ShTe

I elandi System

Þjórsá-and Tungnaá River System

GUMUNDUR BJÖRNSSON

Master's Degree Proje t

September 2009

XR-EE-ES 2009:014

Royal Institute of Te hnology (KTH)

S hool of Ele tri al Engineering

This master thesis ontains my work of studies of a short term planning

model, with the time span of one week, or168 hours. The models are based

on the future hydropower system in Þjórsá- and Tungnaá- river system, lo-

ated inthe south part of I eland.

The purpose of this thesis is to formulate and develop one week operation

s hedules for this future power generation system, whi h for a given inow-

and loadfore ast returnsagoods hedulefor ea hpower stationsinthe sys-

tem.

The planning problem is formulated as a mathemati al programming prob-

lem. The models used to des ribe and implement the system under study

are a pie ewise linear models. For pie ewise linear models the breakpoints

of the model are the lo al best-e ien y points. The obje tive is to return

operation plan for ea h power station in the system, where the the volume

ofstored waterinthe endof theplanningperiodismaximizedthrough opti-

maldis harge plans. It isneeded tosupply ontra ted load, regulation- and

balan epower forea h hour duringthe planningperiodunder study.

Two test ases are made for ea h model in this thesis. The former ase

des ribe winter operation, with high onsumptions and lower naturalinow

to the reservoirs. In the latter ase the onsumptionis low and riverinow

high and is meant todes ribesummer time operation.

Obtainedresultsshowsthatpie ewiselinearmodelgivesmorerealisti results

when the load onsumption is high and the inow is low. During summer

time, with low load and high inow, the pie ewise linear models s hedule

more often dis harge not on lo al best-e ien y points. This behavior an

be de reased by inserting apenalty ost of dis harge hanges.

Keyword: Short term planning, hydropower, ele tri al generation.

This masters thesis over my work arried out at Ele tri Power System

(EPS), Department of Ele tri alEngineering,Royal Institute ofTe hnology

(KTH) inSto kholm, Sweden.

First I would like to thank my supervisor at EPS, Magnus Olsson for all

his support, patien e and guidelines during my thesis work. I also want to

thankProfessorLennartSöderatEPS forhissupportandforapprovingthis

proje t asthis master'sthesis work.

Within Landsvirkjun I would like to to thank my onta t person Eggert

Guðjónsson, head of generation planning, for hissupport and for givingmy

a ess toallthe system dataneeded for this masterthesis. Alsofor approv-

ingthis idea and givingme an opportunity todothis internalthesis.

Within Landsvirkjun Power I want to thank Guðlaugur V. Þórarinsson,

proje t manager, for giving my a ess to all the proje t planning reports

for the new hydropower stations inlowerriver of Þjórsá.

