etransport: investment planning in energy supply systems with
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doi:10.1016/j.en
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Energy 32 (2007) 1676–1689
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eTransport: Investment planning in energy supply systemswith multiple energy carriers
Bjorn H. Bakken�, Hans I. Skjelbred, Ove Wolfgang
Energy Systems, SINTEF Energy Research, Sem Saelands v. 11, NO 7465 Trondheim, Norway
Received 7 July 2006
Abstract
The need for local energy planning is not reduced after liberalization. Both integrated energy companies and local governments have to
consider alternative solutions across traditional supply and demand sectors and make plans for the total integrated energy infrastructure.
This situation has created a need for new improved methodologies and tools for system planning and operation that include multiple
energy carriers and sufficient topological details. In this paper, a novel optimisation model ‘eTransport’ is presented that takes into
account both the topology of multiple energy infrastructures and the technical and economic properties of different investment
alternatives. The model minimises total energy system cost (investments, operation and emissions) of meeting predefined energy demands
of electricity, gas, space heating and tap water heating within a geographical area over a given planning horizon, including alternative
supply infrastructures for multiple energy carriers. The model employs a nested optimisation, calculating both the optimal diurnal
operation of the energy system and the optimal expansion plan typically 20–30 years into the future. The model is tested on a number of
real case studies, and a full graphical user interface has been implemented. A sample case study is included to demonstrate the use of the
model.
r 2007 Elsevier Ltd. All rights reserved.
Keywords: Energy supply systems; Investments; Multiple energy carriers; Mixed integer programming; Dynamic programming
1. Introduction
The energy industry is currently in a transition periodwith large changes in both technology and organisation.Traditionally there has been considerable centralizedcontrol in the industry, where the prime concern has beento secure enough supply to meet the increasing demand.Different suppliers have been responsible for differenttypes of energy, e.g. electrical power, gas and fuel oil withindefined supply areas. The ongoing liberalization process ishowever gradually shifting the focus towards improvedcost-efficiency and profitability in the whole supply chain.This introduces the issue of possible competition betweendifferent energy carriers. It is likely that we will see morehorizontally integrated energy companies that supplyseveral different energy types in the future. Moreover,new emerging technologies like small-scale co-generation,
e front matter r 2007 Elsevier Ltd. All rights reserved.
ergy.2007.01.003
ing author. Tel.: +4773 59 74 45; fax: +4773 59 72 50.
ess: [email protected] (B.H. Bakken).
gas engines and fuel cells enable an increasing flexibility inenergy service systems. This will yield new alternatives andbetter possibilities to design a sustainable energy system,but such technologies will also result in more complexsystems to design, operate and maintain as they introducephysical connections between traditionally separate supplysectors.The need for energy planning is not reduced after
liberalization; more than ever is it of vital importance tokeep an overall system perspective during all stages ofplanning and operation. For example, a planner in anintegrated energy company will have to consider bothcomplementarities within his own company and competition
from other suppliers that may enter his traditional supplyarea in a liberalized market environment. Thus, bothintegrated energy suppliers and local governments mustconsider alternative solutions across traditional supply anddemand sectors and make plans for the total integratedenergy infrastructure. This situation has created a needfor new improved methodologies and tools for system
ARTICLE IN PRESS
Nomenclature
Parameters
Afkt constraint coefficients for component k intimestep t
bft restrictions on resources/capacities in timestep t
cElst electricity prices or generation cost in timestep t
at supply node s, USD/MWhcinv
d investment cost for investment d, USDd annual discount factor; d ¼ 1=ð1þ rÞ
ebe emission coefficient for emission type e fromboiler b, kg/MWh
ld lifetime of investment alternative d, yearsLij length of power line from i to j, kmLEl
lt electricity load at load node l in timestep t,MWh/h
ZBob boiler efficiency, %
PenEmbe emission penalty for emission type e from boiler
b, USD/kgPenEl electricity deficit penalty, USD/MWhpEl
lt price when selling back to the network at nodel, USD/MWh
r interest rate, p.u.Pstart the first year in the first timestep in the planning
periodPend the first year in the final timestep in the
planning periodPstep the number of years in each timestep in the
planning periodwz weight factor for length of segments, daysWmaxBo
b maximum heat output from boiler b, MWXk line reactance, O/km; kAEl_line_types
Variables
ckt operating cost of component k in timestep t,USD
Cp operating cost for different technologies, USD;pATechnologies
CopespB operating cost in a given state s, period p and
time segment z, USDcope
sp annual operating costs for state s in period p,USD
cinvp total investment cost (expenses) in period p,
USDC�p minimum net present value for period p
through ðPend þPstepÞ, USDDEl
lt X0 electricity deficit in timestep t, MWh/hDP(direction)ijt losses calculated for all lines where
power is flowing out from node i; 0 if powerflows into the node, MWh/h
EmitebtX0 amount of emission type e from boiler b intimestep t, kg/h
FBobt X0 fuel used by boiler b in timestep t, MWh/h
jit phase angle at node i in timestep t, radF rest value of investments, USDIdp binary variable that identifies investments.
