Integration of 50 % wind power in a CHP-based ... - Ea Energianalyse

**Integration** **of** **50** % **w ind**

PrefaceiPrefaceThis report has been submitted at the Department **of** Electrical Eng**in**eer**in**g at theTechnical University **of** Denmark as part **of** the requirements to achieve the Master **of**Science **in** Energy Eng**in**eer**in**g.The thesis is developed **in** collaboration with, as well as with guidance from, **Ea** **Energianalyse**A/S (**Ea**), and I owe many thanks to all the employees for fruitful discussions,**in**puts and for creat**in**g a pleasant and **in**spir**in**g atmosphere to work **in**. A special thanksgoes to my supervisor Hans Henrik L**in**dboe (**Ea**) for first **in**troduc**in**g me to the ma**in**objective **of** this thesis plus cont**in**uous guidance, and to Lars Bregnbæk (**Ea**) for essentialguidance regard**in**g the build**in**g **of** the model **in**clud**in**g explanations **of** theoreticalbasics. I would also like to thank my supervisor Zhao Xu from Centre for Electric Technologyat DTU, for constructive comments and guidance throughout the entire processand Liv Bjerre for help on the statistical analysis us**in**g SPSS as well as for feedbackregard**in**g the presentation **of** the content. I would also like to thanks Adam Bank Lentzfor constructive comments. However, the full responsibility **of** the f**in**al design **of** the thesislies with the author.Over the last years much have been written about the **in**tegration **of** large **w ind** capacities

AbstractiiiAbstractBy 2025, **50** per cent **of** the Danish **power** generation is to come from **w ind**

vTable **of** contentsPreface ..................................................................................................................................... iAbstract ................................................................................................................................ iiiNomenclature ......................................................................................................................... 1Chapter 1. Introduction ..................................................................................................... 51.1. Background ............................................................................................................. 51.1.1. A visionary Danish energy policy ................................................................... 51.1.2. Issues to exam**in**e **in** order to meet the visionary Danish energy policy ....... 51.2. Objectives ................................................................................................................ 61.3. Method and Delimitation ........................................................................................ 71.4. Applied concepts ...................................................................................................... 91.5. Outl**in**e **of** the thesis .............................................................................................. 10Chapter 2. Pre-study Results .......................................................................................... 112.1. The objective **of** the pre-study............................................................................... 112.2. Results **of** the pre-study ........................................................................................ 11Chapter 3. Characteristics **of** the Danish energy system ............................................... 133.1. An Insight to the Danish energy system .............................................................. 133.2. Energy system characteristics .............................................................................. 133.2.1. The Danish **power** transmission system ....................................................... 133.2.2. District heat**in**g .............................................................................................. 153.2.3. System plann**in**g – now, and until 2025 ....................................................... 163.2.4. Market composition ....................................................................................... 183.3. Heat and **power** generation – a review **of** the various technologies .................... 223.3.1. Technical and economical properties ............................................................ 223.3.2. Technologies for **in**creased flexibility **in** electricity production ................... 27Chapter 4. The impacts **of** **w ind**

vi4.4. The characteristics **of** critically low prices ........................................................... 384.4.1. The daily distribution **of** low prices .............................................................. 384.4.2. Durations ....................................................................................................... 404.5. The relation between critically low prices and **w ind** production, decentralizedproduction, central production, demand, capacity and hour

viii8.4. Validity **of** the results ......................................................................................... 1608.4.1. Statistical data ............................................................................................ 1608.4.2. The unit commitment model ....................................................................... 1608.4.3. The importance **of** optimization model**in**g .................................................. 162Chapter 9. Conclusion .................................................................................................... 164Chapter 10. Bibliography ............................................................................................. 16810.1.1. Articles and books ....................................................................................... 16810.1.2. Web pages .................................................................................................... 17010.1.3. Personal contact .......................................................................................... 171Chapter 11. Appendix .................................................................................................. 17211.1. Logistic regression – validity **of** the regression model ...................................... 17211.1.1. Likelihood ratio and Wald test ................................................................... 17211.1.2. Hosmer -Lemeshow test .............................................................................. 17211.1.3. Assumptions ................................................................................................ 17311.2. How much **of** the heat supply from heat pumps is renewable energy? ........... 17411.3. The Unit Commitment Problem ......................................................................... 17511.3.1. Optimiz**in**g the Unit Commitment Problem ............................................... 17511.3.2. Solv**in**g the Unit Commitment Problem ..................................................... 17611.3.3. GAMS/CPLEX ............................................................................................. 17811.4. Optimal GAB sizes from GAMS/CPLEX ............................................................ 17911.5. The formulated GAMS model ............................................................................. 18011.5.1. Code for the formulated GAMS model for the Reference and bypassscenario 18011.5.2. Code for the formulated GAMS model for the heat pump scenario .......... 184

Nomenclature 1NomenclatureAbbreviations:BPO:**CHP**:CLPCOPel.ExpLFMIPMWhRETSOUCShort for extraction units be**in**g **in** the state **of** ByPass Operation, **in** whichheat is produced without generat**in**g electricity. Sometimes referred to justas bypass.Comb**in**ed Heat and Power is the use **of** a heat eng**in**e or a **power** station tosimultaneously generate both electricity and useful heat. **CHP** captures theby-product heat for domestic or **in**dustrial heat**in**g purposes - as hot waterfor distric heat**in**g.Critically Low Price. A price on electricity below 6.61 € (**50** Dkk) per MWh.Coefficient Of Performance. Indicates the amount **of** heat from heat pumpsper unit electricity.Short for electricity or electrical.ExponentLoad Factor, or full-load factor.Mixed Integer Programm**in**gMegawatt hourRenewable EnergyTransmission System Operator. The Danish TSO is Energ**in**et.dk.Unit CommitmentGreek letters:βαηbpη**CHP**,iηel,iη **CHP** hWeight **in** the logistic regression.Constant **in** the logistic regression.Heat efficiency dur**in**g bypass operationThe **CHP** net efficiency **of** unit i (equals the heat exchanger efficiency)Electrical net efficiency **of** unit iMarg**in**al **CHP** heat-efficiencyLat**in** letters:b t i B**in**ary variable **in**dicat**in**g whether to switch BPO on or **of**f (0;1)CStochastic objective function

2 NomenclatureCi(e,h)cv,icm,iMmcimccpmccbpmcdcbmcxO&MPP t cb,iP t chp,iP t dcbP t dchP t D,xP t D,elP t D,h,dcP t D,h,iP t el,iP t el_bp,iP t el_hp,iP t h,iP t h_bp,iP t h,max,iP t iPmax,iPm**in**,iPst,iP t WP t W,maxP t xP t 12Cost functionLoss **of** electricity per unit heat extracted from the turb**in**e buckets **of** unit I(ISO-fuel value)Backpressure value **of** unit iA very large numberMarg**in**al costs **of** unit iMarg**in**al costs **of** central boilersMarg**in**al costs **of** central backpressure unitsMarg**in**al costs **of** decentralized boilersMarg**in**al costs **of** hydro **power** (the fixed value **of** hydro **power**)Operation and Ma**in**tenance (used **in** connection with variable O&M costs)ProbabilityBoiler capacity **of** the central areas **of** unit iBackpressure **CHP** unit **in** the central area **of** unit iDecentralized boiler productionBoiler capacity **of** the decentralized areasDemand **in** exchange areaElectricity demand **in** ma**in** areaHeat demand **in** decentralized areaHeat demand **in** central area iElectricity production from the 11 unitsElectricity production from backpressure **of** unit iElectricity consumption **of** heat pumps **of** central area iHeat production **of** unit iHeat production from decentralized backpressure unit iMaximum heat production **of** unit iFuel constra**in**t **of** unit iMaximum **power** generation on central unit iM**in**imum **power** generation on central unit iMaximum start**in**g **power** **of** unit iProduction from **w ind**Maximum production from

Nomenclature 3P t 12,maxPi(e,h)sc t ist t iURx t iYMaximum capacity on external connectionPower generation as a function **of** electricity and heatStart-up costs **of** unit iStart-up **in**dicator **of** unit iUp-ramp constra**in**t dur**in**g constant operationB**in**ary variable (0;1) **in**dicat**in**g whether the unit i is committed or notDependent variable

6 Introductionthe problem will become when **in**creas**in**g the **w ind** production share to

Introduction 73. Application **of** the model developed **in** (2) to analyze the consequences **of** the future**w ind** capacity, plus an analysis

8 Introductionledge, help develop a model with the exact properties needed **in** order to meet the primaryobjective. Both parts **of** the project imply a preced**in**g literature study. The review **of**the West Danish energy system **in** the project’s first part is a cont**in**uation **of** the literaturestudy started at the pre-study. The strategy **of** the literature study was to select andanalyze previous studies done on **w ind** penetration

Introduction 9The heat supply will be divided **in**to a number **of** central heat distribution areas partlysimilar **in** the real system, whereas – for simplifications – the many decentralized district-heat**in**gareas will be represented by one, large area. On the electrical side, the **in**ternaltransmission **of** the **power** system will be merged as one bus, except from externaltransmission areas. This means that transmission losses and **in**ternal overstresses willbe disregarded. And **in** some cases the results may reflect a stronger network than **in**reality. This is normal for a market model.For market simplifications, the hourly supply **of** heat and **power** is limited to one hour,assum**in**g that all energy is traded by hourly bids (cf. section 3.2). In this way, the supplieswill not be restricted by any forms **of** block bids or long term contracts. As a result,the modeled system may reflect a more efficient spot market than the real one. The **power**and heat demands will be regarded **in**elastic. In this connection, one **of** the model’sgreatest deviations from the real heat system will be the lack **of** heat accumulation tanks**in** the model. This means that, not only **power**, but also the heat supply will have to momentarilybalance the demand each hour, which may result **in** a less flexible **CHP** productionthan **in** the real system. Another simplification regard**in**g the market is that theexternal area only produces hydro **power**. The basic idea **of** this is to imitate the **in**terplay**of** **power** exchange between the Danish **w ind** generation and the Nordic hydro generation,by which an exchange area like the Germany

10 Introductionare most **of** the time used **in** relation with **in**crease **in** the amount **of** **power** generationfrom **w ind** turb

12 Pre-study Resultsroughly estimated 2 to concern no more than around 0.5 % **of** the total turnovers **of** theelectricity market, but one could argue, that this share is not high enough to be consideredreally problematic. Of greater importance, it was found, that when look**in**g at thehours **of** critically low price, the **w ind**

14 Characteristics **of** the Danish energy systemnect**in**g the two non-synchronously Danish systems, is presently under construction andis expected to be commissioned **in** 2010. Furthermore, plans are to establish a third connectionto Norway with**in** a few years, **in** order to meet the **in**creas**in**g need for exportation(Energ**in**et.dk 2007).Import / export (MW)NO1Connections:ACDCUnder construction1000 / 1000 MW680 / 740 MWSwedenWest-DK**Ea**st-DK9**50** / 1700 MWEEXFigure 3.1. Overview **of** the connection capacities between the two Danish Transmission systemsand the surround**in**g countries (data source: Energ**in**et.dk).In the Nordic area, the different TSO companies have assembled **in** a corporation calledNordel **in** order to achieve a uniform Nordic system operation. The first step **in** thisprocess is to make the transmission between the Nordic countries more efficient. Unfortunately,the effectiveness **of** the collaboration with the German TSO has still notreached the Nordic level (Energ**in**et.dk 2007). A symptom **of** this is seen from the differentcapacities on the connection between West-DK and Germany (Energ**in**et.dk 2006). Inaddition, the Swedish TSO Kraftnett, has occasionally been accused **of** exploit**in**g thefrequent bottleneck situation between the north and the south **of** Sweden (Hvidsten2006) and hence, manipulat**in**g the **in**ternal Swedish market price.The state owned Danish TSO Company Energ**in**et.dk has the overall responsibility forthe development and ma**in**tenance **of** the transmission network, as well as for the momentaryactive and reactive **power** balanc**in**g. Additionally Energ**in**et.dk is **in** charge **of**the primary and secondary frequency control, although other balance-responsible parties(BRPs) **of**ten are handl**in**g this **in** practice. The TSO Company’s role can be describedwith the fallow**in**g two keywords: system security and system adequacy (**Ea** **Energianalyse**2007). Security covers the adjustment **of** rapid and unexpected changes **in** productionand demand **of** active and reactive **power**, and adequacy covers the secur**in**g **of** sufficientgeneration capacity for the more rare cases **of** energy shortage. To be able to fulfillthese ma**in** responsibilities the TSOs, among these Energ**in**et.dk, have a set **of** fundamentaltools at their disposal – one **of** these be**in**g ancillary services.One **of** the ancillary services purchased by Energ**in**et.dk for immediate balanc**in**g is thecommitment **of** at least three central **power** plants for each transmission system, whichcontrols speed and grid voltage. A service made possible through contract**in**g with companiesable to deliver this service (Ørum 2008). For balanc**in**g on a lower time scale the

16 Characteristics **of** the Danish energy systemFigure 3.2, Picture **of** a larger branched heat-system **in** Copenhagen that **in**cludes a number **of**heat producers (Source: Varmeplan Hovedestaden)3.2.3. System plann**in**g – now, and until 2025As mentioned earlier Government plans are to **in**crease the level **of** renewable energy **in**the system with**in** 2025 to 30 %. It has been derived that an **in**crease **of** the current **w ind**penetration level from approximately 25 pct. to

Characteristics **of** the Danish energy system 17The first **in**itiative implies a need for controll**in**g the **power** output **of** the **w ind** turb

18 Characteristics **of** the Danish energy system3.2.4. Market compositionGeographical market division **in** the Elspot area:Norway 2Norway 3SwedenNorway 1F**in**landWest‐DKEEX**Ea**st‐DKKontekFigure 3.3. A geographical overview **of** the markets **in** the El Spot-area. Note that Sweden andF**in**land have not be**in**g **in**ternally divided **in**to markets like the rest, and that the Kontek arearepresents the former **Ea**st Germany, while the rema**in****in**g German system goes under EEX.(Source: Nordpool Spot)The Spot marketThe Spot market is the place where producers and buyers trade physical **power**. Theprimary function **of** an organized spot market for electricity is to maximize cost efficiencyby ensur**in**g that the most economic supplier get to satisfy the demand for **power** (NordPool Spot)Ever s**in**ce the Danish **power** systems and its parties fully switched to market conditions,all trad**in**g activities **in** the Nordic area have been tak**in**g place at the physical spot market:Elspot – owned and managed by the company Nordpool Spot. Here, **power** is tradedone day ahead on an hourly basis every day. Other goods such as CO2 certificates aretraded on Nordpool as well. Entrants on Elspot are primarily producers, heavy **in**dustrialconsumers buy**in**g for themselves and f**in**ally; retailers – resell**in**g the energy to “regular”consumers such as households.Today, Elspot prices are formed **in** eight different price areas allocated on five countries 7 .Although the **power** is traded on an hourly basis, not all energy on Elspot is traded viathe hourly bid. Some quantities are **of**fered for much longer time periods, **in** fact, somebids are **in**dependent **of** price for all hours. Also, a part **of** the suppliers make use **of** blockbidd**in**g while sett**in**g a sort **of** 'all or noth**in**g' condition (Elspot). In this way they ensurethe plants generat**in**g the **power** (usually the ones with cost heavy start-ups) a fixed7Countries **in**clude Denmark (2 price areas), Sweden (1), Norway (3), North-east Germany (Kontek) (1),and F**in**land (1). Political bodies have for some years tried to encourage Swedish TSO authorities toperform a much needed fragmentation **in**to more price areas **in** order to encounter the frequent bottlenecksituations.

Characteristics **of** the Danish energy system 19price and volume throughout the respective hours. A block bid is accepted if the follow**in**gconditions are met (Elspot):−−If the bid price **of** a sales block is lower than the average Elspot area priceIf the bid price **of** a purchase block is higher than the average Elspot area priceProducers can also choose to **of**fer available capacities **in** the form **of** balanc**in**g-**power**.This takes place on the market for regulation **power**: Elbas, which is open as soon as upto an hour before the physical exchange (**in**tra-day trad**in**g), opposed to the spot marketwhere deals are closed the day before (Elspot).Hourly formation **of** pricesDue to the markets cont**in**uous **in**ability to store electricity, the price formations on theSpot market are first and foremost characterized by a number **of** producers supply**in**g aconstantly fluctuat**in**g and relatively **in**elastic demand (Krist**of**fersen & Stouge 2002).Figure 3.4 shows a pr**in**ciple sketch **of** the capacities **of** the systems cumulated accord**in**gto their **in**dividual marg**in**al supply costs – also known as the Merit Order. For eachhour, the consumer’s marg**in**al utility sets the price (Ravn 2001). One **of** the largest factorsaffect**in**g the prices on an average basis is the sea level **of** the Swedish and Norwegianreservoirs, which determ**in**ates the optimal price levels for the hydro owners. Highsea levels, be**in**g a great **in**centive to supply, opposite to low levels, where the ownersprobably will hold back and wait for “better prices to come”. Thus, wet and dry years arethe overall factor when look**in**g at average prices (**Ea** **Energianalyse** 2007).Contribution from vary**in**gCO2 costs(can redeploy rank**in**g)Figure 3.4, A pr**in**ciple sketch **of** the accumulation **of** marg**in**al costs **of** available capacities.It shows how the outcome **of** price formations varies – typical throughoutthe different periods **of** a normal day. Grey shadow areas above coal (Kul) and gas**in**dicate the unknown contribution from CO2 **in**dulgence, which ma**in**ly affect thecoal proce mora than gas due to higher specific carbon content (data source: **Ea****Energianalyse** 2007).Cross border trad**in**gWhen it comes to cross border trad**in**g the Nordic electricity market turns out to be asuccessful example, transmitt**in**g large volumes **of** energy every day (Togeby, L**in**dboe &Pedersen 2007). The biggest issue **of** cross-border transmission is the degree **of** conges-

20 Characteristics **of** the Danish energy systemtions – or bottlenecks. S**in**ce capacities **of**ten are constra**in****in**g a perfect market situation 8the transfer **of** **power** (and thereby the settlement **of** the supply) **of**ten results **in** a f**in**alprice difference. Market price differences are therefore a symptom **of** bottlenecks. Insuch cases, congestions are managed by divid**in**g the price difference equally **in** favor **of**the two system operators. The concept beh**in**d this: the more prices drop **in** one area, like**in** the extreme cases **of** electrical spillover **in** West-DK, the bigger the price differenceand thus the bottleneck **in**come and the resources for further **in**vestments **in** additionaltransmission capacity 9 .When speak**in**g **of** congestions on external transmission, it is important to dist**in**guishbetween the physical limitation on the sea cables and the more ‘artificial’ limitation fromthe variations **in** announced capacities by the different TSOs 10 – a factor that varies fromcountry to country as shown **in** Table 3.2. As an example, the rated capacities go**in**g toWest-DK from Sweden and Germany, respectively, are (as a rule) lower than the fortransmissions go**in**g the opposite direction, and the same can be said about the averagelyannounced capacities.Capacities to: NO SE DERated physical exchange cap. [MW]Rated physical import 1000 680 9**50**Rated physical export -1000 -740 -1700Average announced cap. [MW]Import capacity. 754 **50**7 820Export capacity. -721 -494 -1184Period **of** no allowed import [%] 0.8 5.5 0.1Period **of** no allowed export [%] 0.9 5.1 0.1Maximum registered exchange [MW]Import 1041 810 1634Export -1913 -998 -1642Table 3.2, Average Capacities from NO, SE and DE to West-DK, respectively, show**in**g thesometimes big differences **in** rated physical capacities the average announced capacities,throughout the observed five year period (2004-09), but also that there are significant differences**in** the rated capacities for each direction on the same connections (data source:Energ**in**et.dk).8A balanced market with no physical limitations on the supply and exchange **of** **power**9One could question the **in**centive to **in**vest **in** additional transmission capacity, whereby the bottleneck**in**come will drop. The bottleneck **in**come is ear marked improvements **in** the transmission systemthough.10 One if the typical reasons why one **of** the TSOs some hours announces a lower capacity on **in**terconnectionsthan the actual rated capacity is hav**in**g to protect its transmission system aga**in**st **in**ner stresslevels.