Sto kholm, September 2009

Guðmundur Björnsson

1 Introdu tion 1

1.1 Ba kground . . . 1

1.2 The aimof the thesis . . . 2

1.3 S ope of thesis . . . 3

1.4 Overview of the thesis . . . 3

2 The I elandi Hydro System 5 2.1 Ele tri energy system inI eland . . . 5

2.2 Hydropower inI eland - histori aloverview. . . 5

2.2.1 The rst period 1904-1934 . . . 6

2.2.2 The se ond period1935-1964 . . . 6

2.2.3 The third period1965 to present days. . . 7

3 The I elandi Ele tri ityMarket 9 3.1 Reformedele tri itymarket . . . 9

3.2 Parti ipants inthe ele tri ity market . . . 9

3.2.1 Transmission system operator . . . 10

3.2.2 Produ ers . . . 10

3.2.3 Balan e responsibility . . . 11

3.2.4 Grid owners . . . 11

3.2.5 Consumers. . . 12

4 The Transmission System in I eland 13 4.1 The transmissionlines . . . 13

4.2 The stru ture of the transmission system . . . 14

5 System Planning 17 5.1 Produ tionplanning . . . 17

5.1.1 Expansion planning. . . 18

5.1.2 Seasonalplanning . . . 18

5.1.3 Short term planning . . . 18

5.2 System operation . . . 19

5.2.1 Frequen y ontrol . . . 19

5.2.2 Primary ontrol . . . 19

5.2.3 Se ondary ontrol . . . 21

6 Modeling of Hydropower Systems 23 6.1 Hydropowergeneration . . . 23

6.2 E ien y and dis harge . . . 24

6.2.1 Hourequivalentof water . . . 25

6.2.2 Produ tionequivalent . . . 25

6.2.3 Constant produ tion equivalent . . . 26

6.2.4 Marginalprodu tionequivalent . . . 26

6.2.5 Relativee ien y . . . 26

6.3 Modelinghydropower generation . . . 27

6.3.1 The linearmodel . . . 27

6.3.2 The pie ewise linear model . . . 28

6.3.3 Totaldis harge and power generation . . . 29

6.4 River inow . . . 30

6.5 Reservoirs . . . 30

6.5.1 Seasonalreservoirs . . . 30

6.5.2 Shortterm reservoirs . . . 31

6.5.3 Reservoirs operation . . . 31

6.5.4 Reservoir onstraints . . . 31

6.6 Spillage . . . 32

6.6.1 Un ontrolled spillage . . . 32

6.6.2 Controlled spillage . . . 32

6.7 Hydrologi al ouplingbetween power stations . . . 32

6.7.1 Delay time between power stations . . . 33

6.8 Reserve requirements . . . 34

6.8.1 Primary ontrol reserve . . . 34

6.8.2 Se ondary ontrolreserve . . . 35

6.9 Penalty ost ondis harge hanges . . . 35

6.10 Short-term planningproblem . . . 37

6.10.1 Formulation ingeneral . . . 37

7 The System Under Study 39 7.1 The NationalPower Company . . . 39

7.2 The power stationsin present system . . . 40

7.2.1 Vatnsfell . . . 40

7.2.2 Sigalda. . . 41

7.2.4 Sultartangi . . . 42

7.2.5 Búrfell . . . 43

7.3 The power stations inthe future system . . . 44

7.3.1 Búðarháls . . . 44

7.3.2 Hvammur . . . 45

7.3.3 Holt . . . 46

7.3.4 Urriðafoss . . . 46

7.4 The model of the system . . . 47

7.4.1 The data used . . . 47

7.4.2 Powergeneration model . . . 48

7.4.3 Contra ted load to supply . . . 48

7.4.4 The inowdata to the system . . . 49

7.4.5 Delay time between powerstations under study . . . . 51

7.4.6 The reservoirsin the system under study . . . 51

7.5 Problemformulation . . . 52

7.5.1 The obje tive fun tions. . . 53

7.5.2 Constraints . . . 54

7.5.3 Limits . . . 55

8 Simulated Cases 57 8.1 Model 1 - Introdu tion . . . 58

8.2 Model 2 - Introdu tion . . . 59

8.3 Model 3 - Introdu tion . . . 60

8.4 Model 4 - Introdu tion . . . 61

9 Results 63 9.1 The layout of the hapter . . . 63

9.2 Generationplanning s hedules . . . 64

9.3 Surplusof powerin the system. . . 65

9.4 Penalty ost ondis harge hanges . . . 68

10 Dis ussions and Con lusions 73 10.1 Dis ussions . . . 73

10.2 Con lusions . . . 75

11 Future Work 77 11.1 Mixedintegerlinear model . . . 77

11.1.1 Spinning reserve. . . 77

11.1.2 Forbidden dis harge. . . 78

11.1.3 Start-up and shut-down osts . . . 78

11.2 Delay time between power stations . . . 78

11.3 Further developments of the proje t . . . 79

11.3.1 Shortterm planning forthe wholesystem . . . 79

11.3.2 Cost of balan epowerin hydropower systems . . . 79

Bibliography 81 A GAMS 85 A.1 General Algebrai ModelingSystem . . . 85

A.1.1 Import and export of data . . . 86

B Figures from Simulated Cases 87

C The Models Statisti s 97

2.1 Total number of hydropower stations in I eland in 2006, in-

stalled apa ity and average annual generation. . . 6

4.1 Lengthof transmission lines at spe i voltage levels. . . 13

7.1 The power stations in Þjórsá- and Tungnaá river area in the

south part of I eland, in present system and expe ted future

system.. . . 47

8.1 Introdu tion tothe dierent simulation ases for ea hmodel . 57

9.1 AveragespillinthesysteminMWh: Win=winter asestudy,

Sum = summer ase study and

Sum ρ

^{= summer ase with}

penalty ost. . . 70

C.1 Themodelsstatisti s: Numberof iteration, omputationtime

and the obje tive value for ea h ase study . . . 97

2.1 ThedevelopmentoftheI elandi ele tri itysystemfrom1960-

2007 . . . 8

4.1 The transmissionsystem inI eland 2008. . . 14

6.1 Anexample of ageneration hara teristi s. Power generation asa fun tion of dis harge through astation. . . 27

6.2 Anexampleofarelativee ien yforhydropowerstationwith two units. Samestation as ingure 6.1. . . 27

6.3 A pie ewise linear model of one of the station under study . . 28

7.1 Þjórsá-and Tungnaá- river area insouth part of I eland. . . . 41

7.2 The layout before and after Hvammurpowerstation and Ha- galón reservoir have been built. . . 45

7.3 The layout beforeand after Holtpower station and Árneslón reservoir havebeen built. . . 46

7.4 ThelayoutbeforeandafterUrriðafosspowerstationandHeiðar- lónreservoirhave been built.. . . 47

7.5 Thetotal loadprolesinthe system,the generation ontribu- tion from other stations outside the area and the load under study during the planningperiod. . . 50

8.1 Model 1 - Hydrosystem layout . . . 58

8.2 Model 2 - Hydrosystem layout . . . 59

8.3 Model 3 - Hydrosystem layout . . . 60

8.4 Model 4 - Hydrosystem layout . . . 61

9.1 Winter Case study: Model 1, model 2 and model 4 - Load urvesand generationplans s hedules. . . 66

9.2 Winter Case study - Model 1, model 2 and model 4: Surplus of power inthe system. . . 67

9.3 Model 4 - Summer ase: Generation ontribution with and withoutpenalty ost . . . 69

9.4 Model 4 -Summer ase: Surplusof powerin the system with

and withoutpenalty ost . . . 71

B.1 Model 1 - Winter: Load urve and generation ontribution,

reservoir ontents, dis harge- and generation plan, reserved

power and surplusof power inthe powerstations . . . 88

B.2 Model 2 - Winter: Load urve and generation ontribution,

reservoir ontents, dis harge- and generation plan, reserved

power and surplusof power inthe powerstations . . . 89

B.3 Model 3 - Winter: Load urve and generation ontribution,

reservoir ontents, dis harge- and generation plan, reserved

power and surplusof power inthe powerstations . . . 90

B.4 Model 4 - Winter: Load urve and generation ontribution,

reservoir ontents, dis harge- and generation plan, reserved

power and surplusof power inthe powerstations . . . 91

B.5 Model 3 - Summer: Load urve and generation ontribution,

reservoir ontents, dis harge- and generation plan, reserved

power and surplusof power inthe powerstations . . . 92

B.6 Model 3 - Summer, with penalty ost on dis harge hanges:

Load urve and generation ontribution, reservoir ontents,

dis harge-and generation plan,reserved powerandsurplus of

power inthe power stations . . . 93

B.7 Model 4 - Summer: Load urve and generation ontribution,

reservoir ontents, dis harge- and generation plan, reserved

power and surplusof power inthe powerstations . . . 94

B.8 Model 4 - Summer, with penalty ost on dis harge hanges:

Load urve and generation ontribution, reservoir ontents,

dis harge-and generation plan,reserved powerandsurplus of

power inthe power stations . . . 95

D.1 Layout gures of lower river of Þjórsá. The lo ation of the

Variables: Explanation:

P i (k)

^{powerprodu tion inpowerstation}

i

^{, hour}

k x i (k)

^{ontents of reservoir}

i

^{atthe end of hour}

k s i (k)

^{spillage past powerstation}

i

^duringhour

k u i (k)

^{dis harge in power station}

i

^{during hour}

k

u i,j (k)

^{dis harge in power station}

i

^{, segment}

j

^{, duringhour}

k

Z

^{obje tive fun tion}

Parameters: Explanation:

u i

^{maximal dis harge through power station}

i x i

^{maximal reservoir ontents of reservoir}

i

x i,pre

^{preferableupper reservoir ontents of reservoir}

i x _i,pre

^{preferablelowerreservoir ontents of reservoir}

i x i,start

^{start ontents of reservoir}

i

s i (k)

^{maximal spillageby power station}

i s _i (k)

^{minimalspillage by powerstation}

i w i (k)

^{water inow toreservoiri during hour k}

γ i

^{produ tion}equivalent, power station

i

µ i,j

^{marginal produ tion} equivalent, power station

i

^{, seg-}

ment

j

η i

^{relative e ien y,power station}

i λ f

^{expe ted future} ele tri ity pri e

τ j,i

^{delaytime forthe water between station}

j

^{andthe los-}

est downstream station

i

n i

^{total segments inpower station}

i P i

^{installed apa ity inpowerstation}

i P b

^{ontra tedbalan e power}

P p

^{ontra tedprimary power/ spinningreserve}

P R

^{total reserved power}

ρ i

^{penalty ost of dis harge hanges, power station}

i

Sets: Explanation:

K _i

^{set of} neighboring power stations dire tly upstream of power station

i

N _i

^{setofindi esforallpowerstationsdownstreamofreser-}

voir

i

^{,in luding station}

i

^itself

I

^{set of allpower stationsin the system}

K

^{time durationinthe planningperiod}

Explanation:

AGC Automati Generation Control

GAMS General Algebrai Modeling System

GDX GAMS Data Ex hange

GL Gigaliter

LN Landsnet

LP Linear Problem

LV Landsvirkjun

TSO Transmission System Operator

Power stations:

VAF Vatnsfell power station

SIG Sigalda powerstation

HRA Hrauneyjafoss power station

BUD Búðarháls powerstation

SUL Sultartangi powerstation

BUR Búrfell power station

HVA Hvammurpowerstation

HOL Holt powerstation

URR Urriðafoss power station

STE Steingrímsstöð power station

LJO Ljósifoss power station

IRA Írafoss power station

BLA Blanda power station

LAX Laxá powerstation

KRA Kraa powerstation

BJA Bjarnarag power station

KAR Kárahnjúkar powerstation

I elandi letters in the thesis:

Þ /þ Dened asTh / th inenglish

 / ð Dened asD / d inenglish

Introdu tion

1.1 Ba kground

Renewable energy sour es are be oming more and more importantat same

time as the threats of limate hanges are in reasing due to pollution. An

importantbenetofrenewableenergysour eslikewind-,hydro-andgeother-

malpoweris that it is lean and does not ontributeto pollution.

I eland is small ountry ompared to other nations, where the population

isin ex ess of threehundred thousand and due tothat the publi ele tri ity

onsumption is very low. The I elandi power system is not onne ted to

othergridsinother ountriesandhas noopportunitytotransport ele tri ity

ross borders likemany other ountries.