Idp ¼ 1 if the investment dAD has been carriedout in period p, and Idp ¼ 0 otherwise.
Iscrapdp binary variable that identifies scrapping of
equipment. Iscrapdp ¼ 1 if the equipment from
project dAD has been scrapped in period p, and0 otherwise.
Load_flowijt energy flow from network node i to loadnode j in timestep t, MWh/h
Local_flowijt energy flow from supply node i to loadnode j in timestep t, MWh/h
Net2net_flowijt energy flow from network nodes i to j intimestep t, MWh/h
PElijt power flow from busbar i to j in timestep t;
negative if power flows from j to i, MWh/hPLd
ilt power flow in timestep t to load connected atnode i, MWh/h
PLocslt power flow in timestep t to load l directly
connected to supply s, MWh/hPN2N
nit power flow in timestep t from/to other networkmodels at node i (e.g. from local CHP model orto heatpump model), MWh/h
PSupsit power flow in timestep t from market or local
generator s (e.g. wind, hydro) connected atnode i, MWh/h
p identifier for investment periods given as firstyear in each period
Sp state identifier; SpAStates
SEllt X0 electricity sold at node l in timestep t, MWh/h
Supply_flowijt energy flow from supply node i tonetwork node j in timestep t, MWh/h
t index for timesteps (h) within operationalmodel, tATime_steps
t index for years within an investment period,tA{1,y,Pstep}
UElst use of electricity at supply point s in timestep t,
MWh/hW Bo
bt heat output from boiler b in timestep t, MWh/hxkt decision variable for component k in timestep t
ydp binary variable that identifies investment his-tory. ydp ¼ 1 if the investment d 2 D has beencarried out before or in period p, and ydp ¼ 0otherwise.
z index for load segments within a year
Sets
Boilers set of boilersD set of investment alternativesEl_busbars set of electricity busbars (nodes)El_line_types set of predefined and user specified line
typesEl_loads set of electricity loads
B.H. Bakken et al. / Energy 32 (2007) 1676–1689 1677
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El_markets set of electricity markets; El_marketsCEl_-
loads
El_power_lines set of power linesEmissions set of (predefined) emission types; Emis-
sions ¼ [CO2, CO, NOx, SOx]Load_points set of load and market nodesNet2load set to define connections between network
nodes and load nodesNet2net set to define connections between two different
networksNetwork_nodes set of network nodesPeriods set of investment periods
States set of system states (alternative system designs)Segments set of load levels within a yearSupply2load set to define direct connections between
supply nodes and load nodesSupply2net set to define connections between supply
nodes and network nodesSupply_points(El) set of supply points (for electricity)Technologies set of technology modules contributing to
the object function; Technolo-
gies ¼ [El_sup,El_load,Bo,y]Time_steps set of hours in the operating model,
typically [1,y, 24]
B.H. Bakken et al. / Energy 32 (2007) 1676–16891678
planning and operation that include multiple energycarriers and sufficient topological details.