Characteristics **of** the Danish energy system 21Management 11 **of** congestions takes place on Nordpool by the specific system operators **of**concern **in** union. The decision whether to regulate the market **in** connection with crossborderstrad**in**g, are taken by the TSOs manag**in**g the particular connection, and thedecisions are ma**in**ly **based** on concerns **of** security **of** supply, environmental issues, andthe **in**ner stress level **of** the transmission system, (Togeby, L**in**dboe & Pedersen 2007). Inthe end, this means, the decisions **of**ten depend on the TSO be**in**g most concerned aboutthe **in**ner stress level. The Swedish system operator Kraftnett is statistically more **in**terested**in** import**in**g than export**in**g **in** Southern Sweden. In Table 3.3 is seen that 20 % **of**the time, no exchange **of** **power** takes place on the connection between West-DK andSweden and, for some reason, **50** % **of** these hours no capacity is allowed.Trade NO Trade SE Trade DEAnnually trade [TWh / year](2004-09 mean)Import 3.31 1.63 1.20Export -1.62 -0.96 -5.30Net, Import 1.70 0.67 -4.10Overall net import -1.73Average transmission **of**:Planned import [MW] 633 392 494Planned export [MW] -5**50** -340 -837Actual import [MW] 588 354 495Actual export [MW] -**50**4 -249 -877Planned trade factor [%]Import 59.6 47.4 27.8Export 33.6 32.1 72.2No transmission 6.8 20.6* 0.0***50**,6% **of** the time, announced transfer capacity is zeroTable 3.3, Key figures for cross-border trad**in**g over a five year period (datasource: Energ**in**et.dk).One could say about theses rated as well as announced **in**terconnection-capacities that –**in** practical – they could (and should) be the same each way. The subject **of** the currenteffectiveness **of** congestion management **in** the Nordel area are regularly up for discussion(Togeby, L**in**dboe & Pedersen 2007)11 Congestion management refers to the pr**in**ciples used to handle the physical flow **of** **power** across cuts**in** the transmission grid with limited capacity. (Nord Pool Spot)

22 Characteristics **of** the Danish energy systemCarbonWith the **in**troduction **of** CO2 quotas 12 the ambition is to promote **in**vestments **in** lesscarbon **based** generation technologies, by add**in**g an overall limit to the total emission,and leave it to market forces to decide the ‘value’ **of** pollution. This relation is attemptedreflected through the grey areas **in** Figure 3.4 from earlier.The system is still tak**in**g form, and the design **of** the system is therefore still up for discussion.Some observers fear that too many free CO2 options have been issued, caus**in**g adevaluation **of** the options and thus a low **in**centive for ‘green’ **in**vestments **based** on this(CAN Europe 2006). One could therefore argue for a significant cut **in** the amount freeCO2 options. None the less, CO2 emission trad**in**g has steadily **in**creased **in** recent years.(CAN Europe 2006), and will be **in**cluded **in** the model**in**g **of** production costs **of** thermalunits the later on.3.3. Heat and **power** generation – a review **of** the various technologies3.3.1. Technical and economical propertiesI this section some **of** the basic properties **of** the different **power** generation technologiesthat constitute the Danish heat and **power** system today will be expla**in**ed. Emphasiswill be on the parts significant to the construction **of** the mathematical model – theseparts be**in**g for example the most frequent or significant types **of** **power** units, primarilyfuel sources etc.Power plants and fuel sourcesMany **of** the centralized **power** plants are focus**in**g on the use **of** different types **of** CO2neutral bio fuels such as wood and straw for fuel**in**g one **of** their blocks – accord**in**g totheir pr**of**iles (DONG Energy 2009). Despite **of** this, facts are that the primary source forgenerat**in**g **power** **in** the Danish **power** system, by far is coal (Dansk Energi 2007). Onthe heat-production side biomass constitutes around one third **of** the fuel consumption,as seen **in** figure Figure 3.5, but still coal and gas represent the ma**in** source.OilCoalWasteNatural GasWaste heatBiomassFigure 3.5, Distribution **of** fuel consumption for district heat**in**g (data source:Energ**in**et.dk)12In April this 2000, the European Commission approved the Act on CO2 Quotas for Electricity Productionpursuant to the state subsidy regulations. The Act therefore entered **in**to force on 15 July 2000with effect from 2001. The quota system entails that the **in**dividual Danish **power** companies receive aCO2 emissions permit each year that will gradually be reduced **in** size (Miljøm**in**isteriet 2000).

Characteristics **of** the Danish energy system 23Regard**in**g production capacity, 53.4 % **of** the total **power** **in** West-DK is generated on thecentral units (all steam units) shown **in** Table 3.4. This corresponds to 96.9 % **of** the totalcentral **power** generation (Table 3.4, Figure 3.6). Two units **in** West-DK have very littleheat output by which they roughly can be characterized as generat**in**g condensed electricity,these are: Nordjyllandsværket block 2 (NJV2), which is quite old and used onlyfor peak loads (Vattenfall 2009), and Enstedsværket (ENV) which represents about 16.4% **of** the total el. generation from central units. The pie chart seen **in** Figure 3.6 belowshows the same.Power units:Annual (2007) el. production [GWh]PercentageNumber **of****of** total productionGWhs[%]Percentage**of** central production[%]BlocknameRated el.capacity[MW]Rated heatcap. [MW]Nordjyllandsværket 3191 13.7 24.7NJV2 225 420NJV3 410 455Studstrupsværket 2413 10.3 18.7SSV3 3**50** 455SSV4 3**50** 460Enstedsværket 2111 9.0 16.4 ENV3 626 340Esbjergværket 2115 9.0 16.4 ESV3 378 475FYV3 235 444Fynsværket 1762 7.0 13.7FYV7 362 42Skærbækværket 897 3.8 7.0 SKV3 392 85Table 3.4, Capacity **of** **power** units **in** West-DK (data source: Dansk Energi 2007).Figure 3.6, Distribution **of** el. production by centralized, de-centralized and**w ind** units. Centralized production divided by the top six units

24 Characteristics **of** the Danish energy systemIn Figure 3.7 is seen a pr**in**ciple diagram **of** an extraction unit, where heat is usuallyextracted at the low pressure turb**in**e and used for district-heat**in**g. What dist**in**guishesextraction units and the more conventional condens**in**g units apart is the steam extractionat the low pressure turb**in**e (4, Figure 3.7) and **in**to the fallow**in**g heat exchanger fordistrict heat**in**g (6 and 7, Figure 3.7). An energy-efficient technique compared to generation**of** condens**in**g **power**. When it comes to the electricity to heat ratio, this technologyhas a set **of** degrees **of** freedom **in** terms **of** the ability to vary heat output, go**in**g fromcompletely condensed el. generation to a maximum heat def**in**ed by the backpressurelimit.1111PG2 3 4 56710 89Figure 3.7, A classic example **of** an extraction unit as seenthermodynamically. The heat-extraction po**in**t is located asseen above heat exchanger (6), from which the thermalheat for district-heat**in**g is pulled out (source: Akraft 2009).1. Boiler2. High pressure turb**in**e (backpressure)3. Medium pressure turb**in**e4. Low pressure turb**in**e5. Power generator (AC)6./7. Extraction for districtheat**in**g8. Low pressure turb**in**e cool**in**g9. cool**in**g water11. Fuel (coal)Although generat**in**g heat this way is not entirely free, the loss **of** electricity generationis rather **in**significant. In Figure 3.8 below it can be seen that - at constant boil**in**g **power**- the marg**in**al loss **of** electricity from extract**in**g one extra unit **of** heat is **in**dicated by theISO-fuel l**in**es (Gronheit 1993). The slopes **of** these ISO-fuel l**in**es are given by the cv coefficient.In this project, the marg**in**al loss will be given by cv = 15 %, correspond**in**g tomodern extraction units (Danish Energy Authorities 2005). With an electrical netefficiency**of** 45-**50** % (condens**in**g), we get an **in**stant, marg**in**al co-generated heatefficiency**of** ~300 % as seen **in** equation (3.1):**CHP** ηelηh= ≈ 300% (3.1)cvIn reality the ISO fuel l**in**es are more curved as seen **in** Figure 3.8 to the left. However,these can with reasonable approximation be regarded l**in**ear accord**in**g to Figure 3.8 tothe right. The maximum heat output is constra**in**ed by the backpressure limit, given bythe backpressure value cm and the maximum capacity **of** the heat exchanger Ph,max.When operat**in**g **in** backpressure mode, the electrical efficiency drops to around 39 %, butwith the heat output added, the total **CHP** efficiency (for new plants) can reach a level **of**93 % (Danish Energy Authorities 2005). **Ea**ch ISO fuel l**in**e corresponds to an extractionpo**in**t at one **of** the low pressure turb**in**e’s buckets. The backpressure rate for extractionunits is **in** this project around 0.75 units **of** electricity per one unit **of** heat.

Characteristics **of** the Danish energy system 25El.El.P el maxP el maxc vc mc mP el m**in**P el m**in**P h maxP h maxFigure 3.8, The ‘curvy’ ISO fuel l**in**es (figure to the left), which express heat vs. el. dur**in**gconstant boiler **power**, can with reasonable approximation be modeled as l**in**ear(figure to the right). Maximum heat capacity is given by the heat exchanger while m**in**and max limits on **power** output are set by the boiler (source: Gronheit 1993).Unfortunately, the option **of** reduc**in**g the heat output when there is no need for it doesnot work the other way around, due to the back pressure constra**in**t. Reduc**in**g **power**while produc**in**g heat would be convenient **in** times **of** low electricity demands and highheat demands, though. A critical disadvantage **of** these units – **in** relation to the currentsystem – is that they **of**ten are designed for base and medium load, which is reflected **in**their large physical size, slower up- and down regulation, as well as high **in**vestmentcosts 13 . Hence they are rather expensive start-up (and shut-down) (Dieu & Ongsakul2007), which can make the operat**in**g schedule more complex. In addition, the lowerboundaries **of** the production capacity are relatively high, which can be unsuitable **in**cases **of** small load demands.The operation economy **of** central units (key figures shown **in** Table 3.5) is characterizedby low fuel- and O&M costs, plus by a very high MWh-specific content **of** carbon.Marg**in**al costs,**CHP** [€/MWh **CHP** ]Marg**in**al costsel. [€/MWh el ]Marg**in**al costheat [€/MWh Heat ]Variable O&M[€/MWh **CHP** ]CO2 costs*[€/MWh **CHP** ]17.97 35.20 31.20 1.80 6.75Table 3.5. Estimated values **of** operation economy for extraction and condens**in**gunits are rounded. *CO2 quote prices are **of** course never certa**in** but **in** this caseset to 20 € per ton. Separate marg. costs **of** el. **in**cludes a valueless heat and viceversa (data sources: Danish Energy Authorties 2005, Danish Energy Authorties2008).13Large **power** plants such as steam units are usually designed for base and medium load **in** order torun for many years and thereby to pay **of**f great **in**vestments.

26 Characteristics **of** the Danish energy systemBack pressure units (decentralized production)Backpressure units are a type **of**, usually small, **CHP** plants with fixed electricity to heatratio, as shown **in** Figure 3.9. The heat and electricity output is **of**ten produced on regulargas turb**in**es operat**in**g on natural gas, but sometimes also on the more efficient comb**in**edcycle units runn**in**g on a comb**in**ation **of** Brayton (turb**in**e combustion) and Rank**in**(steam) cycles. Efficiencies are **in** the area **of** 85-90 % depend**in**g on factors such as plantsize and -age. The cm value varies a great deal for backpressure **CHP** units, rang**in**g from0.25 to 0.4 for smaller plants to 0.60 to 0.80 for medium to large scale plants (DanishEnergy Authorities 2005).El.P maxc mP m**in**HeatFigure 3.9, Electricity-heat ratio is fixed **in** relationto the backpressure value.One **of** the drawbacks **of** these plants is the **in**ability to regulate the electricity/heatrelation.In cases where the value **of** heat greatly exceeds the value **of** electricity for example,hav**in**g constra**in**ed 14 **power** generation can affect the plant economy negatively.On the plus side, however, is the fact that these relatively small **CHP** units are fasterand lesser cost heavy to construct.The operat**in**g economy **of** decentralized units (key figures shown **in** Table 3.6), is characterizedby high fuel costs, relatively low O&M costs plus a low MWh-specific content **of**carbon (compared to steam coal).Marg**in**al costs, **CHP**[€/MWh **CHP** ]Marg**in**al costs el.[€/MWh el ]Marg**in**al costheat [€/MWh Heat ]Variable O&M[€/MWh **CHP** ]CO2 costs*[€/MWh **CHP** ]27.80 87.00 48.00 2.63 3.97Table 3.6. Estimated values **of** operation economy for extraction and condens**in**gunits are rounded. *CO2 quote prices are **of** course never certa**in** but **in** this caseset to 20 € per ton. The marg**in**al costs separate for electricity and heat (Datasources: Danish Energy Authorities 2005 (operat**in**g costs), **Ea** **Energianalyse**2006 (fuel price)).14By forced el. generation is meant the condition **of** hav**in**g to produce either heat or electricity **in** orderto produce the opposite, cf. the fixed electricity to heat ratio.

Characteristics **of** the Danish energy system 27W**in**d turb**in**esW**in**d turb**in**es are usually dist**in**guished between as on- and **of**f shore types, respectively.In 2008, the total West-DK **w ind** capacity was divided as follows; Land mill capacity2232 MW and

28 Characteristics **of** the Danish energy systemthough. Investment costs are estimated to around 0.7 M€ and 0.2 M€ per MW **in**stalledcapacity for heat pumps and cartridges respectively. The marg**in**al O&M costs seems abit uncerta**in** and changeable, but it is estimated that heat pumps cost with**in** the range**of** 0.2-2 €/MWh 15 depend**in**g on size and type (Energ**in**et.dk 2009).Turb**in**e bypassNormally, when want**in**g to produce more heat on extraction units, the backpressurevalue cm quickly limits the heat production by maximum allow**in**g ~130 % heat for eachunit **of** electricity generated. With the **in**creased **w ind** capacity

Characteristics **of** the Danish energy system 29El.G2 3 4 5P el maxc v11BYPASS67c mP el m**in**P10 89P el m**in**η elη **CHP**P h maxHeatFigure 3.12, Extraction unit with bypass. The valve wouldlikely be situated before the high-pressure turb**in**e (2).Figure 3.13, Bypass-switch**in**g **in** theory.Note the lower**in**g **of** the production **in** ordernot to exceed the maximum heat limit.In practical, it will not be possible to momentarily switch **in**to bypass operation, s**in**cethe exist**in**g components for heat exchange are not designed for absorb**in**g the entire boiler**power**. Before perform**in**g the ‘switch’ the boiler **power** would as m**in**imum have to beturned down to a level where the energy flow through the high pressure turb**in**e – whichat backpressure mode is given by equation (3.2) – is below the maximum heat limit.P P + 0.15⋅ P ≈ 300% (3.2)Boiler=elHeatThe short term economy (or variable costs) **of** bypass operation is relatively unknown.That switch**in**g between normal and bypass operations is constra**in**ed by the up- anddown regulation gradient **of** the units however, might po**in**t at a hidden loss **of** value –especially for the smaller bypass periods.In this project, full scale bypass is regarded feasible for all central units, regardless **of**what technical obstructions each central unit **of** the Danish **power** system may have.BoilersThe basic function **of** boilers is to produce heat for the district heat**in**g system. Boilers asheat producers exist already **in** the current heat systems – especially **in** comb**in**ationwith waste **in**c**in**eration and biomass-fuels. The economy **of** boilers is determ**in**ed by theheat exchangers efficiency (which normally ranges from 85-90 %), the fuel used, andf**in**ally; the O&M costs (which can be relatively high for waste **in**c**in**eration and biomassunits (Energ**in**et.dk 2009). Waste as a fuel is **in** pr**in**ciple free (it is go**in**g to be burnedanyway), but given that waste is not the most adequate energy source it will be excludedlater on **in** the model**in**g.