I elandhavelargepotentialinhydro- andgeothermalpowerand onlyapart

of the apa ity, whi h te hni ally an be harnessed, have been harnessed

today. Due to this large potential in environmental friendly power sour es,

manyprodu tion ompanies haveshown theirinterests toinvest inenergyin

I eland. Su h ompaniesare forexamplealuminiumsmeltersand ompanies

inthe eld of data banks enters and a produ ersof solar ells.

Be ause of in reased energy requests, many power ompanies in the oun-

try have started their preparation pro ess for planning new power stations,

who might be build in nearest future, both in the eld of geothermal and

hydropower.

The national power ompany of I eland - Landsvirkjun has re ently started

operation of a 690 MW power station, at Kárahnjúkar in the eastern part

of I eland, mainly build to over ele tri al onsumption in new aluminium

smelter. To be able to meet in reased energy request during oming years,

Landsvirkjunisplanningtoexpanditsgeneration apa itywithinhydropower

insouth part of I eland.

1.2 The aim of the thesis

Thepurposewiththisproje tistoobtaineknowledgeoftheupgradedpower-

and river system in the south part of I eland. In the area, named after the

twomainrivers, ÞjórsáandTungnaá, totalfournewhydropowerstationsare

planned tobebuild in the future.

Three of these new hydropower stations will be lo ated in the lower part

ofÞjórsáriverand thesethree stationswillallbeinseries mostdownstream

in the river. The fourth station is planned to be built in the middle of the

river system. That station would harness water from Tungnaá riverand its

lo ation isthe fourth most downstream inthe present system.

The aimof the thesis istoformulateand develop one week operations hed-

ules for the future power generation system in the south part of I eland,

whi h for a given load- and inow fore ast produ e a good s hedule of the

power stations in the system where the obje tive fun tion is to operate the

stations as often on their lo albest-e ien y points and by that maximize

the value of stored water in the end of the planning period.

Furthermore the aim is to run dierent ases with dierent numbers of hy-

dropower stations, ree ting the new system in southern I eland. These

dierent ases are studied for dierent situations in load and inow to the

system, with the aim to ree t summer- and winter time situations in the

future system.

Theaimisalsotostudy howthe stationsparti ipateinsupplying ontra ted

load during the planning period for ea h ase. Further to investigate if the

balan e-and primary power is fullled, and how great surplus of se ondary

1.3 S ope of thesis

Thes opeofthis thesisistostudy shorttermhydropowerplanningwiththe

times aleofoneweekofthehydropowersysteminÞjórsá-andTungnaáriver

area in south part of I eland. Time period for longer time than one week

will not be under study here therefore seasonal planning or su h questions

are therefore not onsidered inthis thesis.

The model of the power generation hara teristi s inthis thesis ispie ewise

Linear Programming 1

modeling approximation of the dis harge-generation

urve. Another way and also interesting when study multi ma hine hy-

dropower system is to modeling the system as Mixed Integer Linear Pro-

gramming 2

problem, but su h problem isnot withinthe s ope of this thesis

and willnot be onsidered here.

Combinations of units whi h are on-line or o-line is therefore not stud-

ied. Questions regarding how the primary ontrolreserve is shared between

onlineunits an thereforenot be al ulated wherenobinary variableswhi h

presents ombination of on-line units are in use. Due to this limitationthe

totalsurplusofpowerinea hpowerstationeveryhouristhereforeonly on-

sidered in total, but not how the power surplus is divided down to on-line

units.

With same reasoning, start-up and shut-down osts of units or minimum

start-and stop times an notbetaken intoa ount,whereonly LP-modelis

used in this thesis. Units starts and stops are therefore outside the s ope of

the thesis.

1.4 Overview of the thesis

Chapter 2 ontains a presentation of the whole I elandi ele tri power sys-

tem. An introdu tion to the history of ele tri ation and development of

hydropower produ tion inI eland is given. Also introdu tions tothe devel-

opment inthe ele tri onsumptionare presented.

Chapter 3 ontains an overview over the I elandi ele tri ity market, its

parti ipants, the transmission system operator, produ ers, grid owners and

onsumers inI eland.

1

LP

2

Chapter 4 ontains an overview over the transmission system in I eland,

itsstru ture and its hara teristi s feature isexplained briey.

Chapter 5 ontain des riptions of theory regarding dierent planning peri-

ods, expansion-, seasonal-andshort termplanning. Powersystem operation

ispresented and introdu tiontofrequen y-, primary- and se ondary ontrol

isgiven

Chapter 6 ontains the theoreti al part of the thesis. This hapter ontains

the theory behind modeling of hydropower systems. Not only the theory

used in the thesis, but also the theory that might be used to develop and

improve the work already donein a later stage and infuture work.

Chapter 7 ontains short des ription of Landsvirkjun, the National power

ompany of I eland. Introdu tion is given to ea h of Landsvirkjun's power

stations in the present and future systems in the area under study. How

the system is modeled, how the problem is formulated and how the theory

andtheideasfrom hapter6areusedduringthatworkispresentedindetail.

Chapters8 ontains presentationsof test ases,the summerand wintertime

simulationsas well as introdu tion to howthe penalty ost is implemented.

The layout of allthe fourmodels models are presented.

Chapter 9 ontains sele ted part of obtained results of the onsidered ases

inthe models understudy.

Chapter 10 ontains dis ussions about obtained results and what on lu-

sion mightbe drawn from obtained results.

Chapter 11 ontains some ideas and suggestion about how the models an

The I elandi Hydro System

This hapter ontainsa presentation of the I elandi hydro ele tri al system.

Introdu tionsofthepowerprodu tion,as wellas theele tri onsumptionare

presented. An overview over thehistori al stages of ele tri ation in I eland

are given.

2.1 Ele tri energy system in I eland

Total installed apa ity in the I elandi power system in 2008 was 2.574

MW. The share of hydropower in total installed power is 1.879 MW, 575

MW omes from geothermal power and 120 MW from fuel power stations,

but fuel power are mainlyused as ba k-upstations aroundthe ountry [2℄.

Total ele tri energy produ tion in I eland in 2008 was 16.467 GWh, whi h

isequallytoyearly onsumptionofbarely52MWhperinhabitantinI eland.

Between the years 2007 and 2008 the ele tri al generation in reased about

27%mainlyduetoin reasedenergy onsumptioninthe aluminiumindustry,

wherenew aluminiumsmelterstartedoperation. In 2008 around75% ofthe

ele tri ity was generated with hydropower and 25% with geothermal power

inI eland [2℄ .

2.2 Hydropower in I eland - histori al overview

The history of ele tri ation in I eland an roughly be divided to three pe-

riods. In 2006 total 235 hydropower stations are re orded and registered in

I eland. Almost80%aresmallerthan100kWandusedasprivategenerators

on the ountry side [5℄. Table 2.1 gives overview over installedhydropower

inI eland in 2006.

2.2.1 The rst period 1904-1934

The rst period lasted from 1904 to 1934, but the rst hydropower turbine

ame onstream in De ember in 1904. This was a small hydropower station

whi h ele tried a arpenters workshop and manage to ele trify 12 other

houses in nearest surroundings as well. This small hydropower station had

installed apa ity of 6 kW and lo ated in Hafnarfjörður lose to Reykjavik

[27℄.

The rst hydropower station with alternating urrent generation was built

in Seyðisfjörður, in the east part of I eland in 1913. In the beginning, the

power station namedFjarðarselsvirkjun, had an installed apa ity of 55 kW

andsuppliedthe town andits losest surroundings. This wastherst power

stationwhomanagedtoele trifyamuni ipalityonitsown. Todaythis isthe

oldestpowerstationstillinoperationandhavebeenupgradedto172kW[27℄.