In international literature, several approaches haveappeared the last years that integrate two or more energyinfrastructures in the analysis. Many of these focus on theintegrated operation of gas (fuel) and electricity networksfor optimal dispatch of generating units and/or pricing oftransmission capacity [1–6] or downstream optimisation ofelectricity and heat demand from cogeneration units [7,8].Some papers attack the optimisation of multiple energycarriers more generalised, incorporating electricity, gas,heat and hydrogen on the supply side as well as electricity,heating and cooling on the demand side [9–12]. TheGerman model Dynamic Energy Emission and CostOptimization (DEECO) is developed to optimise therational use of energy and utilisation of renewable energyin local energy systems [13–15]. None of these approaches,however, consider the issue of expansion/investmentplanning of such multiple infrastructures.
The area of optimal expansion planning in energysystems with multiple energy carriers is currently domi-nated by large-scale optimisation tools for regional orglobal system studies like MARKAL/TIMES, EFOM,MESSAGE and similar models [16–20]. In large-scaleenergy system studies of this kind, the energy system istypically represented with an aggregated type of modellingwith one energy balance per energy carrier, and withresources deployed on one side and end use extracted onthe other side. Various technologies are modelled withemissions and energy losses. This approach is usuallysufficient for energy system studies on a national orinternational level. In an improved optimisation approachfor expansion planning in local energy supply systems,however, different infrastructures within the geographicalarea of concern have to be identified. Geography, topologyand timing are all key elements in this approach. It is thusnot only a question of which resources and which amountsto use, but also where in the system the necessaryinvestments should take place and when investmentsshould be carried out.
The novel optimisation model ‘eTransport’ has beendeveloped to take into account both the topology andgeographic distance of multiple energy infrastructures, and
the technical and economic properties of differentinvestment alternatives. The model employs a nestedoptimisation, calculating both the optimal diurnal opera-tion of the complete energy system and the optimalexpansion plan typically 20–30 years into the future. Thismodel offers a systematic approach to meet the challengesof planning future energy supply systems with multipleenergy carriers.Section 2 gives a general overview of the eTransport
model. In Section 3, the structure of the operational modelis explained, while Section 4 presents electricity and boilermodules in detail as samples of the implemented metho-dology. Section 5 explains how the operating cost matrix isestablished as input to the investment model described inSection 6. In Section 7, the implemented graphical userinterface is presented. Section 8 elaborates model applica-tions, including a list of real case studies used in thedevelopment and testing of the model, while Section 9contains a sample case study to demonstrated the use of themodel. Section 10 contains the summary and Section 11 anexplanation of current and further work.
2. Model overview
The eTransport model minimises total energy systemcost of meeting predefined energy demands of electricity,space heating and tap water heating within a geographicalarea over a given planning horizon. The object functionincludes investment, operating and environmental costs.The model includes alternative supply infrastructures formultiple energy carriers: electricity, natural gas, liquidnatural gas (LNG), oil, biomass/waste and district heating.The novelty of eTransport is that all physical componentsand geographical topology for different energy infrastruc-tures are included in one single optimisation model forthe whole energy system within the given area. Geogra-phical details like transmission distances and alternativelocations are accounted for, and the competition betweendifferent energy types is implicitly handled by thealgorithm. The actual physical components in thestudied energy system and the energy flow between thesecomponents are modelled explicitly. The modular structureof the model makes it easy to add new components
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Table 1
Implemented technology modules
Energy sources Conversion/storage Transport Energy loads
� Electricity supply (RES-E)
� Gas supply
� Oil supply
� Waste supply
� Ambient heat
� Biomass supply
� Energy markets
� CHP plants
� Boilers
� AC/DC converter
� Warm water tanks
� Heat pumps
� LNG plants
� LNG re-gasification
� Storage
� Power plant w/emission flows
� Electric network
� District heating network
� Gas pipelines
� Discrete transport
� LNG ship
� Electricity loads
� Heat loads
� Warm tapwater loads
� Gas loads
� Dwellings (aggregated load model)
� Energy markets
� Gas market
Mass source Industrial technologies Mass transport Mass sinks
� Industrial CO2 source � CO2 capture plant
� CO2 liquefaction plant
� CO2 storage
� CO2 injection pump
� CO2 pipeline
� CO2 ship
� Industrial CO2 load
� Industrial CO2 market
Existing
system
Existing
system
OPERATIONAL MODEL
(LP/MIP)
/ Day / Season / Year
OPERATIONAL MODEL
(LP/MIP)
/ Day / Season / Year
OPERATIONAL MODEL
(LP/MIP)
/ Day / Season / Year
OPERATIONAL MODEL
(LP/MIP)PROJECTS
Retrofitting /
New projects
PROJECTS
Retrofitting /
New projects
PROJECTS
Retrofitting /
New projects
PROJECTS
Retrofitting/
New projects
INVESTMENT MODEL (DP)
Operation / Investment /
Environment
INVESTMENT MODEL (DP)
Operation/ Investment/
Environment
Range of
alternatives
Range of
alternatives
Hour/ Day/ Season/ Year
Fig. 1. General model structure.