30 Characteristics **of** the Danish energy systemCapacity extensions on **in**terconnectionsThe strengthen**in**g **of** the flow between price systems through build**in**g new connectionsis a well known tool for system operators. In recent years, decid**in**g whether the establishment**of** a new connection should take place or not have been determ**in**ed on the basis**of** bottleneck revenues. Due to **in**creased bottleneck **in**come **in** the Nordel area the lateryears, Nordel predicts a feasible positive economy for a range **of** potential connections(see Figure 3.14). The decision to fallow these through has not taken place though.Figure 3.14, Re**in**forcement **of** external Nordic **in**terconnections **in** general shows a positive costbenefit.Potential re**in**forcements are not prioritized. The proposed re-enforcements are said to benot necessarily mutually exclusive (Nordel 2008)Establish**in**g new **in**terconnections is very cost heavy with **in**vestments **in** the order **of**billions **of** Euros sometimes. At the same time, despite **of** the system load issues mentionedearlier **in** Chapter 1, it is an important tool for balanc**in**g markets – especiallywith the **in**creas**in**g **w ind** capacities be

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Build**in**g the Mathematical Model 47Chapter 5.Build**in**g the Mathematical Model5.1. OverviewIn order to get an **in**sight to the consequences **of** **in**creas**in**g **w ind** penetration on the Danishenergy system, modell

48 Build**in**g the Mathematical Modelsatisfy a number **of** demands with sufficient generation capacity (Petrov & Nicolaisen1999). In a sense, the problem **of** 1) is a logical derivation from 2) which is **of**ten phrasedas the Economic Dispatch Problem (ref a simple). Whereas the Dispatch Problem providesa solution to the current state **of** the network – how much available capacity thereis at hand right now – the unit commitment problem provides a solution to the actualstate **of** the system by schedul**in**g the capacities available. Figure 5.1 represents these **in**a simplified way.Economic dispatch **of**all units G1, G2 … GiEconomic dispatch **of**committed units: G1, G2 and G3G1G2G1G2G3…GiG3…GiG4G4Figure 5.1, Theoretical sketch **of** the Economic Dispatch-problem (left), which is usuallymore simple to solve, and the same problem (right) with the units alternately committ**in**gand de-committ**in**g (Petrov & Nicolaisen 1999).The choice, whether to do economic dispatch model**in**g, which is simple, or to use themore complex unit commitment model, **in**volv**in**g a set **of** 0-1 restrictions (**in**tegers), becomesrelevant the moment one considers to **in**clude boundaries and restrictions that areconnected to the commitment **of** s**in**gle units. Such be**in**g e.g. start-up costs, m**in**imumcapacity limits, ramp rates, sp**in**n**in**g reserve etc. (Petrov & Nicoalisen 1999). By **in**clud**in**gthese, the number **of** committed units suddenly may constra**in** the optimal solution **of**the system’s economy, and another type solv**in**g is required.One **of** the ma**in** reasons for choos**in**g unit commitment model**in**g for the current projectis the existence **of** such restrictions, and the expectation that restrictions are caus**in**g anundesirable quantity **of** constra**in**ed **power** generation **in** the real network. A conditionwhich goes under the scope **of** the problems stated **in** this project.Basically, the unit commitment problem is mathematically characterized by be**in**g constra**in**edby a set **of** b**in**ary **in**teger variables, which makes the optimization problem nonconvex.The problem therefore must be solved through Mixed Integer Programm**in**g(MIP). The methods **of** MIP can be described as f**in**d**in**g the best solution – l**in**ear or nonl**in**ear– **of** each possible 0–1 comb**in**ation (be**in**g committed or de-committed). The appliedsolver algorithm performs a heuristic search for an optimal solution, and as long asthe optimal solution is constra**in**ed by an **in**teger variable (Solver 2009) new subproblems**of** l**in**ear optimization are formed – **of**ten **in** a very large number. The generation**of** multiple sub problems is called branch**in**g (visualized as a tree consist**in**g **of**nodes), and while search**in**g for the optimal 0-1 comb**in**ation throughout the modeledperiod, a cut **of** the solutions, that can be safely disregarded, is performed by the branchand cut algorithm. One **of** the biggest problems with MIP is that as the number **of** possible0-1 comb**in**ations **in**creases – so does the computational time and physical memory

Build**in**g the Mathematical Model 49required for the task – exponentially (GAMS 2007). A further, and much more exhaustive,elaboration **of** the theoretical background **of** the solv**in**g **of** the unit commitmentproblem is found **in** Appendix 11.3.5.2.2. GAMS/CplexThe mathematical tools used **in** this project for this type **of** solv**in**g is a comb**in**ation **of**the model**in**g language GAMS and the MIP solver Cplex, respectively. The programm**in**gs**of**tware GAMS, which stands for General Algebraic Model**in**g System, is a tool specificallydesigned for optimization model**in**g (GAMS 2008). GAMS is known for lett**in**g theuser hav**in**g to concentrate solely on formulat**in**g the optimization problem, and not hav**in**gto th**in**k much about the more ‘technical’ programm**in**g part, which normally comesalong with complex mathematical rout**in**es as the unit commitment problem. This hasbeen a great (and not least time sav**in**g) advantage, which have enabled a stronger focuson the output. The solver selected for this project is Cplex, due to its efficient MIP optimiz**in**g.For further descriptions on the advantages and functionalities **of** model**in**g **in**GAMS see Appendix 11.3.5.2.3. Applied Economic theory and ‐model assumptionsIn this section, the applied economic theory will be review **in** relation to the mathematicalmodel. Furthermore, the necessary assumptions for the justification **of** the model asvalid comparison for the real West-DK-market are presented.Price formationsPrice formations are **in** this context to be understood as the formations **of** prices on heatand electricity. In the model, as well as **in** the real system, price formations are an equilibriumbetween supply and demand (Nord Pool Spot), with the f**in**al price reflect**in**g theproduction costs **of** heat and electricity **of** the cheapest marg**in**al utility among the availableproducer types. As described earlier **in** Chapter 3 the market players on the productionside **in** the Western Danish **power**- and heat system can roughly be split **in**to thefollow**in**g four producer types:1. Comb**in**ed el. and heat producers with variable heat output (extraction units)2. Comb**in**ed el. and heat producers with fixed heat output (backpressure units)3. Pure electricity producers, consist**in**g **of**:a. Condens**in**g units 17b. W**in**d turb**in**es4. Heat producers, consist**in**g **of**:a. Boilers17Also counts as extraction units operat**in**g **in** condens**in**g mode

**50** Build**in**g the Mathematical Modelb. Turb**in**es by-passed extraction unitsc. Heat pumpsWhat separates the characteristics **of** the Danish energy system, and thus the appliedunit commitment model, from other **power** systems, is that a great part **of** the productioncomes from **CHP** units **of** (producer type 1 and 2). Now, as both 1 and 2 are **CHP** units,designed for satisfy**in**g both electricity and heat demands simultaneously (and **in** an economicallyoptimized way) it is **of**ten the case, that **CHP** units only serves as marg**in**alutility on either the heat- or electricity side, which can lead to a constra**in****in**g **of** the correspond**in**g‘product’. In Figure 5.2 below is seen a theoretical description **of** the supplyand demand relations **of** the economic electricity and heat systems, respectively. S**in**cemost **of** the production is produced by comb**in**ed heat- and electricity generation, theprice formation **of** the prices on heat and electricity, **in**dividually, are connected.Cheap units play first. In a **CHP**-**based** system, prices on both the electricity and heatside (as shown **in** Figure 5.2) are formed by the variable costs **of** the cheapest availablecapacity satisfy**in**g the consumer’s marg**in**al utility (Ravn 2001). Units **of** the supplycurve with cheaper productions cost than the marg**in**al producer, will automatically pr**of**it– a pr**of**it given marg**in**al pr**of**it as seen **in** equation (5.1) below. Seen from a producer’spo**in**t **of** view, the optimal situation would always be to have the marg**in**al revenue equalthe marg**in**al costs **in** order to maximize pr**of**it (Bus**in**ess Dictionary 2009) while a marg**in**alpr**of**it different from zero reflects **in**sufficient production capacity. The marg**in**alproducer on the other hand, will have balanced costs and thereby no marg**in**al pr**of**it.Marg**in**al pr**of**it = marg**in**al revenue – marg**in**al production costs (5.1)Normally, producers will only choose to supply if the marg**in**al costs are covered. For**CHP** units this is an ideal scenario, **in** the sense, that the only way **CHP** units canachieve such balanced marg**in**al heat- and el. production costs, is when the productionunit represents the cheapest marg**in**al degree **of** freedom **in** both the electricity- and heatmarket at the same time, which is unlikely to happen – at least for more than one unit.As seen **in** the graphs **of** Figure 5.2 below, the parallel market situation sometimes is,that prices are determ**in**ed by one type **of** **CHP** producer on the electricity market, andyet by another **CHP** unit **in** the heat market. It is then **of**ten the case, as too seen **in** Figure5.2, that the marg**in**al utility on the electricity market has lower electricity generationcosts than the marg**in**al unit **in** the. In the case where **power** is generated by themarg**in**al **CHP** unit on the heat market, the generated **power** is considered constra**in**ed bythe heat demand.

Build**in**g the Mathematical Model 51Electricity marketCentral heat marketEl. priceEl. demandHeat priceHeat demand**CHP** (coal)(a)**CHP** (coal)(b)**CHP** (gas)**CHP** (gas)Q [MW]Q [MW]Figure 5.2, As seen through the model, electricity and heat prices are formed by eachsatisfy**in**g separately **in**elastic demands. Problem is, when the price-sett**in**g marg**in**al**CHP** plant is cheaper on the electricity side (left) than the case for the local heatmarket (right), lost **in**comes on forced electricity (a) will be balanced by rais**in**g themarg**in**al heat generation costs (b).The results **of** **CHP** plants produc**in**g forced electricity, is that these constra**in**ed units nolonger will **in**fluence the marg**in**al quantities (Bregnbæk), as they no longer plays thepart **of** cheapest marg**in**al capacity. Moreover, the constra**in**ed **power** now contributes toa further suppress**in**g **of** the **CHP** plants. Consequently, heat prices reflect how muchextra fuel it will take for the heat system to produce one extra unit **of** heat. Under theseconditions, the correspond**in**g electricity can be considered as a waste- or bi-product **of**heat - and not the other way around as orig**in**ally **in**tended 18 . Whether this relation is aproblem for the system economy as a whole is **in**terest**in**g to look further **in**to, but fact is,that whenever cheaper marg**in**al producers suppress locally heat-constra**in**ed **CHP** unitsfrom the Merit order (on the electricity-side), marg**in**al heat-generation costs **in**creases(**in** order to cover the “loss” on the el. market), ultimately result**in**g **in** high heat prices.As shown **in** section 4.2.2, electricity and heat demand tend to follow the same patternsthroughout a normal day which should decrease the problem caused by forced electricityproduction to some extent. But s**in**ce **w ind** penetration has

52 Build**in**g the Mathematical ModelShadow pricesAs mentioned earlier, the overall objective **of** optimization model**in**g is to m**in**imize asystem’s total costs. However, the optimal value **of** the function **in** itself may conta**in**very little **in**formation, while changes **in** this optimum can be given important **in**terpretations.To evaluate the costs **of** these changes, GAMS/Cplex automatically calculates what isknown as the shadow prices. Shadow prices can **in** this connection be **in**terpreted as thechange **in** the objective value result**in**g from a one-unit **in**crease **in** the constant **of** thespecific constra**in**t function. Most important is properly the shadow price **of** the electricityand heat demand satisfaction constra**in**ts, respectively. They **in**dicate the specificchange **in** the total-cost function C(e t i,h t i) (known as the objective function) when rais**in**gthe consumption levels by just one MWh, which can be **in**terpreted as a heat- and electricityprice, respectively. Shadow prices on constra**in**ts such as **in**terconnectivity capacities,and upper and lower boundaries **of** productions units, **in**dicates the value **of** chang**in**gthese restrictions, and are therefore **of**ten used **in** this project for evaluat**in**g potential**in**vestments. Figure 5.3 shows a pr**in**ciple sketch **of** a two-dimensional situationwhere tree equilibrium po**in**ts, one that is free (a) and two that are restricted (b and c),are generat**in**g shadow prices. The shadow price is zero at a and non-zero at b and c.byacxFigure 5.3, Three types **of** optimal solutions (equilibrium) found with**in** a convexregion “shaped” by l**in**ear constra**in**ts, can assume a shadow price that is eitherzero (a), positive or negative.When the shadow price is positive (b), it is an **in**dication **of** extra costs connected withrais**in**g the upper bound constra**in**t by one unit – and the opposite, if the restriction is alower bound constra**in**t (c). In the case **of** equilibrium a, it would make no (economic)sense to modify the constants **of** the constra**in****in**g functions, as the shadow price at eachl**in**ear constra**in**t is calculated to zero.As the optimal solution found is the equilibrium **of** a number **of** l**in**ear constra**in**ts, theshadow price represents the marg**in**al loss or ga**in**, **of** deviat**in**g one unit from this po**in**t.In the case **of** **CHP** units, every optimal operation po**in**t is a state **of** equilibrium betweenheat and el. production, respectively. In the case **of** extraction units, the operation po**in**tsare **of**ten found positioned along one **of** the limits, represent**in**g either the upper or lowerbound **of** electricity generation or the lower back pressure limit, forc**in**g maximum heat

Build**in**g the Mathematical Model 53out at a given electricity generation. The shadow price can therefore be used for **in**dicat**in**gconstra**in**ed heat- and electricity production.In the case **of** electricity generation be**in**g constra**in**ed by the district heat**in**g demand,electricity prices are **of**ten lower that the price it would take to cover the marg**in**al **power**generation costs. Therefore, the contribution for cover**in**g the loss from generat**in**g constra**in**ed**power** (at a lower price) will additionally come from an **in**creasment **of** the marg**in**alheat cost.As the electricity prices are expected to drop due to an **in**creased **w ind** capacity

54 Build**in**g the Mathematical ModelThe time factor is another ma**in** difference between the model and the real system.Where market players **in** the real system mostly plan operations one day ahead, themodel plans and optimizes operations for the entire model**in**g period, which, as latershown, varies from a week to a month. Only a perfect foresight **of** future events would bethe equivalent to this (Ravn 2001). For example, hav**in**g knowledge **of** the exact **w ind**production as far

Build**in**g the Mathematical Model 55It is **in** this connection relevant to rem**in**d that the scope was to build a model with some**of** the same characteristics as the Danish energy system, which can be used to help clarifyhow **in**creased **w ind** penetration will affect the system, as well as how different toolsfor

56 Build**in**g the Mathematical Model**in** the Nordic area. An exchange area, similar to the North German transmission system,has not been **in**cluded **in** the model. The reason for this is: Because the North Germansystem, like West-DK, is characterized by a comb**in**ation **of** thermal production anda great amount **of** **w ind** capacity, the expectation is that a

Build**in**g the Mathematical Model 572) Bypass scenario: System is “physically” modeled as **in** 1) but this time, all extractionunits have optional BPO. The idea beh**in**d this scenario is to measure the impacts**of** optional switch**in**g from co-generated heat to pure heat - under the **in**fluence**of** vary**in**g **w ind** and consumption data.3) Heat-pump scenario: System is modeled as shown

58 Build**in**g the Mathematical ModelNt tt t t∑( el, i+ Pel_ bp,i) + PW− P12= PDi=1P, el(5.3)The hourly satisfaction **of** the electricity demand is given by equationNt tt t t∑( el, i+ Pel_ bp,i) + PW− P12= PDi=1P, el(5.3(5.4) above. P t el,i is the **power** generation atthe 11 units just described and additionally P t el_bp,i are the **power** generation from backpressure units **in** the seven central areas. P t W is the production from **w ind** and P t 12 theexchanged

Build**in**g the Mathematical Model 59results **in** the two outcomes shown above, where 0 1 respectively symbolizes previousand current state **of** x t i.

60 Build**in**g the Mathematical ModelExtraction units:Pctt el,i v,i tPi= + ⋅ Ph, iηel,iηel,i(5.12)The fuel constra**in**tPctt el,i v,i tPi= + ⋅ Ph, iηel,iηel,i((5.12) calculates the fuel consumption(converted to chemical energy) as a function **of** electricity and heat generation.Recall**in**g Figure 3.8, the relation between electricity and heat is expressed by the is**of**uell**in**es with the flat slope value cv, which represents the marg**in**al loss **of** electricityper extracted unit heat from the turb**in**e. η el,i is the electrical net efficiency **of** unit i.Follow**in**g down along the iso-fuel l**in**es, eventually they stop at the backpressure limitttexpressed by the c m -constra**in**t ≥ c P(5.11(5.13):ttPel, icm,i⋅ Ph, iPel, i m,i⋅h,i≥ (5.11)The maximum and m**in**imum electrical output is expressed by constra**in**ts (5.14) and(5.15) below.P,≥ −c⋅ P + P ⋅ x , x t i ϵ [0;1] (5.12)tel itel iv,iv,ith,ith,im**in**, iP,≤ −c⋅ P + P ⋅ x , x t i ϵ [0;1] (5.13)max, ititiThe maximum heat output, as restricted by the capacity **of** the heat exchanger, is givenby equation (5.16):PPth, i≤h,max, i(5.14)The extraction units are not only constra**in**ed by upper and lower bounds **of** boiler andheat exchanger, but also by the time-differential aspect **of** the operation, referr**in**g to thehourly gradient **of** the boiler output. This restriction is **of**ten known as the ramp-ratet t−1t−1tcondition, here given by equation P − P ≤ UR ⋅ x + P ⋅ st (5.15(5.17) below.iiiist,iiPti− Pt−1i≤ UR ⋅ xit−1i+ Pst,i⋅ stti(5.15)UC comb**in**ation:x t-1 i st t iResult**in**g up-rampcon.:If 1 1 1 0 P t i – P t i < UR iIf 0 1 0 1 P t i – 0 < P st,iIf 1 0 1 0 0 – P t i < UR iIf 0 0 0 0 0 < 0Table 5.1, Different up-ramp conditions **in** relation to the specific operationmode. Reason is, that the ramp conditions must always be satisfied dur**in**geach **of** the four comb**in**ations **of** ‘before-now’ commitment.

