 0.000 0.000
Sc.4: 75WPP+25PVPP 0.309 0.000 0.000
Sc.5: 100WPP+0PVPP 0.369 0.000 0.000
Sc.6: 80WPP+60PVPP 0.372 2.525 2.525
Sc.7: 100WPP+40PVPP 0.420 4.984 4.984
Sc.8: 105WPP+35PVPP 0.432 6.347 6.347
Sc.9: 120WPP+20PVPP 0.468 25.505 25.505
Table 1: DK2 RES Scenarios comparison - Energy Produced and Surplused
RES Scenarios ERE S (t)[T W h/y]Ecurtailed (t)[GW h/y]Ecur tailed(t)[%]
Sc.1: 0WPP+100PVPP 0.129 0.000 0.000
Sc.2: 25WPP+75PVPP 0.189 0.000 0.000
Sc.3: 50WPP+50PVPP 0.249 0.000 0.000
Sc.4: 75WPP+25PVPP 0.309 0.000 0.000
Sc.5: 100WPP+0PVPP 0.369 0.000 0.000
Sc.6: 80WPP+60PVPP 0.372 2.525 0.68
Sc.7: 100WPP+40PVPP 0.420 4.984 1.19
Sc.8: 105WPP+35PVPP 0.432 6.347 1.47
Sc.9: 120WPP+20PVPP 0.468 25.505 5.45
Table 2: DK2 RES Scenarios comparison - Energy Produced Measured, Surplused and
Curtailed
66 Appendix B: Measured Scenarios Comparison
RES Scenarios ERE S (t)[T W h/y]Ecurtailed (t)[GW h/y]Ecur tailed(t)[%] C F [%]
Sc.1: 0WPP+100PVPP 0.129 0.000 0.00 14.70
Sc.2: 25WPP+75PVPP 0.189 0.000 0.00 21.55
Sc.3: 50WPP+50PVPP 0.249 0.000 0.00 28.40
Sc.4: 75WPP+25PVPP 0.309 0.000 0.00 35.25
Sc.5: 100WPP+0PVPP 0.369 0.000 0.00 42.10
Sc.6: 80WPP+60PVPP 0.372 2.525 0.68 42.50
Sc.7: 100WPP+40PVPP 0.42 4.984 1.19 47.98
Sc.8: 105WPP+35PVPP 0.432 6.347 1.47 49.35
Sc.9: 120WPP+20PVPP 0.468 25.505 5.45 53.46
Table 3: DK2 RES Scenarios comparison - Energy Produced Measured, Surplused and
Curtailed
SE2 HPP - Measured 67
SE2 HPP - Measured
SE2 Energy Surplused for hybrid power plant scenarios
comparison
RES Scenarios ERES_F(t)[T W h/y]Esurplused_F(t)[GW h/y]Ecurtailed_F(t)[GW h/y]
Sc.1: 0WPP+100PVPP 0.118 0.000 0.000
Sc.2: 25WPP+75PVPP 0.142 0.000 0.000
Sc.3: 50WPP+50PVPP 0.166 0.000 0.000
Sc.4: 75WPP+25PVPP 0.190 0.000 0.000
Sc.5: 100WPP+0PVPP 0.215 0.000 0.000
Sc.6: 80WPP+60PVPP 0.242 1.228 1.228
Sc.7: 100WPP+40PVPP 0.262 2.029 2.029
Sc.8: 105WPP+35PVPP 0.267 2.445 2.445
Sc.9: 120WPP+20PVPP 0.281 8.997 8.997
Table 4: SE2 RES Scenarios comparison - Energy Produced and Surplused
RES Scenarios ERES_F(t)[T W h/y]Ecurtailed_F(t)[GW h/y]Ecurtailed_F(t)[%]
Sc.1: 0WPP+100PVPP 0.118 0.000 0.000
Sc.2: 25WPP+75PVPP 0.142 0.000 0.000
Sc.3: 50WPP+50PVPP 0.166 0.000 0.000
Sc.4: 75WPP+25PVPP 0.190 0.000 0.000
Sc.5: 100WPP+0PVPP 0.215 0.000 0.000
Sc.6: 80WPP+60PVPP 0.242 1.228 0.51
Sc.7: 100WPP+40PVPP 0.262 2.029 0.77
Sc.8: 105WPP+35PVPP 0.267 2.445 0.92
Sc.9: 120WPP+20PVPP 0.281 8.997 3.20
Table 5: SE2 RES Scenarios comparison - Energy Produced and Surplused
68 Appendix B: Measured Scenarios Comparison
RES Scenarios ERES_F(t)[T W h/y]Ecurtailed_F(t)[GW h/y]Ecurtailed_F(t)[%] C F [%]
Sc.1: 0WPP+100PVPP 0.118 0.000 0.00 13.46
Sc.2: 25WPP+75PVPP 0.142 0.000 0.00 16.22
Sc.3: 50WPP+50PVPP 0.166 0.000 0.00 18.98
Sc.4: 75WPP+25PVPP 0.190 0.000 0.00 21.74
Sc.5: 100WPP+0PVPP 0.215 0.000 0.00 24.50
Sc.6: 80WPP+60PVPP 0.242 1.228 0.51 27.68
Sc.7: 100WPP+40PVPP 0.262 2.029 0.77 29.89
Sc.8: 105WPP+35PVPP 0.267 2.445 0.92 30.44
Sc.9: 120WPP+20PVPP 0.281 8.997 3.20 32.09
Table 6: SE2 RES Scenarios comparison - Energy Produced and Surplused