B.H. Bakken et al. / Energy 32 (2007) 1676–1689 1679
and replace sub-models with improved versions in thefuture. Table 1 shows the modules that have beenimplemented so far.
eTransport is separated into an operational model
(energy system model) and an investment model, seeFig. 1. In the operational model, there are componentlibraries with sub-models for each energy carrier and forconversion components. The dataset for the particular casedefines the specific characteristics of the involved compo-nents. The operational planning horizon is relatively short(1–3 days) and the model solution finds the cost-minimisingoperation for a given infrastructure and for givenenergy loads.
The typical time-step in the operational model is 1 h, andthis is not feasible for investment analysis where theplanning period can be over 20 years. Therefore, theoperational analysis is separated from the investment
analysis, and annual operating costs for different energysystem designs are pre-calculated by solving the opera-tional model repeatedly for different seasons (e.g. peakload, low load, intermediate, etc.), periods (e.g. 5-yearintervals) and relevant system designs (States). Annualoperating and environmental costs for different periodsand energy system designs are sent to the investment model
that finds the investment plan that minimises the presentvalue of all costs over the planning horizon.
3. Operational model
The task for the operational model is to find theoperation of a given energy system that minimises thecosts of satisfying a predefined energy demand at differentlocations within the studied area. The system boundariesare implicitly defined by import and export of energy to themodelled system. The planning horizon is usually 24–72 hand the typical time-step is 1 h.The sub-models for different components are connected
by general energy flow variables that identify theflow between energy sources (Supply_points), networkcomponents for transport, conversion and storage(Network_nodes) and energy sinks like loads and markets(Load_points). The connections between supply points,network nodes and load points are case-specific, and theyare identified by sets of pairs where each pair shows apossible path for the energy flow between componenttypes:
Supply2net:
Set of pairs (i, j), where iASupply_pointsand jANetwork_nodes
Supply2load:
Set of pairs (i, j), where iASupply_pointsand jALoad_points
Net2net:
Set of pairs (i, j), where i, jANetwork_nodesNet2load:
Set of pairs (i, j), where iANetwork_nodesand jALoad_points.
ARTICLE IN PRESSB.H. Bakken et al. / Energy 32 (2007) 1676–16891680
General energy flow variables that are defined over the
energy system structure are used to account for the actualenergy flow between different components (except forinternal flow within the detailed network modules). Thesegeneral variables are included in and restricted by thevarious modules and they are the link between the differentmodules.Supply_flowijt:
Energy flow from i to j at t, where(i, j)ASupply2net and tATime_stepsLocal_flowijt:
Energy flow from i to j at t, where(i, j)ASupply2load and tATime_stepsNet2net_flowijt:
Energy flow from i to j at t, where(i, j)ANet2net and tATime_stepsLoad_flowijt:
Energy flow from i to j at t, where(i, j)ANet2load and tATime_steps.The modules are added together to form a single linearoptimisation problem where the objective function is thesum of the contributions from the different modules, andthe restrictions of the problem include all the restrictionsdefined in the modules
Cope ¼ minP
t
Pk
cktxkt;
subject toPk
Afktxktpbft; f ¼ 1; . . . ;m½ �; 8t;Pk
Afktxkt ¼ bft; f ¼ mþ 1; . . . ; n½ �; 8t:
(1)
Emissions are caused by a subset of components that arecurrently defined as emitting CO2, NOx, CO and SOx
(power plants/CHP, boilers, road/ship transport, etc.).Other environmental consequences can also be defined.Emissions are calculated for each module and accountedfor as separate results. When penalties (e.g. a CO2 tax) areintroduced by the user, the resulting costs are included inthe objective function in Eq. (1) and thus added to otheroperating costs.