The largest hydropower station built within the period was 1.1 MW sta-

tion,built 1919-1921,ownedand operatedby ity ofReykjavik. The station

be amethelargestoneinsixteenyearsandwasbuiltwiththeaimtoele trify

Reykjavik and was lo ated onthe outskirts of the town. Today this station

isstill inoperation but has been upgraded to3.2 MW.

2.2.2 The se ond period 1935-1964

During the years from 1935 to 1964 whi h an bedened as the se ond pe-

riod, a larger hydropower stations were built to meet in reasing population

density in the south west and north part of the ountry. In the beginning

of the period the onsumption in reased mainly be ause of general use of

Installed Numberof Totalinstalled Average annual

apa ity [MW℄ stations apa ity [MW℄ generation [GWh/year℄

0-0,1 180 3,6 25

0,1-1,0 30 9,3 69

1,0-10,0 15 47 415

10-100 5 207 985

>100 5 900 5.520

Total: 235 1.167 7.015

Table 2.1: Totalnumberof hydropowerstations inI elandin2006, installed

ele tri alequipmentathomes, butduring theyears 1953-1964 thepowerin-

tensive industry took larger share of the total ele tri al onsumption. Main

intensive industryat this time was afertiliser- and a ement fa tory.

During these ondperiod,the ity ofReykjavik startedtheSog PowerCom-

pany. The ompany build threehydropowerstation inthe area of Sog, lose

to Reykjavík. The power stations ame on stream the years 1937, 1953

and 1959. The stations are owned and operated by Landsvirkun sin e 1966,

when Reykjavik ity in orporated the stations into Landsvirkjun as part of

the owner's founding ontribution.

Tomeet the in reased onsumptiondue toin reased populationdensity,the

town of Akureyri started the Laxá Power Company, who build three hy-

dropowerstationsinthe riverofLaxá inthenorth east partof I eland. The

aimwastoele trifythe townofAkureyriand itsnearestsurroundings. From

1983 this stationshavebeen owned and operatedby Landsvirkun, whenthe

town of Akureyri in orporatedthe stations intoLandsvirkjun aspart of the

owner's founding ontribution.

2.2.3 The third period 1965 to present days

At the beginningof the sixties a dis ussions took pla e about howit would

be possible to utilize the ountry's energy resour es and at same time to

in rease theexports fromI eland,whi hatthis timewere almostonlybased

onsh produ ts.

The government founded a ommittee with the aim to investigate the pos-

sibilities to start up power intensive industry in I eland. Where the alu-

miniumpro ess isveryenergy onsumingindustry,andthealuminumindus-

try through the world was growing atthis time it was anattra tive idea to

start up aluminiumsmelter as an option to utilize the energy resour es for

ele tri algeneration.

In 1965 the national power ompany of I eland - Landsvirkjun was estab-

lished. The role of Landsvirkjun at this time was tobuild and operate new

powerstations with the aim tosupply the futures power intensive industry.

The dis ussions between the ommittee and foreign power intensive ompa-

nies resulted in an agreement for a onstru tion of an aluminum smelter.

The rst aluminum smelter, then owned by ISAL and Landsvirkjun's rst

Figure 2.1: The development of the I elandi ele tri ity system from 1960-

2007

From 1969, Landsvirkjun has built total eight hydropower stations. Five

are lo ated in the south part of I eland, in the Þjórsá- and Tungnaá river,

one in the north part and the new hydropower station in Kárahnjúkararea

inthe east part if I eland, who started operation inNovember 2007. These

power stations were more orless built parallelto new onsumers within the

intensiveindustry, su h as aluminium-and ferrosili onsmelters.

From 1965 to2008 the ele tri algeneration inI eland have in reased about

96% and about 73% during the twenty years period, from 1988 to 2008. In

gure 2.1 it an be seen how the power system has developed through the

years and how the system has been build up duringthe periodfrom1960 to

The I elandi Ele tri ity Market

This hapter ontains a short introdu tion of the I elandi ele tri ity mar-

ket. A presentation of the I elandi transmissionsystem and its stru ture is

given.

3.1 Reformed ele tri ity market

TheI elandi ele tri itymarketbe amereformedandee tiveinstagesfrom

July 2003, whenall ompanies inthe eld of powerintensive industry ould

hoose its supplier. In January 2005, all nal onsumers who were power

measured ould hoose their own suppliers. The third and the last stage

be ame ee tive in the middle of the year 2006 when all users were able to

hoose theirsupplier of ele tri ity [22℄.

ThepurposeofthenewEle tri ityA tisto ontributetoane onomi alele -

tri itysystem andtoenable ompetitioninthesales ofpower, by separating

the produ tionand saleof ele tri ity fromthe transmissionand distribution

part of the powersystem, whi h willremaina monopoly.

3.2 Parti ipants in the ele tri ity market

Theparti ipantsonthe ele tri itymarkethavebeen gainingtheirexperien e

inafreemarketenvironmentthelast oupleofyears. Comparedtoele tri ity

markets inother ountries, the stru tureof the I elandi marketis dierent.

The market ontain no spot marketand the transmission system is isolated

from other ountries, so no ross border trading with ele tri ity is possible

with other ountries.

Whentheele tri itymarketwasformed,thestru tureand layoutofmarkets

in other ountries were taken into onsideration, but the market is though

partly ustom-made toI elandi ontext andwillbe under onstru tionand

development asparti ipantsgain their market experien e [10℄.

3.2.1 Transmission system operator

The transmission system operator (TSO)is responsible for onstantly keep-

ing all te hni al requirements in the power system within limits, su h as

voltagesand tomaintainthe frequen y requirementsby keepingthemomen-

tarybalan ebetweenprodu tionand onsumptioninthe powersystem. The

system operator has alsothe responsibility for keeping the spinning reserve

in the system within limits to be able to supply primary power when it is

needed.

The system operator is also a onsumer on the market, where he is respon-

sible for buypowerto over the losses in the transmission system.

The system operator in I eland is Landsnet. The owners of Landsnet are

threepower ompanies,Landsvirkjun-TheNationalPowerCompany,RARIK-

I eland State Ele tri ity, Orkuveita Reykjavíkur (Reykjavik Energy) and

Westfjord Power Company, whi h all put their distribution system and all

itsequipment into Landsnet as equity.

All power intensive onsumers and the distributors are onne ted to Land-

snet'stransmissionsystemaswellasallpowerstationswithsevenmegawatts

of installed apa ity and higher. Further,it isalso apart of Landsnet's rule

tomanagethe powertrading onthe balan ing marketand maintain enough

primary reserve powerfor se ured operationof the power system.

3.2.2 Produ ers

The produ erson anele tri ity marketare those who own and operates the

power stationsand produ ethe ele tri ity.

Landsvirkjun produ e ele tri ity for the power intensive industry and for

the wholesale market. The time span of power ontra ts within the power

intensiveindustry deviate between 20-40 years. No spotmarket is inopera-

long term ontra ts. The time spanof ontra ts today withother produ ers

orretailers,wherethe ele tri ityissold tothelo alhouseholds, isinformof

one, three, seven ortwelve years ontra ts.

In addition to Landsvirkjun, there are two other large produ ers on the

I elandi market. TheseareReykjavíkEnergy andSuðurnesHeading,whi h

operate a geothermal power stations. Additionally four other parti ipants

are onthe I elandi ele tri ity markettoday. Threeof them are lo alpower

ompanies, lo ated in the West-fjords, north part and east part of I eland

and one whi h are lo ated all around the ountry, These parti ipants also

operates their own power stations, but in small s ale and buy energy on

wholesale for aresale within their lo alarea.