Build**in**g the Mathematical Model 61In this constra**in**t the difference between the current and previous fuel consumption issystematically measured for compliance with the two ramp-rate restrictions. The challenge**in** this connection however, is to consider the all four before-now states **of** eachunit i **in**dividually, more specifically be**in**g: **in** operation (1-1), start**in**g up (0-1), shutt**in**gdown (1-0), and de-committed (0-0). The solution was to use both b**in**ary variables x t-1 iand st i i. Table 5.1 shows the different equation-outcomes **of** the four comb**in**ations. Here,UR i and P st,i are the up-ramp limits dur**in**g constant operation (1-1) and maximum startup**power** (0-1), respectively. The ramp-rate constra**in**ts concern the up-ramp situationand **in**clude condens**in**g units as well. Other units however, such as backpressure-, peakload-and boiler utilities are chosen not to be restricted by these because they consist **of** alarger number **of** smaller units merged as one.Extraction units with by-pass operation options:Model**in**g units with optional BPO-mode requires a relaxation **of** the lower bound constra**in**ts(5.13) and (5.14), respectively, **in** order to stop generat**in**g **power** while still operat**in**galong the heat axis as an either/or restriction. The constra**in**ts that will be affectedby this adjustment are rewritten **in** the follow**in**g.First th**in**g to do is to **in**troduce a new b**in**ary variable b t i (5.18) that decides whether toswitch BPO on or **of**f.[ 0;1 ]b = , wheretib ti⎧1= ⎨⎩ 0if BPO = onif BPO = **of**f(5.16)S**in**ce the fuel constra**in**t only works with el. generation turned on, eq.(5.19) relaxes thiscondition by subtract**in**g a very large number M **in** case **of** BPO switched on. This is followedby a new fuel constra**in**t (5.20) that, **in** reverse, is relaxed with BPO turned **of**f.Ptt el,i cvti≥ + ⋅ Ph, iηel,iηel,iP− M ⋅bti(5.17)PtitPh, it≥ − M ⋅(1− b )(5.18)ηbpiNext th**in**g is to rewrite the m**in**imum el. output constra**in**t (5.14) for relaxation **in** case **of**BPO, as done **in** (5.21)P,≥ −c⋅ P + P ⋅ x − M ⋅b(5.19)tel iv,ith,im**in**, iAnd additionally, the backpressure constra**in**t (5.13) is disregarded through the fallow**in**gequation (5.22):P,− M ⋅b(5.20)ttel i≥ cm,i⋅ Ph, iNow, ensur**in**g that the el. generation is zero, constra**in**t (5.23) is added:tititiPtel,it≤ M ⋅(1− b )(5.21)iUnder normal operation, the m**in**imum el. generation constra**in**t **in**directly secures thatthe boiler m**in**imum is not deceeded. With the extraction units only produc**in**g heat when

62 Build**in**g the Mathematical Modelswitched to BPO, the m**in**imum limit then have to be expressed as a function **of** onlyheat, as seen **in** equation (5.24). Divid**in**g P m**in**,i by the electrical net-efficiency and multiply**in**gwith the efficiency **of** the heat exchanger, converts the lower bound (**of** the boiler)from electricity to heat.Backpressure units:Pth,i≥ Pm**in**, iη**CHP**,iηel,i⋅ xtit− M ⋅ (1 − b )i(5.22)For backpressure units, fuel consumption as a function **of** electricity and heat is given byequation (5.25), by which the relation between el. and heat is fixed through the backpressurevalue c m,i as seen **in** equation (5.26).Ptit t( P + P )1=el,i h,i⋅(5.23)ηttPel, icm,i⋅ Ph, ii,cph= (5.24)W**in**d **power**:In order to secure the system balance aga**in**st critical electrical spillover **in** hours withextremely large **w ind** penetration,

Build**in**g the Mathematical Model 639∑i= 1x ≥ 3(5.26)tiThe heat-pump scenario:Adjust**in**g to the heat-pump scenario only requires changes **of** the demand satisfactionconstra**in**ts. S**in**ce electricity works as “fuel” when produc**in**g heat on heat-pump, P t el,hpand P t el,hp,i is **in**serted on the consumption side **of** equation (5.5) and (5.6) as seen **in** equation(5.29). The electricity consumption is thus applied to the central and de-centralizedheat-demand constra**in**ts (5.30) and (5.31), multiplied with the COP factor ηhp **of** theelectricity-to-heat conversion.NNt tt t ttt∑ (el, i+ Pel_ bp,i) + PW− P12= PD , el+ ∑ Pel,hp,i+ Peli=1P, hpi=1(5.27)t t tttPh, iPcb,i+ Ph_ bp,i+hp⋅ Pel,hp,i≥ PD , h,i+ η (5.28)t tt tPh, iPdcb+hp⋅ Pel,hp≥ PD , h,dc+ η (5.29)5.4. Generation **of** **in**put dataOne **of** the challenges **of** optimiz**in**g the UC problem is to feed the model with proper data.In this project, all data has one way or the other been taken from the West Danish**power** system, whether it is for **power** units or consumption pr**of**iles.5.4.1. Data for **power** unitsThis section presents the background **of** the data applied to the thermal units **of** the UCmodel. The characteristics **of** the central **power** plants modeled **in** this project, are moreor less taken from the n**in**e largest central **power** plants (production wise) operat**in**g **in**today’s West-DK system. In Table 5.2 is seen, how the real data have been converted**in**to the data applied to the model. It is seen that the heat-production capacity **of** the twolast units: NJV2 and ENV3, are virtually non-existent. They have therefore been assumedzero and will be regarded as purely condens**in**g units.

64 Build**in**g the Mathematical ModelRatet capacities commissioned Primary fuel Source Capacities for UC modelName Block El. [MW] Heat [MW] year Heat [MW] name unit G(i ) El. [MW] Heat [MW]Nordjyllandsværket NJV 3 410 420 1997 Coal Vattenfall G1 400 4**50**Studstrupsværket SSV 3 3**50** 455 1985 Coal DONG Energy G2 3**50** 4**50**Studstrupsværket SSV 4 3**50** 455 1985 Coal DONG Energy G3 3**50** 4**50**Esbjergværket ESV3 378 460 1992 Coal DONG Energy G4 400 **50**0Fynsværket FYV3 235 340 1974 Coal Vattenfall G5 2**50** 3**50**Fynsværket FYV7 362 475 1991 Coal Vattenfall G6 400 475Skærbækværket SKV3 392 444 1997 Coal DONG Energy G7 400 4**50**Nordjyllandsværket NJV 2 225 42 1977 Coal Vattenfall G8 2**50** ~ 0Enstedsværket ENV3 626 85 1979 Coal DONG Energy G9 6**50** ~ 0Total 3328 3176 - - - - 34**50** 3125Table 5.2, Us**in**g real data from central utilities **in** West-DK for use **in** model. The capacities arerounded (data source: DONG energy 2009, Vattenfall 2009).Calculation **of** marg**in**al production costsThe source data beh**in**d the calculation **of** the marg**in**al prices are listed **in** Table 5.3. Thecurrency is stated **in** Dkk because this was the currency used when the results wereprocessed. F**in**al results will be presented **in** Euros 21 .Source data:Energy prices Callorific values CO2 costs currency: O&M per MWh,fuelCoal price Gas price Coal CO2 price Coal Gas Dkk / € Central Decentralized4**50** [Dkk/ton] 45 [Dkk/GJ] 24,40 [GJ/ton] 1**50** [Dkk/ton] 0,34 [t CO2/MWh] 0,2 [t CO2/MWh] 7,56 [Dkk/€] 13,6 [Dkk/MWh] 19 [Dkk/MWh]Table 5.3, Key numbers for calculat**in**g marg**in**al gen. costs. (Data sources: Danish Energy Authorities2005) * F**in**al value assumedThe marg**in**al costs **of** thermal **power** facilities have traditionally been highly sensitive tochanges **in** fuel prices, and s**in**ce the **in**troduction **of** CO2 quotes, sensitive to them aswell. The graph to the left **of** Figure 5.7a shows how prices on coal (which is the ma**in**energy source for el. generation **in** the Danish **power** system), have **in**creased dramaticallythe resent years, peak**in**g **in** July 2008, and then dropp**in**g to a much lower level by theend **of** the same year. It could seem as if a more stable coal price have recently emergedfrom the fog **of** various economic speculations and capacity issues that have characterizedrecent year’s overheated economic system. From this economic po**in**t **of** view, a coalprice **of** 60 € is selected as the constant price **in** this project. In Figure 5.7b to the right isseen how the marg**in**al generation costs **of** backpressure units are sensitive towardschanges **in** the Natural Gas price, and central units be**in**g sensitive to the CO2 price (dueto a high emission factor).Coal price development21100 DKK = 765 Euro

Build**in**g the Mathematical Model 65180,0160,0140,0120,0Coal price $/tonCoal price €/ton120,00100,0080,00Composition **of** marg**in**al generation costsBackpressure units: Extraction and condens**in**g units:100,080,060,040,020,00,060,0040,0020,000,004.02.521.4GAS price0.7CO2 (20 €/ton CO2)6.7O&M 8.8Coal priceCO2 (20 €/ton CO2)O&MJan‐04May‐04Sep‐04Jan‐05May‐05Sep‐05Jan‐06May‐06Sep‐06Jan‐07May‐07Sep‐07Jan‐08May‐08Sep‐08Jan‐09Figure 5.7a, Development **in** coal prices overa five year period (Data source: Energistyrelsen).Figure 5.7b, comparison **of** the marg**in**al generationcosts **of** decentralized (left) and central (right)units.The same is the case when it comes to the Natural gas-prices. An example **of** this is thefact that from August 2008 to January 2009 prices dropped a factor **of** two from an historicpeak level **of** 0.57 €/m 3 down to 0.28 €/m 3 . Prices on fuels and raw materials are **in**general hard to count on when analyz**in**g over a large timeframe.Marg**in**al costs **of** central units:MC = fuel costs + CO2 costs + O&M =4**50** ⋅ 3.6+ 1**50** ⋅ 0.34 + 13 .6 ⋅η el≈ 125 [ Dkk / MWh ] ≈ 16 .5 [€ / MWh ] (5.30)24 .4The O&M costs are corrected for fuel consumption via the el. net efficiency. Marg**in**alcosts are also applied to condens**in**g units.Marg**in**al costs **of** de-centralized units:45⋅3.6+ 1**50** ⋅0.20+ 37 ⋅η ≈ 210 [ Dkk / MWh]≈ 28 [€ / MWh](5.31)elTable 5.4 shows some additional marg**in**al costs per unit fuel used **in** the model. From amodel po**in**t **of** view, it made sense to l**in**k the marg**in**al generation costs **of** peak loadutilities (oil) to the costs **of** backpressure units (gas) 22 , as well as to appo**in**t the samemarg**in**al costs to boilers, s**in**ce a high detail-level on the prices on more expensive unitsis **of** less **in**terest to the current objective. The marg**in**al costs **of** **w ind**

66 Build**in**g the Mathematical ModelPeak load Boilers Heat pumps Heat pumps210 [Dkk/MWh] 210 [Dkk/MWh] 37.8 [Dkk/MWh] 0 (68) [Dkk/MWh]( ~28 €) ( ~28 €) ( ~5 €) ( ~9 €)Table 5.4, costs per-unit consumed fuel applied to different utilities **in** the model(data source: Energistyrelsen).Thermal utility propertiesTable 5.5 below presents the f**in**al technical and economic data **of** thermal units used **in**the model. The technical data is taken from the technology catalogue (Danish EnergyAuthorities 2005) and thus reflects the **power** unit’s properties as if they were constructedtomorrow. Therefore they might be more efficient than those **in** the West-DKsystem.Heat output limits Up-ramp limits Efficencies COSTSunit (i ) typePel,m**in**[MW]Pel,max[MW]Max heat[MW] Pst [MW] RR [MW] ηel η_**CHP** cv [-e/h] cm [e/h]marg**in**al[€/MWh]start-up[€]G1 Extraction (Coal) 80 400 4**50** 700 **50**0 0,47 0,92 0,15 0,75 16,53 1323G2 Extraction (Coal) 70 3**50** 4**50** 700 **50**0 0,47 0,92 0,15 0,75 16,53 1323G3 Extraction (Coal) 70 3**50** 4**50** 700 **50**0 0,47 0,92 0,15 0,75 16,53 1323G4 Extraction (Coal) 80 400 **50**0 700 **50**0 0,47 0,92 0,15 0,75 16,53 1323G5 Extraction (Coal) **50** 2**50** 3**50** 5**50** **50**0 0,47 0,92 0,15 0,75 16,53 1323G6 Extraction (Coal) 80 400 475 700 **50**0 0,47 0,92 0,15 0,75 16,53 1323G7 Extraction (Coal) 80 400 4**50** 700 **50**0 0,47 0,92 0,15 0,75 16,53 1323G8 Condens**in**g (Coal) **50** 2**50** - 1000 **50**0 0,5 - - - 16,53 1323G9 Condens**in**g (Coal) 130 6**50** - 1000 **50**0 0,5 - - - 16,53 1323G10 Peak-load (Oil) 0 1000 - no limit no limit 0,42 - - - 27,78 0G11 Backpressure (Gas) 0 no limit no limit no limit no limit - 0,9 - 0,55 27,78 0OthersBoiler dc Heat (Gas) - - no limit no limit no limit - 0,9 - - 27,78 -Boiler c (i ) Heat (Gas) - - no limit no limit no limit - 0,9 - - 27,78 -**CHP** c (i ) Backpressure (Gas) - no limit no limit 4000 no limit 0,9 0,9 - 0,55 27,78 -Table 5.5, Technical and economic properties **of** the thermal utility types applied to the model. Interms **of** boilers, the η**CHP** value works as pure heat efficiencies (Data source: Danish EnergyAuthorities 2005, DONG Energy 2009, Vattenfall 2009).As seen, the m**in**imum bound for electricity production P el,m**in** is assumed 20 % **of** the maximumrated capacity P el,max because **of** miss**in**g **in**formation on this. Reason for this mightbe, that the m**in**imum boiler capacity **of**ten is an unspecified range, that traditionallynever have be**in**g given much attention from **power**-plant producers and -operators –probably because they never imag**in**ed the plants operat**in**g at such a low level 23 for verylong. The assumed 20 % is a reasonable approximation (Boldt), and the lower efficiencies,which will probably be around this low output level, is not be**in**g corrected for **in** themodel. All non-central units have basically been assigned no upper- and lower capacitylimits, which on a model basis is practical **in** relation to avoid**in**g **in**feasibilities whensolv**in**g.23This is also the case **in** various technology sheets from el. **power** facilities which **of**ten just describeoperation with**in** the load range **50** - 100 %

Build**in**g the Mathematical Model 67The start-up costs is another rather unknown factor (this goes for generation costs **in**general) ma**in**ly connected long **power**-up periods – especially **in** case **of** cold-starts. It isthus assumed 1323 €/startup (10,000 Dkk) for central units **in** order for them to havemarg**in**al **in**fluence on the commitment problem, and zero costs for the rema**in****in**g units.For simplifications, no economic dist**in**guishes have been made between cold and hotstart-ups.Until now, the generation costs **of** the specific utilities have been calculated **in** relation t**of**uel consumption and not for el. and heat **in**dividually. In this connection, Table 5.6shows the marg**in**al productions **of** el. and heat when assum**in**g that the bi-product isvalueless. The third column is marg**in**al **CHP**-generation costs **in** a balanced market.Heatel (condens**in**g) (el.price = 0)co-generation(balanced price)unit (i ) [€/MWh] [€/MWh] [€/MWh]G1 35,17 31,19 17,97G2 35,17 31,19 17,97G3 35,17 31,19 17,97G4 35,17 31,19 17,97G5 35,17 31,19 17,97G6 35,17 31,19 17,97G7 35,17 31,19 17,97G8 33,06 - -G9 33,06 - -G10 66,14 - -G11 86,81 47,90 30,87OthersBoiler dc - 30,87 -Boiler c (i ) - 30,87 -**CHP** c (i ) 86,81 47,90 30,87Table 5.6, Generation costs **of** el., heat and **CHP** production **in**dividually. Inthe case **of** backpressure units (G11), which have fixed heat-el. ratio, condens**in**grefers to el. production with zero heat price (data source: Energistyrelsen).From Table 5.6 is seen, that the central extraction units by far are the most economicefficient when it comes to **CHP** production. It is also seen that boilers are more competitiveat heat production when el. prices is zero, and vice versa, and that condens**in**g unitsare best at electricity production when heat price is zero. Although all three productionscenarios rarely occur, the table however gives a good illustration **of** the economy **of**thermal units **in** the modeled system.Heat pumpsThe selected capacities for central and decentralized production areas are accessed onbasis **of** the results **of** a model sequence with **in**f**in**ite heat pumps capacity. As illustrated**in** Figure 5.8 , a duration curve on the production has been processed and then, the suitablecapacities found where the curves break and start to flatten. The result **of** this methodis the **in**stallation **of** a total heat pump capacity **of** 3**50** MW **in** the central heat

68 Build**in**g the Mathematical Modelareas, while 5**50** MW **in** decentralized areas, which **in**dicates a larger (economic) heatpump-potential **in** decentralized area.HP **power**Time [h]Figure 5.8, The pr**in**ciple beh**in**d estimat**in**g the potential amount **of** heatpump capacity, is by ob-serv**in**g the duration curve **of** the production froma system with **in**f**in**ite heat pump capacity.5.4.2. Creat**in**g **w ind** pr