4. Technology modules
It is not possible to document all the different technologymodules currently implemented in the model. In thefollowing, the electricity and boiler modules are documen-ted as a sample of the methodology used. All variables forenergy flow are expressed in (MWh/h).
4.1. Electricity modules
The implemented electricity modules include electricitysupply, electricity network and electricity loads andmarkets.
4.1.1. Electricity supply
The sub-model for the supply of electricity to the definedenergy system will typically be a power line that enters thearea of study or local generation within the area (hydro,
wind, etc.). The cost of using electricity is given by
CEl_sup ¼X
t2Time_steps
Xs2Supply_pointsðElÞ
cElst UEl
st
!. (2)
The electric energy UElst taken from a given supply point
can either be fed to network nodes or used by a loadconnected directly to the supply. The energy balance forelectricity supply points is
UElst ¼
Xi:ðs;iÞ2Supply2net
PSupsit þ
Xl:ðs;lÞ2Supply2load
PLocslt
8s 2 Supply_pointsðElÞ; t 2 Time_steps. ð3Þ
Similar expressions are defined for other supply modelsfor gas, fuel oil, waste, biomass, etc.
4.1.2. Electricity network
The electricity network is implemented as a direct-current (DC) power flow. Thus, each line or cable isrepresented by its reactance, while the resistance isneglected. The voltage is the same in all nodes and thephase angle determines the load flow. Under thesesimplifications, only active power is flowing in the network
PElijt ¼
jit � jjt
X k � Lij
,
8ði; jÞ 2 El_power_lines; t 2 Time_steps. ð4Þ
The power flow in each line PElijt is restricted by maximum
current specific to the line type used. Incremental losses arecalculated by splitting the power flow into several linearsegments.The amount of energy that goes into a network node
equals the amount of energy that leaves it. The powerbalance equation for electricity node (busbar) i is given byXj:ðj;iÞ2El_power_lines
PEljit þ
Xs:ðs;iÞ2Supply2net
PSupsit þ
Xn:ðn;iÞ2Net2net
PN2Nnit
¼X
j:ði;jÞ2El_power_lines
PElijt þ
Xn:ði;nÞ2Net2net
PN2Nint
þX
l:ði;lÞ2Net2load
PLdilt þ
Xj:ðj;iÞ2El_power_lines
DPðbackÞjit
þX
j:ði;jÞ2El_power_lines
DPðoutÞijt,
8i 2 El_busbars; t 2 Time_steps. ð5Þ
There are no direct costs associated with an electricitynetwork module
CEl_net ¼ 0. (6)
The cost of losses is implicitly accounted for through thesupply costs. If losses increase, the amount of energy that istaken from the energy source(s) has to be increased in orderto supply the same amount of energy to the end-users.
4.1.3. Electricity loads and markets
The module for electricity loads includes variables forlocal consumption, possible sales back to the network and
ARTICLE IN PRESSB.H. Bakken et al. / Energy 32 (2007) 1676–1689 1681
possible energy deficit. The energy deficit variable isexplicitly accounted for since it has relevance for thesolution. The electricity balance in load point l isgiven byXi:ði;lÞ2Net2load
PLdilt þ
Xi:ði;lÞ2Supply2load
PLocilt ¼ LEl
lt þ SEllt �DEl
lt ,
8l 2 El_loads; t 2 Time_steps. ð7Þ
The operating cost for electricity loads consists ofpossible penalty for electricity deficit minus income fromsales back to the network
CEl_load ¼X
t2Time_steps
PenElX
l2El_loads
DEllt �
Xl2El_markets
pEllt SEl
lt
" #.