3.2.3 Balan e responsibility

It an never be known in advan e how mu h ele tri ity ea h onsumer on-

sume and thereforeat sametime how mu hele tri ity ea h produ er ispro-

du ingtimetotime. Ingeneral,thedeviationin onsumptionandprodu tion

between expe tedandrealtime onsumptionis overed bytheplayersonthe

marked whi h are balan eresponsible orbalan eprovider.

The transmission system operator is responsible for the safety and stabil-

ity of the power system. In order to ompensate for the deviation between

plannedgenerationandrealtimegeneration,the TSOthereforeneedstobuy

balan epower onthe balan ing market to over the dieren e.

This balan epoweris boughtfrom Landsvirkjun, who isthe onlyprodu ers

who has ontra ts with Landsnet as a balan e provider. The minimum re-

quirementsforthe volumeof balan epowerinI eland isset to

±

^40MWh/h

for upward- and downward regulation.

Primary power reserve is also needed in the system. Where Landsvirkjun

is the only large produ er with hydropower, the ompany has signed a long

term ontra twithLandsnetforhavingtotal100 MWh/hofprimaryreserve

power in the whole ountry. This power is distributed and lo ated in the

south, north and east part of the island and explained in hapter 4.

3.2.4 Grid owners

Themain roleof thegrid owners istomaintain andoperate thegrid intheir

power inowand poweroutowinthe grid. Where some losses o ur inthe

system, the grid owner is responsible to over these losses and needtherefor

tobuy ele tri ity to over these losses inhisown system.

3.2.5 Consumers

Consumers are all from normal households to large onsumers, like power

intensiveindustries. All onsumershavetosigna ontra t withtheprodu er

they want to buy the ele tri ity from. Further this same onsumers have to

sign a ontra t with the grid owners tobe onne ted tohisnetwork and get

The Transmission System in

I eland

4.1 The transmission lines

Allmainele tri altransmissionlinesinI elandisoperatedbyLandsnet. The

maintransmissionsystem onsistsoflines withvoltagelevelbetween 132 kV

and 220 kV. Landsnet also operates few lines on lower voltages su h as 66

kV and 33kV whi halsoare part of the transmission system [10℄.

ThetotallengthoftransmissionlinesinI elandis2.911km. Totallengthfor

ea hvoltagelevel an beseen intable 4.1. The highesttransmissionvoltage

inI elandis220kV,but the mostre entlines arebuilt for400kVvoltageto

be able tomeet in reased onsumption in the future. This lines are though

urrently operated at 220 KV.The round onne tion around the ountry is

operated at132 kV.

Length of transmission lines atspe i voltage level km

220 kV 612

132 kV 1.244

33 kV and 66 kV 1.055

Totallength of transmission lines: 2.911

Table 4.1: Lengthof transmission lines at spe i voltagelevels.

4.2 The stru ture of the transmission system

The transmission system as it looks today is presented in gure 4.1. As

mentioned all power stations above seven megawatts of installed power are

onne ted to the transmission system. Total 19 su h onne tion points for

inow of power are in the system today. The onne tion points where en-

ergy is taken out from the transmission system today is on 57 pla es and

onne tion points for power intensive industry have four onne tion points

tothe system. Landsnet's transmissionsystem is shown in gure4.1, where

the system is divided up tove areas roundthe ountry [11℄.

Figure4.1: The transmissionsystem inI eland 2008.

Areaone - the south part, in ludeslarge amount of hydropower stationand

approximately40%ofinstalledpowerinthe I elandi system. Thetransmis-

sion networkis strong inthis area and onsistsof meshed 220 kV lines. The

produ tionis dominant in area one and therefore a high share of the power

istransmittedtosouth west part, wherethe main onsumptioninI eland is

lo ated. Totalprimarypowerreserveinthe areais60MWh/handislo ated

inthe power stationsat Þórsá- and Tungnaáriverarea [11℄.

tion in the system and most of the largest onsumer, Reykjavik ity and

surrounding towns, as well as three of four ompanies within the power in-

tensive industry. The power stations in this area are mostly geothermal

power stations with approximately 20% of total installed power in the sys-

tem. Large volume of imported power is needed to supply the onsumption

inthe area. This power istransmittedfrom the southpart 1

and north part 2

through the west part of I eland [11℄.

Area tree - the west part of I eland and the west fjords in ludesquite weak

transmission system with long 132 kV as well as 66 kV lines. This area has

small share of energy produ tion, therefore it is needed to import largest

share of onsumed power to the area from north part of I eland, from area

four[11℄.

Area four - the north part of I eland ontains long 132 kV transmission

lines whi h is a part of the round- onne ted lines round the island. In the

north part, the onsumption is low ompared tothe generated power inthe

area. Installed power in the north part of I eland is approximately 10% of

installedpowerinthesystem, where7%ishydropowerand3%isgeothermal

power. Surplus of power in area four is transmitted out from the area and

even to the west- and/or east part of I eland. Total primary power reserve

intheareais10MWh/handislo atedinthehydropowerstationBlanda[11℄.

Area ve - the east and southeast part of I eland onsist of long 132 kV

whi h form part of the round onne tion round I eland. Also 220 kV lines

from the new Fljótsdalurstation to the aluminiumsmelterin the east part,

around 50 km distan e. Approximately 30% of installed power in the I e-

landi system are lo ated in this area. The majority of generated power is

suppliedto the Aluminium smelter,but alsoit is transmissionto- and from

thenorth-andsouthpart ifI eland. Totalprimarypowerreserve inthe area

is 30 MWh/h and is lo ated in the new hydropower station at the Kárahn-

júkar area [11℄.

Compared to total supplied power to the transmission system in 2008, the

total losses in the transmission system be ame 400 GWh or 2,4% of trans-

mittedpower [2℄

1

Areaonein gure4.1

2

System Planning

This hapter ontains introdu tion of dierent planning periods used when

operationof powersystemsareplanned. Theideabehindthetheoryregarding

system operation and frequen y ontrol isgiven.

5.1 Produ tion planning

Whenpowerstationsare operated,itmaybeoneof themostimportanttask

for the owner and the operator,to run the units in su h a way that natural

resour esare utilizedinasoptimalway aspossible. Bydoingthatthepower

station owner maximize itsin ome at same time, whi h must be one of the

main issue.

When produ tion plans for hydropower systems are made, wheremany sta-

tionsandmanylo alinowrivers arein luded,manyparametersneedstobe

taken intoa ount to makereliable, e ien y and useable produ tionplan.

Many parameter like inow and onsumptions are not known in advan e.

Therefore some un ertainties o ur in ea h made s hedule, whi h lead to

that planning s hedules are needed to be made over and over again, when

new and more reliabledata are a essible.

Byupdatingimportantparameters onstantlywithnewinformationgivethe

planner opportunity to make asreliable produ tion plan as possible though

it willneverbeperfe t.

Dierent planning periods and planningmethods an be dened in atleast

three groups:

•

^{ExpansionPlanning}

•

^{SeasonalPlanning}

•

^{ShortTerm Planning}

5.1.1 Expansion planning

The time horizon within expansion planning an be years or even de ades.

Within the time horizon of expansion planning, power produ ers makes a

s hedule for futures proje ts like building new power stations. When on-

siderexpansionplanningthe un ertaintyisobviouswhere theplanninghave

to onsider the future growth in ele tri al onsumption, the environmental

impa tas wellas development of investment and operational ost [20℄.