Build**in**g the Mathematical Model 691,201,000,800,60Land millsOffshore: HornsRev0,400,200,0019172533414957657381899710511312112913714515316116917718519313527031054140517562107245828093160351138624213456449155266561759686319667070217372772380748425Figure 5.9, Left: a January-sample **of** production pr**of**iles from Offshore (160 MW at HornsRev) and land mills (2232 MW onshore), respectively. Right: comparison **of** the two productiontype’s **in**dividual duration over a whole year (data source: **Ea** **Energianalyse**).The two comparisons **in** Figure 5.10 show how the production from the **of**fshore turb**in**eshas more extreme fluctuations than the production from the turb**in**es spread all over theregion. They also show that **of**fshore production reaches maximum rated production (orat least a controlled maximum level) quite **of**ten compared to land mill production whichis quite unlikely to ever do so. Although the **of**fshore pr**of**ile represents just 160 MWcompared to the 2232 MW on land, it is likely that an **in**crease **in** **of**fshore capacity willenhance the amount **of** hours with extreme variations.More precisely, the challenge **of** generat**in**g the 2025 pr**of**ile (and the steps **in**-between) ishow to upscale the **of**fshore pr**of**ile while **in**clud**in**g the effects from the distribution to thethree described locations.1,201,000,800,600,400,20DK-Vest: meanøst pr**of**il forstørret0,001 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151Figure 5.10, Comparison **of** **w ind** pr

70 Build**in**g the Mathematical Model**50**00,00W**in**dPower[MWh]4000,003000,002000,001000,00Offshore (with delay)Land millsnot delayeddelayed pr**of**ile0,00146392513871849231127733235369741594621**50**835545600764696931739378558317Figure 5.11, W**in**d pr**of**ile anno 2025. By apply**in**g the delay-method to the **of**fshore pr**of**ile,the result is a more smoothed out curve with fewer hours **of** maximum productionthan else – but, as seen, the number **of** these hours is still quite high. Look**in**g at the result**in**gpr**of**ile **of** total **w ind** production (appear

Build**in**g the Mathematical Model 71

72 Model resultsChapter 6.Model results6.1. Overview **of** the modeled resultsIn this chapter, the results **of** the model calculations will be reviewed and analyzed. Theresults will be addressed one by one accord**in**g to subject, which means, that for eachsubject, the results **of** the three different system scenarios (reference, bypass and heatpump) subjected to the different **w ind** pr

Model results 73therefore been modeled **in** two different ways: as a full-scale BPO where all extractionunits have optional BPO, and as a full-scale BPO where just one extraction unit haveoptional BPO.Ma**in**ly the full-scale BPO scenario was optimized with solution gabs, as seen **in** Table6.2 below. Correspond**in**gly, some **of** the optimized month-pr**of**iles too resulted **in** exhaustive25 tree searches which needed to be term**in**ated with**in** reasonable time (GAMS 2007),but still with much better optimization than **in** the full-scale BPO scenario, as it appears**in** appendix 11.4.GAB sizes, BPO scenario (full‐scale)**w ind**ynon‐

74 Model resultssystem, and is therefore **in**terest**in**g **in** a more present perspective. For comparison, themean **w ind**-production is presented too. F

Model results 75**50**Criticallylow prices40Prices only be**in**g criticallylow **in** (2025)4003**50**300El. price[Dkk/MWh]LP 2008El. price30[€/MWh]2**50**200LP 2017LP 2025201**50**200810100**50**2017202**50**0122436485106127148169190211232253274295316337358379400421442463484**50**5526547568589610631652673694715736Time [h]Figure 6.2, Comparison **of** price fluctuations **in** the three reference scenarios **in** July.What seems to look like barcodes above the curves, **in**dicates when prices are criticallylow (price ~ 0 €). The three scenarios are **based** on the **w ind**-penetration level

76 Model results(2017), which is given by a **w ind**-capacity expansion

Model results 77Maximum low-price period [h] 17 49 120Table 6.4, Key figures from modeled electricity prices.6.2.2. Heat pricesAs with electricity, the calculated shadow prices **of** the heat-demand constra**in**t will be**in**terpreted as the heat price. However, when model**in**g the co-production **of** heat andelectricity, it is **of**ten the case that heat is more needed than **power**. The co-generatedheat and electricity on extraction- and backpressure facilities to some extend are mutuallydependent, by which one **of** the goods may be produced at a lower price than itsbasic marg**in**al production cost, thereby no longer directly form**in**g the price. As expla**in**ed**in** section 5.2.3, the marg**in**al **in**come-loss **of** one good can be regarded as wasteconnected with produc**in**g the other, and is therefore reflected by an **in**creased price onthis. Figure 6.5, which is a sample **of** electricity prices and de-centralized heat prices,plotted together, shows an example **of** how electricity-price variations affect the heatprice and the other way around.El./heatprice[€/MWh]4540353025201510**50**1 2 3 4 5 6 7 8 9 1011121314151617181920212223Time [h]DC heatEl. priceFigure 6.5, Plot **of** electricity- and heat price. It shows that (when **CHP** are themarg**in**al utility **in** the heat market) prices are mutually connected by which adecreas**in**g value **of** the one causes an **in**crease **in** the value **of** the other.The heat price **of** the three reference scenarios **in** the central distribution areas can beseen **in** Figure 6.6 and Figure 6.7 plotted for January and July, respectively. Althoughthe average heat prices **of** the two month are close to identical, the variations **in** the heatprices are characterized by much greater fluctuations **in** July than **in** January. Additionally,the heat prices **in** July have much deeper “price valleys” than **in** January. Whencompar**in**g the 2008- , 2017- and 2025 scenarios, the general picture is that the heatprices **in**crease as time goes by, as a result **of** additional lower prices on the electricityside.

78 Model resultsHeatprice[€/MWh]**50**40Heat prices January, central areas400,003**50**,00300,00Heatprice[Dkk/MWh]302**50**,00200,0020082017201**50**,002025100100,00**50**,000,00Mean 2008Mean 2017Mean 20251275379105131157183209235261287313339365391417443469495521547573599625651677703729Figure 6.6, Plot **of** central area heat prices **in** the reference system subjected to thethree **w ind** scenarios

Model results 79HeatPrice[€/MWh]**50**403020Heat prices duration curve (annual)(48 €) el. price iszero (**w ind**y)400,003

80 Model resultspacities and some do not. The s**in**gle, decentralized area has been modeled with boilercapacity (as an option for hours where switch**in**g to full heat production is more pr**of**itable),but the **in**stalled capacity **of** **50**0 MW it not enough for full coverage at all time. Iwill go **in**to further details on this later on **in** section 6.3 on the production patterns.In chapter 4 it was statistically proven that **in** West-DK, central **power** plants cont**in**ueto generate electricity despite **of** low prices, and it was assumed that this production isforced by the additional heat demand. One could wonder, whether not react**in**g to the el.market is due to lack **of** boil**in**g capacity (the amount **of** decentralized boil**in**g capacity **of**the current system is presently unknown), perhaps pla**in** conservatism among local **CHP**operators, or due to some third reason. Nevertheless, it could be **in**terest**in**g to discussthe sense **in** keep lett**in**g local heat consumer co-f**in**ance low electricity prices for thebenefit **of** all consumers (**in**clud**in**g the ones **in** external **power** systems). In practice, decentralizedproducers are **of**ten **in** a position **of** natural monopoly when it comes to thesupply **of** district heat**in**g. Heat-consumers are therefore obligated to pay whatever pricemight be.6.2.3. Price formations **in** the by‐pass scenarioIn the current project, runn**in**g **in** bypass mode means bypass**in**g the high-pressure turb**in**eand, by do**in**g so, giv**in**g central **CHP** plants an opportunity to run entirely as a boiler**in** times where heat is more valuable than electricity.As mentioned **in** the beg**in**n**in**g **of** this chapter, the model**in**g **of** the bypass scenario hasbeen divided **in**to two system scenarios. The first is a full-scale scenario, where the systemhas optional turb**in**e-bypass on all seven extraction units. This scenario is very computeheavy, and has therefore been limited to one-week operation samples as mentionedabove. The samples have been modeled on the basis **of** pr**of**iles **of** the first week **of** January,April and November, **in** order to cover different times **of** the year. July was optimizedtoo, but did not result **in** any bypass operation and does therefore not differ fromthe reference scenario. In addition, the samples have been subjected to the ‘**w ind**y’ andnon-

Model results 81found with**in**). Unfortunately, as seen **in** the full-scaled model, these values were with**in**the range **of** 6.5 % - 11 %, due to the complexity **of** the bypass constra**in**ts. Although theoptimal unit commitment-solution is to be found with**in** a rather big solution area, it isassessed that the results below can be **in**terpreted as reasonable approaches to the affects**of** full-scale bypass on the electricity price formation.When observ**in**g the unit commitment solutions **of** the full-scale BPO model below, one **of**the most **in**terest**in**g th**in**gs is that no bypass-operation has been “selected” with**in** theestimated optimal solutions **in** the non-**w ind**y scenarios (right-side plots). However, thisis by far the case

82 Model resultsBPO**50**Solution GAB: 11.0 %**50**4003**50**4040300El. price, BPOHeat price, BPOEl./heatprice[€/MWh]302030202**50**2001**50**El. price, ref1010100**50**Heat price, ref000181522293643**50**57647178859299106113120127134141148155162169Time [h]181522293643**50**57647178859299106113120127134141148155162169Time [h]Figure 6.9, Comparison **of** prices **in** the bypass and reference scenario, subjected to the**w ind**y and non-

Model results 8380,0070,0060,00**50**,0040,0030,0020,0010,000,00BPO impacts on electricity pricesEl. price,January[€/MWh]El. price,April[€/MWh]El. price,November[€/MWh]Share **of**critical lowel. prices[%]Bypass (full‐scale)ReferencePrices[€/MWh]SCENARIOSW**in**dyNot **w ind**ymonth:BPO ref BPO refEL Jan 8.29 3.05 17.00 17.20Apr 9.63 4.90 17.43 17.52Nov 9.61 5.25 18.75 18.75mean 9.18 4.40 17.73 17.82HEAT Jan 19.26 29.14 18.42 18.76Apr 9.13 27.62 18.59 18.52Nov 9.96 27.46 17.60 17.60mean 12.78 28.07 18.20 18.29Figure 6.10, A comparison

84 Model results1) Heat price-level at31 € means el. price iszero2) Increased **w ind** penetrationextends thisprice level further3) 18 € - el. and heatprice is balancedHeatPrice[€/MWh]3020100Comparison

Model results 85April, July and November, respectively. As **in** the previous scenarios, the dotted l**in**es**in**dicates the heat price **of** the reference scenario and the massive ones the heat pumpscenario. What is strik**in**g, is how the heat pumps more or less turn around the heat andelectricity price formations, caus**in**g an **in**creased electricity price- and a fall **in** the heatprice level. An example **of** this is the non-**w ind**y week

86 Model resultsEl. price, HP.**50**4003**50****50**4003**50**Heat price, HP.4030040300El. price, Ref.Heat price, Ref.El./heatprice[€/MWh]30202**50**2001**50**30202**50**2001**50**10100**50**10100**50**0000181522293643**50**57647178859299106113120127134141148155162Time [h]181522293643**50**57647178859299106113120127134141148155162169Time [h]Figure 6.12, Comparison **of** prices **in** the Heat pump and reference scenario, respectively,subjected to the **w ind**y and non-

Model results 87pumps almost completely manages to prevent changes **in** the prices despite **of** the **in**creased**w ind** capacity (as seen

88 Model resultsDe-centralized heat price duration: heat pump/reference scenarioHeatPrice[€/MWh]**50**400,003**50**,00Heat Price[Dkk/MWh40300,00302**50**,00200,0020101**50**,00100,00**50**,002008 HP2008 ref2017 HP2017 ref0131462794012531566187921922**50**52818313134443757407043834696**50**09532256355948626165746887720075137826813984520,002025 HP2025 reftime [h]Figure 6.15, Duration **of** heat prices **in** the decentralized distribution area show**in**gsignificantly lower prices **in** the heat-pump scenario.6.2.5. Comparison **of** price characteristics **of** the heat pump, the BPO and the reference scenarioF**in**ally, Table 6.8 below conta**in**s details on the electricity- and heat price characteristics**of** the heat pump scenario, the full-scale BPO scenario and the reference scenario. Thetable is **based** on the on the optimized one-week samples **of** a **w ind**y and non-

Model results 89SCENARIOS:PricesW**in**dy (~3000 MW)Not **w ind**y (~1000 MW)month:[€/MWh]HP ref BPO HP ref BPOJan 15.70 3.05 8.29 27.39 17.20 17.00ELApr 16.07 4.90 9.63 28.25 17.52 17.43Jul 10.57 8.55 - 27.44 22.43 -Nov 16.46 5.25 9.61 27.98 18.75 18.75mean 14.70 5.44 9.18 27.77 18.97 17.73HEATJan 15.67 29.14 19.26 15.67 18.76 18.42Apr 19.74 27.62 9.13 19.74 18.52 18.59Jul 5.19 30.79 - 5.19 21.89 -Nov 15.76 27.46 9.96 15.76 17.60 17.60mean 14.09 28.75 12.78 14.09 19.19 18.20Table 6.8, Comparison

90 Model resultsdue to the unfortunate high level **of** complexity caus**in**g gaps on 6-11 % on the optimalsolutions. For better comparison, the reference and heat-pump scenarios have thereforebeen modeled this way too.S**in**ce the focus **of** this section has been price formations alone, one **of** the ma**in** topics **of****in**terest have been the amount **of** critically low prices. In this connection it was foundthat under normal conditions (reference scenario) this amount **in**creases strongly as the**w ind** penetration changes, from a relative

Model results 91thermore be analyzed **in** relation to the balanc**in**g **of** consumption **of** heat and electricity,and the result**in**g export and import. As the modeled systems are exposed to **in**creas**in**g**w ind** capacity, their ability to fully exploit the

92 Model resultsEl. gen.[MWh]**50**004**50**040003**50**030002**50**020001**50**01000**50**00Electricity generation: reference scenario,January (**w ind**

Model results 93El. gen.[MWh]**50**004**50**040003**50**030002**50**020001**50**01000**50**00Electricity generation: reference scenario,January (**w ind**

94 Model resultsFigure 6.19 below shows the characteristics **of** the production patterns over the entiremodeled year, highlight**in**g some **of** these critical issues.Total annualproduction[GWh]30.00025.00020.00015.00010.0005.000Annual production:Reference system **of** 2008, 2017 and 2025Total **w ind**productionUnexploited

Model results 95Comparison **of** average production betweenUC model and West‐DK [MWh/year]Large importfactor due to“cheap” hydro**power** **in** modelMuch highercentral production**in** real system2008UC Model2004‐09WEST‐DKFigure 6.20, Comparison **of** model to West-DK by mean production 27 .As **in** Figure 6.20 above, the production patterns **of** the three **w ind** pr

96 Model resultsOne **of** the problems with the model is seen when compar**in**g with the distribution-barsfrom the real West-DK system (2004-2009 average). Figure 6.22 below compares theproduction **in** critically low hours for the modeled system and West-DK, respectively.One **of** the ma**in** differences is that whereas central production **in** the model is almostcompletely suppressed, this is not the case **in** West-DK where the amount **of** constra**in**ed**power** 28 from central units is relatively higher. The modeled central units simply seemtoo “perfect” respond**in**g to low prices, when compared to the data from the real system.The ma**in** reason for this though, is that the model has more boil**in**g capacity **in**stalled **in**the central heat-distributions than the West-DK area. However, know**in**g that centralproducers usually possess a fare amount **of** boil**in**g capacity as back-up, there could beother reasons beh**in**d the refus**in**g **of** produc**in**g at a low scale as well (observed **in** thereal system).Larger **w ind** production

Model results 97Another ma**in** difference between the model and West-DK, allow**in**g higher **w ind** production

98 Model resultsEl. gen.[MWh]**50**004**50**040003**50**030002**50**020001**50**01000**50**00Electricity generation: bypass scenario (full‐scale), January(**w ind**y pr

Model results 99El. gen.[MWh]**50**004**50**040003**50**030002**50**020001**50**01000**50**00Electricity generation: bypass scenario (full‐scale), November(**w ind**y pr

100 Model results3 week comparison **of** Total electricity generation **in** Bypass and referencescenario, **w ind**y pr

Model results 101erence scenario), as well as the replacement **of** constra**in**ed **power** from backpressureunits with heat pump production. In addition, a great part **of** the **power** generation fromextraction units have been displaced with **w ind**

102 Model resultsEl. gen.[MWh]**50**004**50**040003**50**030002**50**020001**50**01000**50**00Electricity generation: Heat pump‐scenario,January (**w ind** 2017)1611162126313641465156616671768186919610110611111612112613113614114615115616116640353025201510

Model results 103pletely displac**in**g central production **in** **w ind**y periods with additionally low consumption)as long as hydro or

104 Model results6.3.2. Balanc**in**g the heat demandIn this section the production patterns **of** the optimized heat production **in** the model willbe accounted for. The procedure will be the same as with the electricity patterns **in** theprevious section - beg**in**n**in**g with the reference scenario, mov**in**g on to the full-scale bypassscenario and f**in**ish**in**g with the heat pump scenario. The reference and heat pumpscenario subjected to the three **w ind** pr

Model results 105Heat[MWh]**50**004**50**040003**50**030002**50**020001**50**01000**50**00Heat production: reference scenario,January (**w ind** 2008)1Boiler committed when el. price drops7131925313743495561677379859197103109115121127133139145151157163Time [h]

106 Model resultsunits **in** the periods with critically low electricity prices – and for some periods even witha complete de-commitment **of** these (except for the last three units committed by agreement).But then aga**in**, **in** some **of** the peak periods, production from extraction units**in**creases to fully supply**in**g the demand. What is particularly **in**terest**in**g here, is thelevel **of** down-regulation **in** the different low-price periods, which varies depend**in**g on thelength **of** the period with low price.Heat[MWh]Different no. **of**units committeddepend**in**g on thelength **of** low priceperiod**50**004**50**040003**50**030002**50**020001**50**01000**50**00Heat production: reference scenario,January (**w ind** 2025)13 units7 units7131925313743495561677379859197103109115121127133139145151157163Time [h]

Model results 107When look**in**g at the production patterns **in** the hours with critically low prices, the bars**in** Figure 6.34 below show, that with**in** these particular hours, heat production from extractionunits is gradually reduced while heat production from boilers **in**creases, as the**w ind** capacity