(8)
If electricity is traded back and forth in a common spotmarket, pEl
lt ¼ cElst . On the other hand, if an independent
power producer is selling electricity back to the networkowner with an infeed tariff on top of the spot market price,pEl
lt acElst .
4.2. Boilers
Boilers convert energy from electricity or fuels to heat.A heat central in a district heating network may consist ofone or more boilers. The efficiency defines the energy lossand is component specific. The heat production for a boileris given by
W Bobt ¼ ZBo
b F Bobt , (9)
where
W Bobt pW max Bo
b ,
8b 2 Boilers; t 2 Time_steps. ð10Þ
Each conversion technology is defined as networkelements, thus both the input and the output node of theboiler belongs to the set Network_nodes. In case the boilerfuel is taken directly from a supply node (e.g. gas source),the input node of the boiler is included in the setSupply2net. If the fuel is taken from another networkelement (e.g. gas pipeline or electricity busbar), the inputnode belongs to the set Net2net. Similarly, the output nodebelongs to Net2load if the heat is delivered directly to aload node, and to Net2net if the boiler is delivering to adistrict heating network.
The boilers’ fuel consumption is not directly included inthe object function, since this is accounted for in the importof fuel to the system. However, when emission penalties aredefined the boilers will give a specific contribution to thesystem cost:
CBo ¼X
t2Time_steps
Xb2Boilers
Xe2Emissions
PenEmbe Emitebt, (11)
where
Emitebt ¼ �beFBobt
8e 2 Emissions; b 2 Boilers; t 2 Time_steps. ð12Þ
5. Operating cost matrix
Fig. 2 shows the flowchart for the algorithm that is usedto calculate the matrix of annual operating cost. Thealgorithm starts in a given State s (e.g. present layout of thesystem), Period p and Segment z in the analysis.A State is defined as a given design of the energy system
under consideration. Periods are identified by a user-defined list of years. If the years 2010, 2015, 2020 and2025 are included in the list, the periods 2010–2014,2015–2019 and 2020–2024 will be analysed, respectively.In the investment model (Section 7), the followingparameters will then be used: Pstart ¼ 2010, Pend ¼ 2020and Pstep ¼ 5. The periods do not have to be uniform inlength, though. Pstep will be declared as a variable if theuser specifies years with varying intervals. Several para-meters can change from one period to the next, inparticular loads and prices. It is also possible that someof the infrastructure that existed in the beginning of theplanning period will be scrapped during a given period, andthis is defined by the user. Similarly, the user can alsospecify new infrastructure that must be introduced in acertain period.A Segment represents a given period within a calendar
year. The segments can represent different seasons(Summer, Winter, Spring, Autumn), but also specialperiods like weekends or work days. It is up to the userto specify the set of segments to be analysed. Pricesand loads will typically be different for the differentsegments, and the user must define the number of daysrepresented by each segment. The specification of segmentscan also be used to handle stochastic variation withina year. If for instance the user wants two stochasticoutcomes (with equal probability) for a season of 30 days,two segments with a length of 15 days (0.5� 30) each arespecified. In this case, the calculated annual operatingcost will be the expected annual operating costs. It isalso possible to represent stochastic variation betweendifferent years within the same period by defining severalsegments.When the first State s, Period p and Segment z have
been selected, the operational model is solved to minimisethe hourly operating costs for all technologies in themodel
CopespB ¼
Xp2Technologies
Cp,
8s 2 States; p 2 Periods; B 2 Segments. ð13Þ
If more than one segment has been defined the modelwill go to the next segment and update load profiles, etc.,and then the operational model is solved again. When the
ARTICLE IN PRESS
Fig. 2. Flow chart for calculation of operating cost.