5.1.2 Seasonal planning

Thetimehorizonwithinseasonalplanningisbetween6-12months. Theaim

with seasonal planningis tomake s hedule for the water storagewithin the

timehorizonandmakede isionsaboutappropriatetimeoflargemaintenan e

workinthepowerstations[25℄. Themainun ertainties inseasonalplanning

are the riverinow, availabilityof powerstations and the load.

5.1.3 Short term planning

The time horizon within short term planning is from one week down to 24

hours. Theaimofshort termplanningistomakes heduleforthepowersta-

tions understudy. The s hedule has to full ontra ts about sold ele tri ity

as well as the requirement regarding reserved power and other physi al re-

quirements. In short termplanning, more detaileddes riptionsof the power

stationsareneeded aswellasthehydrologi al ouplingsbetween thestations

have tobewellknown tomakereasonableprodu tionanddis hargeplan for

the whole system.

In short term planningthe un ertainties are mainlythe same asin seasonal

planning. Butwhereshortterm plannings hedulesare madedailyandeven

several times per day, when and if new and more reliabledata appears, the

variationof the un ertainties are not aslarge asfor largerplanninghorizons

[20℄.

system intoa ount. If there is any bottlene ks due to amaintenan e work

in the transmission system on spe i area. If that is the ase it may ee t

the operation of the power stations inthe nearest surrounding.

5.2 System operation

Ele tri alenergy an not bestored. Duetothat reason, allele tri alenergy

needtobegeneratedatsametimeasitis onsumed. Thetransmissionsystem

operatoris responsibleto keep momentarilybalan ebetween the generation

and onsumption in a power system and maintain se ure operation of the

system.

5.2.1 Frequen y ontrol

Tokeepthemomentarybalan ebetween theprodu tionand onsumptionin

a power system it is ne essary to have automati ontrol system whi h an

respond within few se onds to deviation between generation and onsump-

tion. Su hautomati ontrolsystem is alledprimaryregulationand itsaim

is tostabilizethe frequen y in the power system.

When disturban es o ur in a power system, where loss of load or loss of

generation o ur, the new stable frequen y will deviate from the nominal

value. The new frequen y will be higher - for the ase with loss of load, or

lower - inthe ase of loss of generation.

Whenthe primary ontrolreservehasbeen usedtostabilizethe frequen yin

the powersystem afterdisturban es, anadditional ontrolis needed toreset

the frequen y toitsnominalvalues. Todothat, se ondary ontrolis usedto

regain the primary ontrol ba k, whi h then an be used again during next

disturban es.

5.2.2 Primary ontrol

Primary ontrol determines the apa ity of the power system to meet un-

expe ted load- or generation hanges. Primary power is automati ontrol

systemwiththe aimtokeep themomentarybalan ebetween generationand

onsumption. The total primary power in multi ma hine hydropower sys-

tem, are dened as the sum of dieren e between the maximum generation

apa ity for the ombination of units s heduled on line and their present

In a syn hronous power system, the deviationbetween produ tion and on-

sumptiono ursinfrequen y deviationinthe system. Thenominalvalueof

the frequen y an vary between power systems and ountries. In North and

South Ameri a the nominal value is usually 60 Hz, whereas in the Nordi

ountries, Europe and most of the remaining world uses 50 Hz [26℄.

Asmentionedbefore, energy an not bestored ina power system,but there

isalarge rotationalmass storedinthe system, so alledmoment ofinertia -

rotating. Thismassisstoredinalltherotatingsyn hronous rotorsandtheir

turbineshafts.

Assume loss of generating unit ina syn hronous power system. From other

generatorspointofview, lossofgenerationisequaltoin reaseinload. Right

after the failure in this generating unit, there is a shortage of power in the

system.

Sin e the generation and the onsumption always need to to be in balan e,

the de it of power is ompensated by using the rotational energy in the

rotors and their shafts, whi h lead to de rease in rotational speed of all the

rotatingma hines inthe system.

Where there is a strong onne tion between rotor speed and ele tri fre-

quen y in syn hronous ma hines, the redu ed rotor speed results in a fre-

quen y de rease in the grid.

To response to the falling frequen y in the grid, frequen y sensitive equip-

ment, lo ated onsome of the primary ontrolunits in hydropower stations,

give a signalto in rease the openingof the guidevane of the turbines to in-

reasethedis hargethrough theturbine, andatsametimethe poweroutput

fromthe generator.

When parti ipating generators in the primary ontrol have in reased their

generationto ompensateforthelostunit,thefrequen y stopde reasingand

stabilizeagain, but atfrequen y lower than the nominalfrequen y. Balan e

has been obtained between generation and onsumption again.

Similar ourses of events appears in the ase of load de rease or genera-

tion in rease. Then only dieren e is that the frequen y in reases, whi h

results in need of de rease the generation in units parti ipating to the pri-

How mu h ea h generators parti ipate in the primary ontrol depends on

their installed frequen y sensitive equipment. Generally, the minimum re-

quirements of speed droop hara teristi s is set by the transmission system

operator inea h ountry.

The I elandi TSO has set minimum requirements regarding the volume

of speed droop hara teristi s to 400 MW/Hz. As des ribed in Chapter

4, the spinning reserve requirements is now set to total 100 MWh/h in the

whole ountry. Additionalminimumbalan epowerneededtobeavailablefor

upward- and downward regulation on the balan ing market is

±

^40MWh/h

for se ondary response ontrol.

Sin ethe I elandi system issmall omparedwiththe powersysteminother

ountries, allthe dynami alswings happen very fast. Therefore the need of

systems su h as fast and well tuned fault breakers and frequen y sensitive

equipments are of grate important.

5.2.3 Se ondary ontrol

The primary ontrol only stabilize the frequen y in the power system. It

does not restorethe system frequen y to the nominalfrequen y again.

Afterthefrequen yinthepowersystemisstable,apartofitssystemreserve

has been usedup tomaintain thebalan ebetween generationand onsump-

tion. In su h ondition, the system isnot able towithstand another faultor

hanges inthe system inform of lostgeneration orin reased load.

It is therefore important to restore the frequen y to its nominal value, to

release the primary ontrol reserves and by that prepare the system to be

able towithstand another faultand frequen y deviation.

Tosolvethesekindofproblemsthese ondary ontrolisused. These ondary

ontrolisslowresponse ontroland an bea tivatedwithin fewminutes. In

the Nordi ountries all se ondary ontrol is ontrolled manually from the

ontrolroomsof the system operators,whi h allforup- ordown regulation

fromthe balan eproviders on the ele tri ity market.

In some powersystems, where the I elandi system is amongthem, the se -

ondary ontrolismanaged with automati generation ontrol(AGC), tore-

reserves.

Modeling of Hydropower Systems

This hapter ontains the theoreti al part of the thesis - the theory behind

modelingahydropowersystem. Apartofthetheoryintrodu edinthis hapter

are then used to built the simulation models studied in the test ases.

6.1 Hydropower generation

Hydropower generation utilizes the dieren e in potential energy between

the headwater surfa e and the tailwater surfa e for power produ tion. The

layout anddesign ofhydropower stationsare largelyinuen ed by lo alnat-

ural onditionsand the generation apa ity isusually expressed inkilowatts

(kW) for small power generation or megawatts (MW) for large power gen-

eration. The sele tion is based on a areful evaluation of several important

parameters, i.e. the gross head and the dis harge. The gross head is the

dieren e inelevation between the the headwater surfa e, and the tailwater

surfa e.