108 Model resultsHeat production **in** bypass scenarioThe optimized results **of** the heat production **in** the full-scale bypass scenario (modeledfor a couple **of** weeks), as well as the s**in**gle-unit bypass scenario (modeled for the entireyear), will be presented **in** the fallow**in**g. First, the impacts **of** the full-scale BPO scenario,under the **in**fluence **of** the **w ind**y pr

Model results 109Heat[MWh]**50**004**50**040003**50**030002**50**020001**50**01000**50**0Heat production: reference scenario,November (W**in**dy pr**of**ile)BPO caused spillover **of** heat,result**in**g **in** a zero heat price**50**45403530252015105Heat/elprice[€/MWh]Heat demand (central)Heat demand (decentralized)Heat price [€/MWh]El. price [€/MWh]Extraction units (central, coal)Boiler, central (gas)Backpressure (dc, gas)Boiler, decentralized (gas)0017131925313743495561677379859197103109115121127133139145151157163Time [h]Figure 6.36, Plot **of** heat production **in** bypass scenario (November), subjected to the**w ind**y pr

110 Model resultsis furthermore seen, that **in** the BPO scenario the mentioned surplus heat **in**creases approach**in**g2025. F**in**ally, the figures recalls that the heat shadow prices **in** the referencescenario **in**creases from an average **of** ~15 to ~17 € per MW heat, as a result **of** the **in**creas**in**g**w ind** capacity, while this price

Model results 111Heat production: Heat pump‐scenario,January (2008 **w ind**)Heat[MWh]

112 Model resultsareas. In low consumption periods, the el. price additionally drops, caus**in**g extractionunits to de-commit for a period, while boilers fill out the gab.As the **w ind** capacity

Model results 113Total annualproduction[GWh]20.00018.00016.00014.00012.00010.0008.0006.0004.0002.000‐Comparison **of** heat production:Heat pump scenarioExtraction units (central, coal)Boiler, central (gas)Backpressure (dc, gas)Boiler, decentralized (gas)Heat pump, centralHeat pump, decentralized2008 2017 2025HEAT PUMP SCENARIOS: W**in**d capacity anno:Figure 6.42, Comparison **of** heat production from the different facilities,show**in**g a significant overweight **of** heat produced on electricalheat pumps, and decentralized **CHP** be**in**g non-prioritized.When seen over the years modeled (figure above), heat produced on heat pumps make upa large share **of** the total amount **of** heat produced **in** the decentralized areas, regardless**of** the amount **of** **w ind** capacity (mean

114 Model resultsWhen analyz**in**g the hours with critically low electricity prices, it is shown that theseprices occur dur**in**g hours with **in**creas**in**g demands, as a result **of** the **in**creas**in**g **w ind**capacity, and so do the amount

Model results 115**in**creas**in**g **w ind** capacity, thus reduc

116 Economic AnalysesChapter 7.Economic Analyses7.1. Overview **of** the economic analysesThe Unit Commitment model is basically an economic optimization model designed tosearch for an optimal comb**in**ation **of** a number **of** available utilities, given a set characteristicsthat can satisfy a number **of** demands at the lowest, total costs. Therefore theresults presented **in** the previous chapter represent the most economically optimal outputgiven the respective conditions – when seen from “the market’s” po**in**t **of** view.As mentioned earlier, this chapter will look at some **of** the economic aspects **of** the modelresults for further comparison **of** the different scenarios. The reason for this is to evaluatenot only the economic consequences that implementation **of** **w ind** capacity correspond

Economic Analyses 1177.2. S**in**gle **power** plant economyIn this section, the economic characteristics **of** the different **in**dividual utilities will beanalyzed **in** relation to the full load factors, the total hours **of** commitments, number **of**start-ups per week, and f**in**ally the total **in**come and pr**of**it – all on the basis **of** one year.When analyz**in**g the impact **of** these factors (subjected to the different **w ind** pr

118 Economic AnalysesLoad factors (el.) [%] Extraction units Condens**in**g unitsTotal el. genSCENARIOS: Central unit: G1 G2 G3 G4 G5 G6 G7 G8 G9[GWh el.]2008 28 32 31 30 34 29 27 0 3 10,238Reference -2017 25 30 29 27 31 25 24 0 1 9,3172025 19 27 27 22 28 20 19 0 1 8,2812008 20 31 31 31 33 29 27 0 1 9,867Bypass, s**in**gle unit (G1)2017 10 30 29 27 31 26 23 0 1 8,7962025 10 26 26 22 28 19 18 0 1 7,7892008 27 32 31 28 34 26 24 35 30 8,968Heat pump -2017 19 25 25 20 28 19 17 25 18 6,4592025 15 22 21 16 25 15 14 21 12 5190Table 7.1, Comparison **of** electrical load factors for centralized units.The total **in**come **of** a **CHP** plant **in**cludes the heat production too. The modeled **CHP**load factors are therefore shown **in** Table 7.2 below. The **CHP** load factors are **in** generala bit higher than the electrical load factors seen above. They decrease with approximatelythe same rate, though, which could be a symptom **of** the **power** generation be**in**g constra**in**edby the heat demand. When look**in**g at the bypass scenario and compar**in**g the**CHP** LF to the electricity LF for G1, it is seen, that the decrease **in** LF, approach**in**g2025, is much smaller for the comb**in**ed heat and electricity production (from 28 to 24 %)than for just the electricity production. This means that the heat production rema**in**salmost **in**tact **in** the bypass scenario. Other than that, the two load factors seem coupledto each other when compar**in**g the scenarios.Load factors (**CHP**) [%]Extraction unitsSCENARIOS: Central unit: G1 G2 G3 G4 G5 G6 G7Reference -Bypass, s**in**gle unit (G1)Total **CHP**[GWh]2008 32 36 36 35 39 33 31 24,6412017 29 34 34 31 36 29 28 22,6362025 22 31 31 25 33 23 22 20,2932008 28 36 36 35 38 33 31 24,3162017 24 34 34 31 36 30 27 22,3472025 24 30 29 25 33 22 20 20,0782008 28 34 33 31 36 29 27 16,244Heat pump -2017 21 28 27 23 30 21 19 12,1592025 16 25 23 18 28 17 16 9,937Table 7.2, Comparison **of** **CHP** load factors for centralized units.Follow**in**g up on the bypass scenario, Table 7.3 below compares the calculated electricityand**CHP** load factors **of** the reference and the full-scale bypass scenarios subjected to the**w ind**y pr

Economic Analyses 119the particular heat and electricity prices **of** the given week, the numbers could **in**dicate apotential improvement **of** the **power** plant economy if convert**in**g **in**to BPO – **in** **w ind**y periodsthough.Full load factor (el. and

120 Economic AnalysesAnnual Commitment [%] Extraction units Condens**in**g unitsSCENARIOS: Centralized units: G1 G2 G3 G4 G5 G6 G7 G8 G9 Average2008 91 100 100 96 100 94 91 0 6 75Reference - 2017 85 100 100 89 100 87 86 0 3 722025 67 100 100 73 100 71 66 0 2 642008 100 98 98 95 96 93 86 0 2 74Bypass, s**in**gle unit (G1) 2017 99 98 95 89 100 88 78 0 2 722025 99 91 89 73 100 67 63 0 1 652008 79 98 96 88 100 85 76 48 40 79Heat pump - 2017 62 90 90 69 100 66 57 48 24 672025 **50** 88 81 57 100 55 48 **50** 17 61Table 7.4, Comparison **of** commitment factors for centralized units.To elaborate on the commitment factors **in** the bypass scenario, the full scale version isseen **in** Table 7.5 below (calculated **in** accordance with the **w ind**y weeks). As it appears,apply

Economic Analyses 121ups is 0.4 31 per week, which, compared to the 1-1.5 per week **in** the reference scenario,might be **of** **in**terest **of** worried plant operators. A part **of** this decl**in**e can be expla**in**ed bythe **in**creased commitment factor due to the BPO (as seen above **in** Table 7.5). F**in**ally,the system scenario result**in**g **in** the highest number **of** start-ups is the heat-pump scenario,where some **of** the extraction units have around three start-ups per week.No. **of** start-ups per week Extraction units Condens**in**g unitsSYSTEM SCENARIOS: Central units: G1 G2 G3 G4 G5 G6 G7 G8 G9 Average2008 1.02 0.23 0.23 0.75 0.23 0.87 1.04 0.08 0.85 0.59Reference -2017 1.12 0.23 0.23 0.98 0.23 1.10 1.19 0.00 0.40 0.612025 1.**50** 0.23 0.23 1.54 0.23 1.54 1.69 0.04 0.29 0.812008 0.44 0.46 0.40 0.88 0.23 0.87 0.98 0.00 0.23 0.**50**Bypass, s**in**gle unit (G1) 2017 0.44 0.38 0.62 1.06 0.23 1.04 1.19 0.00 0.29 0.582025 0.42 0.69 0.69 1.56 0.23 1.54 1.56 0.00 0.25 0.772008 2.88 0.37 0.56 1.94 0.23 2.**50** 2.77 2.73 5.88 2.21Heat pump -2017 3.17 0.77 0.65 2.96 0.23 3.12 2.83 2.02 4.00 2.192025 3.00 0.73 1.08 3.10 0.23 3.06 2.71 1.**50** 2.87 2.03Table 7.6, Comparison **of** the weekly number **of** start-up for central units **in** the different scenariosand **w ind** pr

122 Economic Analyses**of** the seven extraction units is switched on. The white areas **in**dicate conventional operation(bypass be**in**g switched ‘**of**f’). The correspond**in**g **w ind** and central heat demand isdisplayed to the right. Remember

Economic Analyses 123when subjected to the 2008, 2017 and 2025 **w ind** scenarios, respectively. As seen

124 Economic Analyses7.2.4. Total **in**come **of** **power** unitsUntil now we have seen how the expansion **of** the **w ind** capacity towards the 2025

Economic Analyses 1252025 20.14 24.16 23.20 22.34 18.95 20.84 18.98 13.49 23.34 20.60Table 7.7, Comparison **of** total **in**come **of** central units **in** the different system- and **w ind** scenarios.Annual pr

126 Economic Analysesthe bypass scenario than **in** the reference scenario, while the other units will have ahigher **in**come.Annual **in**come (Mill. € per year)Extraction unitsAnnual **in**come G1 G2 G3 G4 G5 G6 G7 MEANIncomeBypass 1.33 1.**50** 1.51 1.63 1.24 1.52 1.32 1.44Reference 1.04 1.88 1.78 1.23 1.39 1.13 0.98 1.35Pr**of**itBypass -0.72 -0.54 -0.57 -0.68 -0.15 -0.80 -0.52 -0.57Reference -0.01 -0.33 -0.33 0.00 -0.24 0.00 0.00 -0.13Production costsBypass 2.05 2.04 2.08 2.31 1.40 2.32 1.84 2.01Reference 1.05 2.21 2.11 1.23 1.62 1.13 0.98 1.48Table 7.9, Comparison **of** total production costs, **in**come and pr**of**it **of** the central units, **in** theweek-samples **of** the full-scale BPO and reference scenario, subjected to the **w ind**y pr

Economic Analyses 127In the reference scenario is seen that the **in**come **of** boilers, both **in** the central and dedecentralized areas, will **in**crease as the **w ind** capacity is expanded. A particularly large(relatively)

128 Economic Analysesmore frequently chooses to oversupply heat rather than operat**in**g **in** the lowest backpressurepo**in**t **of** operation, when approach**in**g 2017 and 2025.Heat pumps generally have a negative impact on the **in**dividual economy **of** **CHP** plants.This is especially the case for units specialis**in**g **in** heat production such as boiler- andbackpressure units, while extraction units are affected less negatively, due to their lowproduction costs and ability to **in**crease the **power** generation relative to the heat production(towards condens**in**g). Opposite to this, the economic base **of** condens**in**g units istransformed from be**in**g non-exist**in**g to be**in**g on equal foot**in**g with extraction units.Moreover, the annual commitment factors **of** extraction units averagely drops, alongwith a number **of** start-ups be**in**g three times as high as **in** the reference scenario, whichis argued not to be an optimal condition for central units.7.3. Constra**in**t analysisIn chapter 5, it was expla**in**ed that the ma**in** objective **of** the model is to m**in**imize thetotal costs **of** a system consist**in**g **of** a number **of** production units, while satisfy**in**g anumber **of** constra**in**ts (first **of** all **in**clud**in**g the satisfaction **of** an electricity and heatdemand). In addition it was mentioned that the change **in** optimized total costs, connectedto the relaxation **of** a constra**in**t by one unit, can be **in**terpret as the shadow prices**of** the particular constra**in**t. Until now, shadow prices have only been analyzed **in** connectionwith the constra**in**ts satisfy**in**g the heat and electricity demand, which **in** thisproject is directly **in**terpreted as the electricity and heat price, respectively. In this section,shadow prices will be used to determ**in**e how some **of** the restrictions **in** the modelconstra**in** the optimal balanc**in**g **of** the heat and electricity demand. As the physicalproperties **of** central units is one **of** the ma**in** focuses **of** the current project, the first part**of** this analyse will concentrate on the different physical limitations characteriz**in**g thecentral **power** units. Secondly, the electricity-heat relation **of** backpressure units, capacitylimits on **in**terconnections and the maximum production **of** decentralized boilers willbe analysed, and f**in**ally, the value **of** **in**creas**in**g the **w ind** capacity will be exam

Economic Analyses 129ure 7.3 below, the production po**in**ts **of** the reference system **in** the months: January,May and September, subjected to the **w ind** pr

130 Economic Analysescat**in**g that heat is more needed than electricity. As a consequence, there is no demandfor production from condens**in**g units.Look**in**g at the production **in** May **in** 2008, there seems to be a relatively large amount **of**production hours ly**in**g **in**-between the constra**in**ts. Still however, a great amount **of** theproduction seems constra**in**ed by partly the lower part **of** the backpressure l**in**e as well asby the m**in**imum **power** generation, **in**dicat**in**g a small heat demand. As the **w ind** capacity

Economic Analyses 131With this be**in**g said, it is important to stress the fact that extraction units operat**in**g **in**backpressure mode not automatically means that electricity generation is completelyconstra**in**ed by the heat. This is illustrated by Figure 7.5 below, show**in**g a plot **of** theproduction **in** April and November both subjected to the **w ind** penetration anno 2017,

132 Economic AnalysesHeat pump scenarioJanuary, 2017 May, 2017Figure 7.6, Two months **of** the heat pump scenario, subjected to the **w ind**

Economic Analyses 133order to balance the **power** generation costs. To expla**in** this, an example is seen **in** Table7.11 below which shows a sample **of** two operat**in**g hours **of** an extraction unit with differentproduction and price levels. The shadow price **of** the backpressure l**in**e is differentfrom zero which tells us that the unit is cogenerat**in**g heat and electricity **in** backpressuremode. In the first hour the shadow price **of** electricity is 17.20 €/MWh, the heatprice 18.20 €/MWh and additionally the shadow price **of** the backpressure l**in**e is 17.98€/MWh. Now, s**in**ce the marg**in**al generation costs **of** electricity (see section 5.4) is 35.18(when there is no **in**come from heat), the difference between the electricity price and themarg**in**al costs is reflected **in** the shadow price, thereby **in**dicat**in**g the amount **of** electricitythat needs to come from heat (or elsewhere). In the second hour, the electricity pricedrops to a critically low 1.06 €/MWh result**in**g **in** a higher shadow price on the backpressureconstra**in**t **of** 34.12, **in** order to level out the marg**in**al generation costs. In additionto this, the heat price **of** the particular hour **in**creases. S**in**ce the extraction unit seenhere is the marg**in**al utility **of** the total heat supply, the heat price level balances the**in**come, result**in**g **in** a pr**of**it **of** zero.Shadow prices from an extraction unit:Hour **of** Energy converted [MWh] Shadow prices **of**: (€/MWh) El. supply +operation Fuel El. Heat Heat supply El. supply Backpressure limit BackpressureMarg**in**al el.gen. costst442 496 194 259 18.76 17.20 + 17.98 = 35.18 35.18t443 482 189 252 30.86 1.06 + 34.12 = 35.18 35.18Table 7.11, A numeric example **of** shadow prices from extraction units.It is important to stress that the shadow price **of** the backpressure l**in**e **in** the exampleabove, constra**in****in**g the relation between heat and electricity, not reflects an immediateeconomic loss from the constra**in**t, but rather the contribution from additional heat production.In this relation, the shadow price can be used to determ**in**e whether the purpose**of** a production-hour **of** a particular unit is to produce heat **in** order to generate electricity,or the other way around.Table 7.12 below shows the amount **of** shadow prices different from zero result**in**g from aone-unit relaxation **of** the backpressure l**in**e. The shadow prices that equal zero are notconstra**in**ed by the backpressure limit. The table figures are calculated relative to thefactor **of** annual commitment. In the reference scenario 2008, averagely 67 % **of** the yeara shadow price is generated from the backpressure constra**in**t, a number which **in**creasesto 69 % **in** both 2017 and 2025. This means, that the drastic expansion **of** the **w ind** capacitytowards 2025 does not significantly change the amount electricity constra

134 Economic AnalysesShadow price factor, backpressure [%]Extraction unitsEl.SYSTEM SCENARIOS: Central units: G1 G2 G3 G4 G5 G6 G7 Meanc v2008 66.2 65.7 65.6 67.5 68.5 66.7 66.1 66.6Reference2017 70.0 66.6 66.6 70.3 69.7 69.4 69.6 68.9c m2025 68.6 66.9 66.9 69.6 70.0 69.2 68.0 68.52008 46.2 46.2 46.8 45.7 47.4 45.7 47.5 46.5Pel m**in**Heat pump2017 57.6 57.9 55.0 55.7 56.6 56.6 58.9 56.9Heat2025 63.6 61.2 62.2 62.0 61.0 62.4 66.0 62.6Table 7.12, Shadow price factors – the amount **of** operat**in**g hours with shadow prices differentfrom zero, **in**dicat**in**g the share **of** electricity generation constra**in**ed by the heat demand. Asseen on the red l**in**e, shadow prices are generated by relax**in**g the l**in**ear constra**in**t one unit **in**the electricity’s direction (y-axis).One th**in**g is how frequent the backpressure limit causes (or forces) the electricity to beconstra**in**ed, another, is the size **of** the particular shadow prices and thus, the necessarycontribution from heat. Table 7.13 below shows a comparison **of** the average shadowprices **of** the extraction units **in** the different system scenarios, show**in**g significant differencesbetween the reference and heat pump scenarios as well as difference betweenthe different **w ind** penetration levels. In the reference scenario, the average shadowprice