B.H. Bakken et al. / Energy 32 (2007) 1676–16891682
operational model has been solved for all segments withinthe year, the annual operating costs cope
sp are calculated asthe sum of the daily operating costs multiplied withweighing factor wz for the number of days represented bythe respective segments as defined in Eq. (14). This annualoperating cost is assumed equal for all Pstep years within agiven period.
Copesp ¼
XB2Segments
CopespBwB,
8s 2 States; p 2 Periods. ð14Þ
The model continues to the next period (i.e. the next stepin the planning period identified by the first year p in thatstep) and updates loads and prices. Possible scrapping ofinitial infrastructure is taken into account. The operationalmodel is solved for the first segment in the new period, thenfor the second segment etc so that annual operating costscan be calculated for the second period. Finally, this
procedure is repeated for all states sAStates (alternativesystem designs).
6. Investment model
The task for the investment model is to find the optimalset of investments during the period of analysis, based oninvestment costs for different projects and the pre-calculated annual operating costs for different periodsand states. The optimal investment plan is defined as theplan that minimises the discounted present value of allcosts in the planning period, i.e. operating costs plusinvestment costs minus the rest value of investments. Theoptimal plan will therefore identify the optimal design ofthe energy system (i.e. the optimal state) in differentperiods. The optimisation problem for operational analysisis formulated as a mixed integer linear programmingproblem solved with the COIN solver [21], while the
ARTICLE IN PRESSB.H. Bakken et al. / Energy 32 (2007) 1676–1689 1683
investment model is formulated as a dynamic programmingalgorithm implemented in C++.
6.1. Definition of states
The user defines a set of investment alternatives that isrepresented by the set D, where each investment alternativetypically consists of several physical components withpredefined connections to the rest of the energy system.The same components can be included in several competinginvestment alternatives, making the different alternativesmutually exclusive from an economic point of view.Mutually exclusive alternatives can be identified exogen-ously by the user, but this is not necessary since the modelwill detect these in the search for the best expansion plan.Investment alternatives may also include scrapping ofexisting components since it can be profitable to replaceexisting components with newer and more efficient units.Scrapping will also occur when the planning period exceedsthe lifetime of a component.
Let the variable y1 be 1 if the first investment in D iscarried out (and this investment has not been scrapped yet)and let y1 be zero otherwise. Let the variable y2 be 1 if thesecond investment in D is carried out (and this investmenthas not been scrapped yet), and let y2 be zero otherwise,etc. Any unique set of investments that has been carried outbefore or in period p can now be identified by the value ofSp in
Sp ¼Xðy1p þ 2y2p þ 4y3p þ � � � þ 2n�1ynpÞ
¼Xd2D
2ordðdÞ�1ydp, ð15Þ
where
ydp ¼Xp
g¼Pstart
Idg � Iscrapdg
� �,
8p 2 Periods; d 2 D ð16Þ
and n is the number of elements in the set D. For example,if Sp ¼ 9 the first and the fourth investments in D havebeen carried out. Since the logic of the binary numbersystem has been utilised in Eq. (15) there is no othercombination of alternatives that gives Sp ¼ 9. If noinvestments are carried out then Sp ¼ 0, and if allinvestment are carried out then Sp ¼ 2n
�1.The set States is now defined to be the set of all possible
combinations of the elements in D, and the combinationsare represented by their corresponding Sp values fromEq. (15) so that
States ¼ 0; 1; 2; 3; . . . ; 2n � 1f g. (17)
Each element in this set represents a unique combinationof investment alternatives; they are the subsets of D. If noinvestment has been carried out, the energy system is inState 0; if the first alternative in D is realized, y1 will be 1and the energy system changes to State 1, and theinfrastructure of the energy system is updated in accor-
dance with the components that are specified for thatinvestment, etc.It is important to note that the user of the model
only has to specify investment alternatives and not allpossible energy system design alternatives prior to theoptimisation. If n investment alternatives are defined by theuser the model must in principle account for 2n differentstates. This can give long computational times if manyinvestment alternatives have been defined. However, manystates are usually irrelevant combinations that can beskipped. The computational time can be significantlyreduced if the user specifies the following type ofinformation:
�
Mutually exclusive alternatives: any pair of investmentalternatives are assumed to be mutually exclusive unlessthe user specifies that they are not. � Time window for investments: a first and a final relevantyear for each investment alternative.