Inthepro esswhendeliveringthe waterfromtheintakegate,down thepen-

sto k intothe turbine losses o urs resultingin de reased gross head. With

in reased dis harge through a hydropower station the gross head de rease

where the headwater surfa e lowered a bit and in same way the tailwater

surfa e rise. Also the losses will in rease in the pensto k with in reased

dis harge. The losses are therefore a fun tion of the head- and tailwater

surfa e level or up- and downstream reservoirs levels. The generation in a

hydropowerstationwillthereforebeafun tionofup-and downstreamreser-

voirlevel as wellas the dis harge through the turbines [23℄,[21℄.

The losses has an impa t on the station's e ien y often alled station or

plant e ien y [23℄. The plant e ien y des ribes how large share of the

potential energy stored in the water in the reservoirs an be onverted to

ele tri alenergy.

The main losses in ahydropower station, ee ting the station e ien y are

informoflossesinawaterways,turbineandgenerator. Wherenotwopower

stationshaveneitherthe samelayout nor the same design,their statione-

ien y are dierent. Forea h powerstation the e ien y,

η tot

^{, is a onstant}

and an be dened as [23℄:

η tot = η w · η t · η g

^(6.1)

where

η w

^{is the e ien y in a waterways,}

η t

^{is turbine e ien y and}

η g

^the

e ien y inthe generator. Normal values of thesee ien ies anbearound

η w ≈ 0.90

^,

η t ≈ 0.93

^and

η g ≈ 0.98

^[23℄.

The power outputof a hydropower station isproportionaltothe produ tof

the head and dis harge and within the statione ien y it an be expressed

as:

P = ρ · g · H · u · η tot

^(6.2)

where

P= powerprodu tion[kW℄

ρ

^{= water density [kg/litre℄}

g= a elerationdue to gravity [m/s

2

℄

H =gross head [m℄

u= dis hargethrough the station [m

3

/s℄

The total energy produ tion, over a time period an then be al ulated

as:

E =

Z

P (t) dt

^{[MWh℄ (6.3)}

6.2 E ien y and dis harge

Oneof the hara teristi sforhydropowersystemis limitationamountofen-

ergy. The energy is stored in the reservoirs, in form of water, and an be

used for ele tri alprodu tion in the future. Where this energy is limited it

optimalway aspossible.

To be able to operate a hydropower system in e ien y way a model is

needed to des ribe the ouplings between dierent parts of the system su h

asreservoirsandtheriversaswellasthepowerstationslo atedinthesystem.

Forshorttermplanningproblemsitisimportanttoobtainasdetailedrepre-

sentationofthepowerstationsaspossiblewheretheoutputoftheshort-term

planning s hedule will be used to operate the system during the up oming

planningperiod.

To determine a generation in a power station it is ne essary toobtain data

aboutitsgeneration hara teristi swhi hdes ribesthe generationasafun -

tion of the dis harge through the station and data about the station's e-

ien y.

Few on epts are needed to des ribe a hara teristi s for a power station.

This on epts haveto be lear in mindand well dened when modeling and

al ulating the power generation in a hydropower station. These on epts

are theprodu tionequivalent,marginalprodu tionequivalentand e ien y

orrelative e ien y.

6.2.1 Hour equivalent of water

In following se tions within this hapter the water dis harge, water spillage

and reservoir ontents are all dened in the equations as hour equivalents

[HE℄.One HE orresponds to the volume of 1m

3

/s water dis harged during

one hour, whi h means 3600 m

3

[26℄.

6.2.2 Produ tion equivalent

The produ tion equivalent is the quota between energy generation and the

dis harge through the turbines and is dierent for dierent dis harge. The

produ tionequivalentishere denoted by

γ

^{and measured inMWh/HE. Ob-}

taining data for a generation and dis harge, the produ tion equivalent for

powerstation

i

^{atthe dis harge}

u

^{an be al ulated by [26℄:}

γ i (u) = P i (u)

u

^{[MWh/HE℄ (6.4)}

6.2.3 Constant produ tion equivalent

The onstant produ tion equivalent, for power station

i

^{at the dis harge}

u

an be dened as the onstant:

γ _i = P i

u

^{[MWh/HE℄ (6.5)}

where

P i

^and

u

^{are installed apa ity for power station}

i

^{and maximal dis-}

harge through the station respe tively.

6.2.4 Marginal produ tion equivalent

To measure how mu h the power generation will deviate for a small hange

indis hargethe marginalprodu tionequivalentisintrodu ed. Themarginal

produ tionequivalentis de lared as:

µ = d

du P (u)

^{[MWh/HE℄ (6.6)}

6.2.5 Relative e ien y

The relative e ien y is a measure of how mu h energy an be extra ted

fromea hm

3

ofwater omparedtothemaximalpossible,i.e. itmeasure the

produ tionequivalentfor some dis harge ompared tothe maximal produ -

tion equivalent obtained for the power station.

Therelativee ien y ispresented as

η

^{and is measured inper ent. Having}

a ess todata showing produ tion equivalentas afun tion of the dis harge,

the relativeprodu tion equivalent an be al ulated as:

η(u) = γ(u) γ max

[%℄ (6.7)

where

γ max

^{isthemaximalprodu tionequivalentobtainedforthestation[26℄.}

If the main obje t of a short-term planning s hedule was only to onsider

the energy generation, without taking other onstraints into a ount, then

the power stations would always been operated attheir maximal e ien y.

For a station with more than one unit, it an be preferable to share the

dis harge between the units in su h a way that the e ien y is maximized,

whereforea h ombinationofunits,therewillbealo albest-e ien ypoint

0 50 100 150 200 250 300 350 0

20 40 60 80 100 120 140

Generation vs. Discharge

Discharge [m ³ /s]

Generation [MW]

Figure 6.1: An example of a genera-

tion hara teristi s. Power generation

as a fun tion of dis harge through a

station.

0 50 100 150 200 250 300 350

0.5 0.6 0.7 0.8 0.9 1

Relative Efficiency vs Dicharge

Discharge [m ³ /s]

Relative Efficiency

Figure 6.2: An example of a relative

e ien y for hydropower station with

two units. Same station as in gure

6.1.

Figures 6.1 and 6.2 shows a generation as a fun tion of dis harge and the

relativee ien y urverespe tivelyforoneofthe powerstationunderstudy.

As anbeseen ingure6.2 alo albest-e ien ypointappearforea h om-

bination of units. When the dis harge rea h the lo al best-e ien y point

with highest dis harge the e ien y de rease fast.

During high load periods, or during spring oods and summer time when

largeinowisintothe system,powerstationsmightbeoperatedabove their

lo albest-e ien y pointwith highest ow toavoidspillage.

6.3 Modeling hydropower generation

Where the relationbetween power generation, dis harge and head is a non-

linearornon- on averelationship,itissomehowneeded toapproximatethis

relationstobeabletomodelingthepowergenerationasalinearprogramming

problem. Several models are on ave approximations of this non-linear or

non- on averelationshipsasthepowergenerationis. The mostsimplestand

ommon models for the generation hara teristi s are a linear model and a

pie ewise linear model.

6.3.1 The linear model

In a linear model the generation is proportional to the dis harge and have

lem.

On the other hand, using linear model have several disadvantages. In a

linear model the solutionmay often ontain operation points far away from

the lo albest e ien y points,resulting inlow e ien y solutions point.

Also itis not possible to onsider osts for start-ups or shutdowns in power

stationsnor forbiddendis harge intervals. Tobeable totakethis point into

a ountmixed integerlinear programminghas to be onsideredwith binary

integerstopresentthe unitstatusinthepowerstations[20℄,[21℄, butwillnot

be onsidered inthis thesis.