Economic Analyses 135the reference system subjected to the different **w ind** capacities. Compared to the backpressureconstra

136 Economic AnalysesFurthermore, the shadow price will be used as an **in**dicator **of** the impacts **of** the vary**in**g**w ind** capacities on this imbalance. As it was the case for extraction units, the shadowprice

Economic Analyses 137the electricity generation is constra**in**ed by the heat demand, the average price goes fromapproximately 13 €/MWh **in** 2008 to 15 €/MWh and 17 €/MWh **in** 2017 and 2025, respectively.In the relatively few hours where heat is constra**in**ed by the electricity supply, theshadow prices on the other hand are relative small, around -3 €/MWh at all **w ind** penetrationlevels. This trend is a natural consequence

138 Economic AnalysesShadowBPO, **w ind**ySYSTEM SCENARIOSReferenceBPO (full-scale)prices,Backpressure unitsShadowprice > 0Shadowprice < 0Boiler,decentralizedExternal connectionsExportImportW

Economic Analyses 139tive to the amount **of** **w ind**

140 Economic Analysesthe amount **of** hours with critical electrical spillover. Moreover, the average shadow price**of** 11.7 €/MWh on **w ind** capacity as seen

Economic Analyses 141The delimited systempart observed**in** relation to theassessment **of** thetotal system economyThe system part be**in**g optimizedby the model (be**in**gthe entire system)Figure 7.7, A repetition **of** the geographical model shown **in** chapter 5, **in** order to illustrate(by the dashed boxes) the system part be**in**g optimized and the system partbe**in**g assessed **in** relation to the total system economy.7.4.1. Total costs **of** the reference systemThe calculated total costs **of** the reference and heat pump system is seen **in** Figure 7.8below, and the correspond**in**g numbers are seen **in** Table 7.18 further below. When look**in**gat the reference system isolated, the total production costs seem relatively unaffectedby the expansion **of** the **w ind** capacity, decreas

142 Economic Analysescosts to the **in**creased **w ind** penetration is simply a consequence

Economic Analyses 143rio) the **in**crease **in** export has stagnated and the **in**come from bottlenecks on export ismore than doubled.The system **in**come **of** the heat pump scenario **in** 2008 is entirely **based** on import-relatedbottleneck **in**come and the **in**come is more than twice as high as the total **in**come **of** thecorrespond**in**g reference scenario. The **in**come level reflects a system with full utilization**of** **w ind**

144 Economic Analyses**in**creased amount **of** “cash” flow**in**g directly between market players, rather than to theTSO companies, **in** the BPO scenario. Because we are look**in**g at the **w ind**y pr

Economic Analyses 1457.5. Green account**in**g7.5.1. Applied methods for assess**in**g the environmental impactsOrig**in**ally, the ma**in** motivation beh**in**d the political goal **of** the **50** % **w ind** scenario is toreduce the CO2 emission by

146 Economic AnalysesW**in**dCoalGasHydro (import only)PRIMARY ENERGY CONSUMPTIONFossil fuelsRenewable energyLossEnergy conversionThe ‘cut’ where the share **of**different energy types isassessed relative to the electricityconsumptionHeatDistributionTransmissionExportDistrict heat**in**gElectricityFINAL CONSUMPTION (ma**in** region)Figure 7.11, Illustration **of** the calculation method used **in** this project to assess theamount **of** renewable energy. **Ea**rlier, this relative share was measured aga**in**st the primaryenergy consumption while it today is measured relative to the produced heat andelectricity (own illustration).7.5.2. Comparison **of** reference scenario and heat pumps scenarioFigure 7.12 and Figure 7.13 below show the relative shares **of** electricity and heat productionto the total consumption, calculated from the method from Figure 7.11, compar**in**gthe reference- to the heat pump scenario. The values are rated such that the f**in**altotal consumption gives 100 percent, by which it is seen that the total share **of** **power**generation (left) is larger **in** the heat pump scenario, due to the 17-21 % (2008-2025) **in**crease**in** absolute electricity consumption that the heat pumps create. Regard**in**g theelectricity production **of** 2008, the share **of** **w ind**

Economic Analyses 147When look**in**g at the sources **of** the heat supply (Figure 7.13 to the right), it is seen thatthe total share **of** the f**in**al heat consumption is smaller **in** the heat pump scenario (relativeto the total heat and electricity consumption). In the reference system, the share **of**Natural gas-related heat production **in**creases from 25 % to 30 % towards the **w ind** capacity

148 Economic Analysesis a very large share **of** renewable energy, com**in**g from earth heat, **in**creased import andimproved utilization **of** **w ind**

Economic Analyses 149As for the reference- and the heat pump scenario, Figure 7.17 below shows the distribution**of** sources for the total heat and electricity supply. Aga**in**, earth heat, hydro and**w ind**

1**50** Economic Analysesgreater sensitivity to the **in**creased **w ind** penetration is the heat pumps ability to exploitthe oversupply

Economic Analyses 151as the **w ind** capacity

152 DiscussionChapter 8.Discussion8.1. Reach**in**g the objectivesThe ma**in** objective **of** the present thesis is an exam**in**ation **of** the economic and environmentalimpacts **of** **w ind**

Discussion 1538.2. The Challenges **of** **50** % **w ind**

154 Discussionity accord**in**g to 2017 and 2025. By 2017 the amount **of** critically low prices will **in**creaseby a factor **of** 8 (to 13 % share) on an annual basis, and by 2025 to a factor **of** 17 (29 %),when compared to 2008 (2 %). In addition, the average duration **of** these price periodsare last**in**g 2 and 3 times longer **in** 2017 and 2025, which is an **in**terest**in**g development**in** relation to the mentioned lack **of** market response from **CHP** units. Therefore, if nosystem measures are **in**troduced by the time the **w ind** capacity reaches the level

Discussion 155F**in**ally, hav**in**g analyzed the different aspects **of** the results from the reference scenario,what stands out, is that the two greatest obstructions to a successful **in**tegration **of** **w ind**

156 Discussion8.3.1. Turb**in**e bypassAn optional bypass **of** the high-pressure turb**in**e **in** central units has been exam**in**ed **in**the model**in**g part. The BPO option have been modeled the simplest way possible, bylett**in**g the solver consider the choice: bypass – yes or no? This means that the plant willhave to either produce heat alone, or co-generate – no middle-**of**-the-road operation.The results **of** the bypass scenarios were **in**terest**in**g – especially **in** relation to the consequences**of** **in**creased **w ind** penetration. It was proved that,

Discussion 157a heat demand that is not too low. In fact, when the electricity price is critically low, it is**of**ten more convenient to operate **in** BPO mode while oversupply**in**g the heat demand,than balanc**in**g it **in** normal mode (as a lesser **of** two evils).The benefit **of** BPO does not require extreme **w ind** conditions. In the s

158 Discussion8.3.2. Heat pumpsThe heat pumps used **in** the model are all **of** the geothermal type with an estimated COPfactor **of** 300 %. However, other heat pumps such as the air-to-air types (which arecheaper but with a lower COP factor **of** approximately 200 %), could also have been considered,as these can be **in**stalled **in** households – someth**in**g which might help **in**creas**in**gthe capacity more rapidly (Energ**in**et.dk 2009). However, as the heat pump capacity**in** the model corresponds to a type **of** heat pump that responds to the market, the (large)geothermal type are the ones the model tries to capture the effects **of**. Feed**in**g marketsignals to consumers on household level is nevertheless a relevant subject **in** this relation.Compared to the bypass scenario, the **in**clusion **of** heat pumps **in** the modeled is a muchmore drastic modification **of** the system characteristics (given the selected capacities),when seen from a market- and **in**vestment po**in**t **of** view. The results showed that heatfrom decentralized **CHP** units cannot compete with the production costs **of** heat pumpsat any time, while **in** the central heat-supply areas, heat pumps be**in**g **in** a more equalcompetition with extraction units as consumer-related electricity demand **in**creases (seeFigure 6.42). As a result **of** the strong competition from heat pumps with**in** the heatsupply areas, the total system cost is reduced by approximately **50** % **in** 2017 and furtherby 57 % **in** 2025, when compared to the reference system, **in**dicat**in**g a potentially largesocio-economic improvement from **in**stallation **of** heat pumps. Because **of** the variablecosts **of** earth-heat be**in**g proportional to the correspond**in**g electricity price, the **in**creased**w ind** penetration has a positive impact on the heat supply, contrary to the referencescenario, where the positive effects on the electricity price (from the

Discussion 159pumps will thus not reduce the need for external capacities, but contrary expand it (givenwet seasons **in** the Nordic hydro area).Includ**in**g a greater shortage on the water reservoirs **in** the model, could very well affectthe costs **of** hydro, and thereby the results **of** the optimization – especially when recall**in**gthe large import rates **in** the heat pump scenario. S**in**ce the model **in**cludes a fixed, lowcosts on hydro generation (assum**in**g sufficient water supply at all time), it is **of** concern,that the demand for coal-**based** electricity could **in**crease **in**tensively dur**in**g more dryseasons, which then could affect the share **of** renewable energy and the CO2 emissionsignificantly. A further analysis – that **in**cludes the impacts **of** **in**creased heat pumprelatedelectricity consumption on the costs **of** hydro – would therefore be **of** great **in**terest**in** order to analyze if heat pumps as a consequence revives coal-**based** steam units.Besides from that, the results **of** heat pump scenarios clearly suggest that heat pumps(rightly) should play an important role **in** order to achieve the political target **of** **50** %**w ind**

160 Discussionpotential. The model results therefore **in**dicate a potential **of** **in**creased flexibility, alreadyconta**in**ed by the present system.In the resent years, much has been said about the necessity **of** heat pumps, electricalcars, and other tools for **in**creased flexibility. While plann**in**g large **in**vestments **in**to amore advanced network **of** the future, this project suggests a simultaneously conduction**of** further studies **of** the different obstructions caus**in**g the **in**flexibility beh**in**d the heatconstra**in**ed**power**, **based** on the flexibility **of** extraction units seen **in** the modelled referencescenario **of** the project – obstructions which could be market-related as well astechnically founded. And then, as a further step, a study **in**to the concept **of** turb**in**ebypassis suggested **based** on the positive economic results found **in** this project – especiallywhen seen from a plant-owner’s perspective. The results **of** this project fundamentallysupport the thesis that heat pumps should play a large role **in** the future energysystem due to their ability **of** produc**in**g renewable heat, and even today, steps **in** thisdirection should be taken before chang**in**g the entire system (which to some extent isrequired **in** order to **in**corporate electrical cars for example). However, as the results obta**in**edfrom the modelled heat pumps scenarios **in**dicate, an **in**creased demand for coal**based****power** by might develop **in** this system, and the report stresses the importance **of**further studies **in**to the correspond**in**g role **of** central units **in** the future **in** relation toCO2 emissions. However, flexible production is easy to implement and does not rely somuch on change **of** attitude among the general consumer.8.4. Validity **of** the results8.4.1. Statistical dataData used for the analysis is first and foremost data from the Danish TSO on the WestDanish energy market, rang**in**g from 2004 to 2009 (the correspond**in**g heat data coveredonly 2001), and data on the **power** units from 2006 (see section 4.1 and 5.4.1). By us**in**gfive-year data for the analyses, the variations from year to year **in** for example temperatureand ra**in**fall are evened out, and extreme data are **in**cluded but are not critical tothe results. Furthermore, the five-year data provide an excessive amount **of** data – morethan 40,000 observations – which provide a better data basis for the calculations. Theaccuracy **of** the estimates **of** the relation between critically low prices and the explanatoryvariables (section 4.5) **in**creases as the number **of** observations **in**creases, and themean values used to demonstrate the impact **of** **w ind**

Discussion 161tions on this see section 5.2.4). As these ideal market conditions do not characterize theWest-DK system (where a large part **of** the production is owned by two companies), theresults are expected to deviate a bit from a real system, **in** that the total cost **of** the systemis a bit underestimated. Although this may add a level **of** uncerta**in**ty **in** relation to areal market system, the results are still a good approximat**in**g when regard**in**g this. Inrelation to this, another market characteristic **of** the modeled system, dist**in**guish**in**g itfrom the real, is the ability to “perfect foresight” – weeks and months ahead. A perfectexample **of** this is the **w ind** production. Where the exact quantities

162 Discussion8.4.3. The importance **of** optimization model**in**gThe model is **based** on the West-Danish energy system. Although many simplificationshave been made on various parameters, rang**in**g from energy prices to physical and environmentalcharacteristics, the modeled approximation **of** the impacts are **of** great relevanceto the evaluation **of** a future Danish **power** system with **50** % **w ind**

Discussion 163

164 ConclusionChapter 9.ConclusionBy year 2025, **50** % **of** the Danish **power** generation is to be supplied by **w ind**

Conclusion 165(from electrical spill over) and the duration **of** these low-price periods **in**creases significantas a result **of** expand**in**g the **w ind** capacity towards 2025. Simultaneously, the marg

166 Conclusionthe plant economy further. Opposite to the BPO-system, heat pumps **in** general have anegative impact on the **in**dividual **power** plant economy – except for condens**in**g units,which are likely to experience a revival if this scenario is implemented. Units with amore heat-produc**in**g purpose however (such as backpressure- and boiler units) will beeconomically harmed the most, as they are be**in**g completely replaced by the heat-supply**of** heat pumps – this, **of** course, when optimiz**in**g from a system po**in**t **of** view.When observ**in**g the total system costs, the **in**creased **w ind** penetration is shown hav

Conclusion 167not as a forecast **of** the future. However, s**in**ce the model is **based** on the West Danishenergy system and calculated on basis **of** data conta**in**ed with**in** here, the model providesresults that highlight the problems connected to the **50** % **w ind**

168 BibliographyChapter 10.Bibliography10.1.1. Articles and booksAckermann, Thomas (ed.) (2005): W**in**d Power **in** Power Systems. John Wiley and Sons,Ltd.Agresti, Alan & Barbara F**in**ley (1997): Statistical Methods for the Social Sciences. NewJersey: Prentice Hall.Andersen, Thorbjørn Vest (2008): Statistical analysis **of** production patterns. Pre-projectto master thesis. Lyngby: Danmarks Teknisk Universitet.Bregnbæk, Lars (2008): The Balmorel Model. Background and Methodology. Copenhagen:EA **Energianalyse** A/S.CAN Europe (2006): National allocation plans 2005-7: Do they deliver? Key lessons forphase II **of** the EU ETS. Brussels: CAN Europe.Danish Energy Authority (2005): Technology data for electricity and heat generationplants. Copenhagen: Danish Energy Authority.Danish Energy Authority (2007): A visionary Danish energy policy 2025. Copenhagen:Danish Energy Authority.Danish Energy Authorities (2008): Energi statistik. Copenhagen: Danish Energy Authorities.Dansk Energi (2008): Dansk elforsyn**in**g statistik 2007. Kailow Graphic A/S.Dansk Energi (2009): Dansk elforsyn**in**g statistik 2008. Kailow Graphic A/S.Dansk fjernvarme (2007): Danmark er Europas førende kraftvarmeland. Dansk Fjernvarme24.02.06.Dansk fjernvarme (2008): EU kommisionen beregner nu energiforbrug som slutforbrug.Dansk fjernvarme, 25.01.08.Dieu, V.N. & W. Ongsakul (2007): “Improved merit order and argumented LagrangeHopfield network for unit commitment”, **in**: IET Generation, Transmission & Distribution1 (4) p. 548-556.

Bibliography 169Dong Energy (2009): Grønt regnskab 2008, for Asnæsværket, Avedøreværket, Enstedværket,Esbjergværket, H.C. Ørtsedsværket, Kyndbyværket, Skærbækværket,Stigsnæsværket, Studstrupværket og Svanemølleværket, Fredericia: Dong Energy.**Ea** **Energianalyse** (2006): Elproduktionsomkostn**in**ger for nye danske anlæg. København:**Ea** **Energianalyse** A/S.**Ea** **Energianalyse** (2007): **50** pct. v**in**d i 2025. København: **Ea** **Energianalyse** A/S.**Ea** **Energianalyse** & Risø/DTU (2009): Indplacer**in**g af stigende mængder VE i elsystemet.Delrapport 2: Katalog over løsn**in**ger. København: **Ea** energianalyse A/S.Eis**in**g, Jens (1999): L**in**eær Algebra. Institut for Matematik. Danmarks Teknisk Universitet.Energ**in**et.dk (2006): Systemplan 2006. Fredericia: Energ**in**et.dkEnerg**in**et.dk (2007): Systemplan 2007. Fredericia: Energ**in**et.dkEnerg**in**et.dk (2009): Effektiv anvendelse af v**in**dkraftbaseret el i Danmark. Fredericia:Energ**in**et.dk.GAMS (2007): CPLEX 11. Wash**in**gton DC: GAMS Development Corporation.GAMS (2008): GAMS – a User’s Guide. Wash**in**gton DC: GAMS Development Corporation.Grohnheit, Poul Erik (1993): ”Modell**in**g **CHP** with**in** a national **power** system”, **in**: EnergyPolicy. Butterworth-He**in**emann Ltd, p. 418-429.Hvidsten, Torben (2006): Sverige har kostet danske elforbrugere dyrt. Dansk energi,13.12.2006.Kogelschatz, Bernhard (2004): Power Labell**in**g is a Fiction. Berl**in**: Berl**in** University **of**Technology.Krist**of**fersen, Hans-Erik & Anders Sandbergh Stouge (2002): ”Behov for fleksibelt elforbrugi et liberaliseret elmarked” i: Erhvervspolitisk **in**dsigt. Nyhedsbrev fra DanskIndustri nr. 13.Meyers, Lawrence S., Glenn Gamst & A.J. Guar**in**o (2006): Applied Multivariate Research.Design and Interpretation. Sage Publication.Miljøm**in**isteriet (2000): Danish Environment & Energy Newsletter, No 2.Nielsen, Jørgen Steen (2009): ”V**in**dkraften overhaler alt” i: Information, 04.02.2009.Nordel (2008): Nordic Grid Master Plan 2008. Organisation for the Nordic TransmissionOperators.