6.3.2 The pie ewise linear model

In the pie ewise linear model, shown in gure 6.3, the generation asa fun -

tion of the dis harge isdivided into one ormore segments. The breakpoints

between the segments are lo ated to those dis harges where lo al maxima

appears inthe e ien y. This isone of the main advantages with the pie e-

wise linear model, be ause these dis harges are then more likely to appear

inthe solution for s heduled dis harge. The marginalprodu tionequivalent

0 50 100 150 200 250 300 350

0 20 40 60 80 100 120 140

Generation vs. Discharge

Generation [MW]

0 50 100 150 200 250 300 350

0.5 0.6 0.7 0.8 0.9 1

Relative Efficiency vs Dicharge

Discharge [m ³ /s]

Relative Efficiency

µ _i,1

µ _i,2

µ _i,3

u i,1

u i,2

u _i,3

for station

i

^{and in ea h segment}

j

^is approximated by the onstant

µ i,j

^,

a ording togure 6.3 and alsoinequation (6.6) [26℄.

But it is however possible that the model give solution, where s heduled

power stations are not operated lose to their lo al best-e ien y points.

In gure 6.3 it an be seen that if the dis harge is between the lo al best-

e ien y points the power generation will be overestimated. On the other

hand,ifs heduleddis hargeisplannedbetweenthelo albest-e ien ypoint

with highest dis harge and maximaldis harge through the station,the gen-

eration willbeunderestimated [21℄,[20℄.

So the model work properly the marginal produ tion equivalent have to be

de reasing with in reased number of segments. That is, generation in the

rst segment have to be more protable than the se ond segment, se ond

segment has to bemore protable than the thirdand soon.

Here, protable means that more ele tri energy an by subtra ted out of

ea h HE of water. To fulll this requirements following have to be valid

µ i,j > µ i,k

^if

j < k

^{. Here}

µ i,j

^{is the marginalprodu tion equivalent inpower}

station iand segmentj [26℄.

6.3.3 Total dis harge and power generation

Where the marginalprodu tionequivalent isapproximated by a onstantin

ea h segment, the total dis harge through power station have tobe divided

in one variable per segment. For the power station i, the total dis harge

through the power station an mathemati ally be expressed as:

u i (k) =

n i

X

j=1

u i,j (k)

^(6.8)

u i (k)

^{= dis harge through power stationi, during hourk.}

u i,j (k)

^{= dis harge in power station i,segment j, during hour k.}

n i

^{= numberof segmentsin power stationi.}

The total power generation in a power station an then be expressed as

:

P i (k) =

n i

X

j=1

µ i,j u i,j (k)

^(6.9)

P i (k)

^{= power generation inpowerstation i,during hour k.}

µ i,j

^{= marginal produ tion equivalent in power station i, seg-}

6.4 River inow

To be able to make reliable produ tion plans for a hydropower system and

operatethe system in anoptimalmanner, itis importanttohave asreliable

inowfore asttoea hpowerstationand reservoir inthe systemaspossible.

Inthisthesisthe riverinowtopowerstation

i

^duringhour

k

^{isexpressed as}

w i (k)

^{. Weather onditions su hasrain,} temperatureand snow meltinghave great ee t on the river inow. However it an be very di ult to make a

good fore ast wherethe weatherfore asts is not always reliable.

For a short term planning, whi h normally span the time s ale from one

day to one week, it is ommon approximation to onsider the fore asts for

the riverinow and the ele tri al onsumptions asperfe t and reliable fore-

asts. Whennew fore asts are available forthe riverinowor onsumptions

the s hedules are updated.

6.5 Reservoirs

Where the ele tri al onsumption is high during periods when natural ow

in the rivers are low, like during winter time, reservoirs are needed to store

the water, whi hthen an beused for energy generation later in the future.

Many reservoirs are often lo ated in the same river system, with dierent

ontents volume and dierent role fromthe system operation point of view.

Thereservoirswithlargestvolume ontentsinariversystem arenormallylo-

atedintheupperpartof thesystem, whilethesmallerreservoirarelo ated

inthe lowerpart.

6.5.1 Seasonal reservoirs

Some reservoirs have large storage volume in order to store water from the

spring ood to the winter when the onsumption is high. These type of

reservoirs are normally lo ated in the upper part of the river system, as

previouslymentioned,andarenormallyusedforlongtermorseasonalenergy

storage. If there is no rivers onne ted to the system downstream, these

6.5.2 Short term reservoirs

Reservoirs used for water storage on weekly and daily basis are normally

lo ated in the lower part of the river system. These kind of reservoirs are

often used for short term operation su h as weekly or daily operation of a

powerstationsandarenormallylo atedinthelowerpartoftheriversystem.

6.5.3 Reservoirs operation

Reservoirwitha powerstation downstreammay have somerequirementsre-

garding how mu h the water level in a reservoir an variate up and down

from some spe i normal level time to time. Often the normal operation

levelforareservoirisdened fromthe situationwhen allunits forthepower

stationunder study are inoperation. Theserequirementsmay be set due to

environmental orte hni al reasons and an variatefor dierent periods and

dierent season of the year.

From a ele tri al produ er point of view it is also important to keep the

reservoirlevelwithin spe i limitstoobtain and maintain good generation

e ien y.

6.5.4 Reservoir onstraints

For a power station

i

^{, with the reservoir storage ontents}

x i

^{, it may be}

desirable to keep the reservoir level within some upper and lower limits,

denedhereas

x i

^and

x _i

respe tively. Preferableoperationlevelofareservoir for apower station

i

^{an then be be dened as:}

x _i (k) ≤ x i (k) ≤ x i (k)

^(6.10)

Requirementsregarding how fast the water surfa e an beregulated up and

down an also be found in some reservoirs. Normally this an be found in

those reservoirs where the reservoirs ontents are quite small or where the

reservoirswater levelis sensitivedue toinow, dis harge orspillage.

Su h onstraints an also be found where large and high dis harging hy-

dropower station is lo ated with many units. These stations are often able

todis harge large volume of water through the turbines duringshort period

6.6 Spillage

The spillageisthe volumeof water owing froma reservoir, by apowersta-

tion without owing through the turbines. Here, the spillage, dened as

s

^,

inpowerstation

i

^hour

k

^{is expressed as}

s i (k)

^.

Spillage an be ontrolled and un ontrolled. Controlled spill an havelower

limit

s _i

^{and anupperlimit}

s i

^.

s _i (k) ≤ s i (k) ≤ s i (k)

^(6.11)

6.6.1 Un ontrolled spillage

Un ontrolled spillage an appears during spring oods when river inow is

large and all the reservoirs in the system are full and an not store more

water. During su h situation the water ows normally over the spe ially

designed overowspillways on the dam and down its naturalriverbed.

6.6.2 Controlled spillage

Controlled spillage is the ontents of water owing through a ontrollable

gates. Due to environmental reasons it may be stated by spe ial water- or

environmental ourt that it may be needed to spill some minimum ow of

waterpast apowerstation,down naturalriverbed whi hotherwise wouldbe

dry.

It may also be needed to spill water during maintenan e periods to fulll

minimumrequiredinows todownstreampowerstations,where somepower

stationsdo not have any naturalinow. Howsu h power stationsare oper-

ated fromhour tohour, depends on howthe losest power stationupstream

are operated atsame time and the spillage fromthat power station.

6.7 Hydrologi al oupling between power sta-

tions

Hydropower stations an form quite ompli ated system when they are lo-

ated in the same river with many reservoirs, dierent in size and with dif-

ferent role in the system. Cas aded power stations form a oupled system

where the operation of the power stations lo ated in the upper part of the