170 BibliographyPetrov, Valentín & James Nicolaisen (1999): A Simple Unit Commitment Problem. NSFmeet**in**g 18.10.1999.Ravn, Hans F. (2001): The Balmorel Model: Theoretical Background. Balmorel.Ravn, Hans F. (2004): The Balmorel Model Structure. Balmorel.Solver.com (2009): Optimization Problem Types – Mixed-Integer Programm**in**g (MIP)Problems. Available at: http://www.solver.com/probtype3.htm.Togeby, Mikael, Hans Henrik L**in**dboe & Thomas Engberg Pedersen (2007): Steps forimproved congestion management and cost allocation for transit. TemaNord 2007:537, Copenhagen: Nordic Council **of** M**in**isters.Varmeplan Hovedstaden (2008): ”Varmeplan skal sætte dagsordenen. Nyt projekt omfremtidens varmeforsyn**in**g i hovedstadsområdet”, i: Varmeplan Hovedstaden Nyhedsbrevnr. 1, juni 2008.Vattenfall (2009): Nordjyllandsværket. København: Vattenfall A/S.W**in**je, Dietmar (2007/2008 a): Grundzüge der Elektrizitatsmärkte. Berl**in**: Berl**in** University**of** Technology.W**in**je, Dietmar (2007/2008 b): Grundzüge der Ölmärkte. Berl**in**: Berl**in** University **of**Technology.W**in**je, Dietmar (2007/2008 c): Grundzüge der Gasmärkte. Berl**in**: Berl**in** University **of**Technology.10.1.2. Web pagesAkraft.dk (2009): El-produktion v. dampkraft. http://www.akraft.dk/dampkraft.htm, lastvisited: 28.05.09.Bus**in**ess Dictionary (2009): Marg**in**al pr**of**it,http://www.bus**in**essdictionary.com/def**in**ition/marg**in**al-pr**of**it.html, last visited29.05.2009.Den store danske encyklopædi (2009): Fjernvarme.http://www.denstoredanske.dk/It,_teknik_og_naturvidenskab/Energi,_varme_og_k%C3%B8leteknik/Varme,_ventilation,_ovne_og_kedler/fjernvarme?highlight=fjernvarme, last visted 30.05.2009.Elspot at Nord Pool Spot: http://www.nordpoolspot.com/trad**in**g/The_Elspot_market/, lastvisited 29.05.2009.Energ**in**et.dks hjemmeside: www.energ**in**et.dk, last visited 28.05.2009.

Bibliography 171Energistyrelsens hjemmeside: www.ens.dkFjernevarmesektorens organiser**in**g og aktører – en oversigt,http://www.energiforskn**in**g.dk/sw13846.asp, last visited 30.05.2009.Kulpriser: http://www.ens.dk/dadk/**in**fo/talogkort/statistik_og_noegletal/energipriser_og_afgifter/kulpriser/sider/forside.aspx last visited 30.05.2009.Investopedia (2009): http://www.**in**vestopedia.com, last visisted 01.06.2009.Nord Pool Spot: http://www.nordpoolspot.com/, last visited 29.05.2009.NordREG (2009): The Development on the Nordic Electricity Market,https://www.nordicenergyregulators.org/The-Development-on-the-Nordic-Electricity-Market/, last visited: 27.05.2009.Wikipedia (2009): L**in**ear programm**in**g,http://en.wikipedia.org/wiki/L**in**ear_programm**in**g, last visited 27.05.09.10.1.3. Personal contactBoldt, Jørgen, Ingeniør **Ea** **Energianalyse**, regular contact **in** person.Bregnbæk, Lars, Ingeniør **Ea** **Energianalyse**, regular contact **in** person.L**in**dboe, Hans Henrik, Ingeniør **Ea** **Energianalyse**, regular contact **in** person.Ørum, Erik, Ingeniør Systemdrift, Energ**in**et.dk, contact per e-mail 29.08.2008.

172 AppendixChapter 11.Appendix11.1. Logistic regression – validity **of** the regression modelIn chapter 4 the relation between critically low prices and **w ind** production, demand,decentralized production, central production, hour

AppendixNomenclature 173The test is highly significant which means that there is **in**congruence between the observedand the predicted values. This might be a result **of** the great number **of** observations**in** the dataset (43,848), thus be**in**g less **of** a problem.11.1.3. AssumptionsAlthough logistic regression makes fewer assumptions than l**in**ear regression, logisticregression does require the fallow**in**g:1. There must be an absence **of** perfect multicoll**in**earity2. There must be no specific errors (i.e. the relevant predictors are **in**cluded and irrelevantpredictors are excluded)3. The **in**dependent variables must be measured at the summative response scale,**in**terval or ratio level (although dichotomous variables are also allowed).(Meyers, Gamst & Guar**in**o 2006: 222)To beg**in** with the latter, all the **in**dependent variables, except for hour which is categorical,are either **in**terval/ratio level.Multicoll**in**earity refers to a situation where two or more explanatory variables **in** a regressionmodel are highly correlated, thereby affect**in**g the estimation **of** the predictors.We have perfect multicoll**in**earity if the correlation between two **in**dependent variables isequal to 1 or -1. There is absence **of** perfect multicoll**in**earity **in** the model although some**of** the **in**dependent variables correlate (for example hour and decentralized or hour anddemand). This is not considered a huge problem s**in**ce the change **in** the estimates isrelatively small when subtract**in**g on **of** the variables from the model plus the multicoll**in**earityis considered **of** the “good k**in**d” where the variables measure someth**in**g different(theoretically – and **in** practice **in** this case).Regard**in**g the assumption **of** no specific errors, it has been tested **of** other variablesshould be **in**cluded **in** the model, or if data should have been recoded differently, by test**in**gthe distribution **of** the conditional means **of** the standardized residuals on **in**cludedas well excluded variables. However, this was not the case.

174 Appendix11.2. How much **of** the heat supply fromheat pumps is renewable energy?In chapter 7 it was argued, that only two thirds **of** the heat supply from heat pumps(earth heat) can be regarded as pure RE sources, while the third part (electricity) cannot.In figure Figure 11.1 below the distribution **of** sources for the electricity used by the heatpumps is seen. It shows that when subjected to the 2008 **w ind** capacity, two thirds

AppendixNomenclature 17511.3. The Unit Commitment ProblemThis section conta**in**s additional explanation and graphs on the solv**in**g **of** the unit commitmentproblem.11.3.1. Optimiz**in**g the Unit Commitment ProblemThe fundamental task, when optimiz**in**g the unit commitment problem, is to m**in**imizethe overall costs **of** the system. The overall costs are given by the stochastic objectivefunction C(e t i,h t i), where e t i and h t i refer to electricity and heat, mean**in**g that the total costdepends on both **of** these parameters when model**in**g **power** systems with co-generat**in**gunits (Ravn 2001). Here, the **in**dex values i and t denotes the particular unit and hour **of**operation, respectively.A fundamental part **of** optimiz**in**g the unit commitment problems is to perform l**in**earoptimizations **of** the total cost function C, subjected to a set **of** constra**in**ts that expressdifferent conditions or boundaries. In Figure 11.2, which presents this **in** a very simplifiedway, the optimal solution x and y **of** f(x,y) is found with**in** the convex solution spaceA by maximiz**in**g function f(x,y). When subjected to a constra**in**t function – an **in**equalityfor example – the optimal solution is to be found with**in** the convex solution space B **in**stead.The constra**in**ed solution therefore is the equilibrium **of** a series **of** restrictions.(Bregnbæk)The solution to a simple optimization problem can be found analytically by use **of** theLagrange Multipliers. As further constra**in**ts start complicat**in**g the problem, mathematicals**of**tware can usually solve this more easily through iterative processes.Constra**in**ed optimized solu-BAGlobal optimized solutionFigure 11.2, A pr**in**ciple sketch **of** the optimal solution. If the global optimized solutionhappens to be **in** A, then the solution found **in** B **in** this case represents the second bestoptimum. If not, the applied constra**in**t does not affect the outcome and the ‘system’ **in**balance.When it comes to f**in**d**in**g the optimal comb**in**ation **of** committed capacities, the methodused for mathematically committ**in**g and de-committ**in**g production capacities, is for eachtime step t to **in**troduce a set i **of** b**in**ary variables xi t = {0;1}, where xi t is a positive **in**tegerwith the property **of** assum**in**g the two values; zero and one. This way, capacity i iscommitted when xi = 1 and de-committed when zero. Figure 11.3 shows the pr**in**ciplehere.i \ t hoursunits 1 1 10 0 1Figure 11.3, the variables: time and units forms a T x N matrix (T be**in**g the optimizedperiod and N the number **of** units to commit (1) and de-commit (0), respectively.

176 AppendixThe key task then is to figure out an optimal comb**in**atorial solution **of** committed plants.Not just for the specific hour, but for the entire optimized period **of** operation as well,s**in**ce a number **of** parameters can **in**fluence the optimal comb**in**ation **of** committed capacitiesover time as a total. One **of** the big difficulties **of** optimiz**in**g these types **of** problemsis that the region **of** feasible solutions no longer is constra**in**ed by a series **of** l**in**earconstra**in**t functions alone, but additionally be**in**g subjected to a set **in**teger constra**in**ts,which ultimately results **in** a solution space that no longer is convex 36 (Wikipedia, L**in**earprogramm**in**g) (see Figure 11.4).yConstra**in**ed regionwith feasible solutionf(x,y)yxxFigure 11.4, As the graph to the left illustrates a convex solution area solvable byregular l**in**ear programm**in**g, the right illustrates a l**in**early **in**solvable concave (nonconvex)area which is usually produced when add**in**g b**in**ary constra**in**ts.Because the unit commitment problem **of**ten is mathematically stated as a comb**in**ation**of** rational (**of**ten positive) variables on one hand, and b**in**ary **in**teger variables on theother, which makes the optimization problem non-convex by hav**in**g multiple locally optimalpo**in**ts, a feasible solution can sometimes be found via Mixed Integer Programm**in**g(MIP). The methods **of** MIP can be described as f**in**d**in**g the best solution – l**in**ear or nonl**in**ear– **of** each possible 0–1 comb**in**ation. Characteristic for MIP programm**in**g is thegeneration **of** a number **of** sub-problems which are to be solved by an additional number**of** l**in**ear optimizations. However, one **of** the biggest problems with MIP is that as thenumber **of** possible 0-1 comb**in**ations **in**creases – so does the computations time andphysical memory required for the task – exponentially (GAMS 2007).Feasibility is yet another problem with this method. MIP problems have feasible solutionsif, and only if, the constra**in**t matrix on left hand side is fully unimodular as well asthe right-hand sides **of** the constra**in**t functions be**in**g **in**tegers (Wikipedia L**in**ear Programm**in**g).In practice, this means that the decision variables **of** stated unit commitmentproblem, this be**in**g e.g. the **power** generation **of** the units, never must be constra**in**edfrom assum**in**g zero.11.3.2. Solv**in**g the Unit Commitment ProblemIn the section above, the possibility **of** solv**in**g the unit commitment problem by MixedInteger Programm**in**g (MIP) was described. I this section some **of** the ma**in** procedures,connected to the MIP solv**in**g **of** the optimization problem def**in**ed **in** this project will bedescribed.36In the concave solution space, one can no longer l**in**early connect all po**in**ts with**in** the constra**in**t area(Eis**in**g 1999).

AppendixNomenclature 177It was previously mentioned that, given the available model**in**g tools used for thisproject, the solv**in**g process, which normally is considered a programm**in**g-heavy part,only will be expla**in**ed **in** pr**in**ciple **in** this project. This section will therefore be a more orless **in**tuitive and practical **in**troduction to the basic pr**in**ciples beh**in**d the methods usedby the solver applied for the optimization.Search**in**g, Branch**in**g and cutt**in**gAt first, when a solution space to the root problem is found by the solv**in**g algorithm to berestricted by **in**teger-constra**in**ts, and it thereby becomes concave, the root problem isdivided **in**to two sub problems from the 0-1 variable. This process proceeds, and eventually,as seen **in** Figure 11.5 below, a tree structure is produced, or branched, accord**in**gto the number **of** applied **in**teger constra**in**ts caus**in**g non-convex solution spaces. Thesearch only stops when until the optimal solution space emerges. Usually, the tree size**in**creases dramatically along with the applied number **of** time steps wanted for the simulation,but the exact scope **of** this varies a lot 37 .ROOT PROBLEMSub problemsgenerated due to**in**teger constra**in**tsA BNodesABApplied method choosesB, when A may safelybe disregarded from thesearch.No. **of** sub problems **in**creases as feasible solutionsareas are still **in**teger constra**in**ed (concave)No. **of** feasible solution outcomesdecreases as the branched tree is prunedFigure 11.5, Left: Branch**in**g - a tree structure emerges from the number **of** 0-1 variablesthat still constra**in** the solution space. Right: Cutt**in**g: the applied algorithm cuts waypossible solutions that safely can be disregarded from the search.Now, each possible path down along the nodes **of** the tree structure represents a l**in**ear(or non-l**in**ear) sub-problem to be optimized. The applied MIP algorithm first f**in**ds theglobal optimal solution **of** the root problem (via standard l**in**ear or non-l**in**ear optimizationmethods) by relax**in**g the **in**teger constra**in**ts (Solver 2009). When this is done, itchecks to see if one or more **in**teger variables have non-**in**tegral solutions (hence the concavesolution area), and if so, sub-problems A and B are created as shown above. Thesesub problems are then solved and the non-satisfy**in**g solutions are cut away. This procedurecont**in**ues until a solution satisfy**in**g all constra**in**ts are found. Sometimes the number**of** tree nodes becomes too comprehensive, and one would have to settle with a devia-37The complexity, and here**of** branched tree sizes, varies a lot from simulation to simulation. Sometimes,with a given set **of** **in**put data, one can be lucky to have a balanced optimization with fewer createdsub-problems.

178 Appendixtion given by the gap between best possible solution found and the overall optimal solution.The described optimization usually starts out with a heuristic search algorithm thatuses a Branch and Cut method. Branch**in**g, which means def**in****in**g the tree structure andcutt**in**g, to safely “cut” away the nodes not represent**in**g an optimal solution, and thusprune the solution outcome. It is **of**ten the case, that a s**in**gle MIT problem can generatea great amount **of** sub-problems, which quickly turns the model**in**g **in**to a compute **in**tensiveprocess that requires a great amount **of** physical memory as well (GAMS 2007).11.3.3. GAMS/CPLEXAs mentioned **in** chapter 5, the mathematical tools used **in** this project for solv**in**g theunit commitment problem is a comb**in**ation **of** the model**in**g language GAMS and theMIP solver Cplex, respectively. Regard**in**g the model language, GAMS operates **in** generalwith sets, **in**digenously and endogenously sizes which **in** normal terms best can be**in**terpret as **in**dexes, variables and scalar items, respectively. One **of** the greatest advantages**of** this particular tool, **in** connection with the current project, is that it from thebeg**in**n**in**g has build **in** different types **of** variables such as positive variables, **in**tegersand b**in**ary variables. Especially the use **of** positive variables is a factor that trims downthe programm**in**g language as well as heavy comput**in**g processes. Another advantage isthe rather easy use **of** tables and vectors **in** comb**in**ation between **in**dexes (for example(i,t)) and **in**put parameters (scalars).S**in**ce GAMS is mostly a programm**in**g language, the code is also used for “call**in**g” thespecific solver to perform the desired optimization. This way, GAMS translates thestated mathematical problem for the user **in**to the solver’s language. When it comes topick**in**g out an appropriate solver for a specific assignment a great selection **of** differenttools is presented - vary**in**g from simple l**in**ear programm**in**g-solvers (LP) to more advancedones. When choos**in**g the solver, it is important to carefully consider what particulartype **of** problem is to be optimized, avoid**in**g greater complexity than necessary 38 –especially s**in**ce the solvers more **of**ten than not are quite expensive (although GAMS asa tool is free **of** charge).The solver chosen for this project is Cplex, due to its efficient MIP optimiz**in**g, and thefact, that an academic s**of**tware license for Cplex already was available through the university.38Sometimes, a small simplification can mean the difference between a simple l**in**ear problem (LP), andan advanced non-l**in**ear (NLP) or a NLPEC, MPEC, MSNLP and so on.

AppendixNomenclature 17911.4. Optimal GAB sizes from GAMS/CPLEXIn this section further tables on the necessary limitation **of** the solv**in**g process given bythe solution gaps are presented.Solution Gaps on the modeledreference systemGABS 2008 2017 2025January 0 0 0.005February 0 0.02 0.005March 0 0 0.005April 0 0 0May 0.02 0.001 0.005June 0.015 0.03 0.005July 0.025 0.09 0.025August 0.025 0.02 0.015September 0.00015 0.01 0.005October 0.005 0.01 0.005November 0 0.01 0December 0 0 0.005Solution Gaps on the modeledbypass system (s**in**gle unit)GABS 2008 2017 2025January 0.75 1.41 1.32February 1.48 1.44 1.47March 1.29 1.42 1.47April 1.47 1.5 1.49May 1.33 1.49 1.45June 0.79 1.11 1.15July 1.26 1.05 1.20August 1.05 1.38 1.36September 0.86 1.45 1.23October 1.32 1.39 1.47November 1.47 1.47 1.41December 1.43 2.48 4.2211.1, Gap sizes restra**in****in**g the optimal solution **in** the reference and the bypass scenario.

180 Appendix11.5. The formulated GAMS modelIn this section the code for the formulated GAMS model is presented.11.5.1. Code for the formulated GAMS model for the Reference and bypass scenario

AppendixNomenclature 181

182 Appendix

AppendixNomenclature 183

184 Appendix11.5.2. Code for the formulated GAMS model for the heat pump scenario

AppendixNomenclature 185

186 Appendix

AppendixNomenclature 187

188 Appendix