� Dependent alternatives: some alternatives are relevantonly if some other alternatives also are carried out. Forinstance, a district heating network is relevant only if aheat central is also included (e.g. one of the twocompeting alternatives ‘‘boiler’’ and ‘‘CHP’’). Severalsets of dependent alternatives can be specified for eachinvestment.
� Necessary alternatives: a set of investment alternativeswhere at least one of the alternatives must be carried outwithin a specified year. Several sets for necessaryalternatives can be defined for each year.
6.2. Dynamic programming formulation
The dynamic programming formulation of the invest-ment model is given in Eqs. (18)–(21).
C�p Spð Þ ¼ min dp�Pstart
Xt2 1;...;Pstepf g
dt�1copeSp ;p þ
Xd2D
cinvd Idp
0@
1A
8<:
�dPendþPstep�PstartFþ C�pþ1 Spþ1ð Þ
9=;
8p 2 Periods, ð18Þ
where
Spþ1 ¼ Sp þXd2D
2ordðdÞ�1 Idp � Iscrapdp
� �, (19)
F ¼X
p2 Pstart;Pend½ �
Xd2D
cinvd Idp max 0; 1�
Pend � pþPstep
ld
� �,
(20)
C�Pendþ1¼ 0, (21)
SPstart¼ 0. (22)
ARTICLE IN PRESSB.H. Bakken et al. / Energy 32 (2007) 1676–16891684
The solution of Eqs. (18)–(22) subject to all theconstraints in the problem gives an investment plan thatminimises the discounted present value of all costs minusthe scrap value of new investments. The operating costsc
opeSp;p from Eq. (14) are annual values and they are assumedconstant for the Pstep years within a given period.
The investment cost for period p is given by
cinvp ¼
Xd2D
cinvd Idp,
8p 2 Periods, ð23Þ
where cinvd is the investment cost for project d specified by the
user. If for instance investments u and v are carried out inperiod p, then Iup ¼ Ivp ¼ 1, and cinv
p ¼ cinvu þ cinv
v . As asimplification, all components included in a specific invest-ment alternative d are assumed to have the same lifetime ld
where dAD. With a linear depreciation of investments thescrapping value at the end of the planning horizon is givenby F in Eq. (20). The investment cost for the initialinfrastructure that exists in the beginning of the planningperiod is sunk cost, however, so the end value of thisinfrastructure does not have to be accounted for in Eq. (18).
The dynamic programming algorithm iterates back-wards through all periods investigating all possible statesin each period. When all states in all periods areinvestigated, the expansion plan resulting in the lowest
Pan & Zoom window
'Drag & drop'
component
library
Fig. 3. User interface o
net present value is found. To find the second bestexpansion plan the algorithm defines the state in the lastperiod of the best plan as infeasible and runs the scriptagain with this new limitation. This process is repeated asmany times as specified by the user to generate a ranked listof alternative expansion plans. The following informationis provided for each expansion plan on the ranking list:
�
f eT
investments that are carried out in different periods;
� net present value of all costs; � annual operating costs for different periods; � investment costs for different periods; � emissions of different types.7. Graphical user interface (GUI)
To increase the user value of the model for current andfuture industrial partners and other users, a GUI isimplemented in MS Visio as shown in Fig. 3. It consistsof three main parts: The Component Library to the left, themain Drawing Area, and the Operation and Investment
Analysis Window at the bottom of the screen. Variousinvestment alternatives are ranked according to total costat the bottom right. As several components can be includedin one investment alternative, the list is formatted as adirectory tree. There is a link between this tree structure
Energy system
drawing
Operation and
investment analysis
ransport model.
ARTICLE IN PRESSB.H. Bakken et al. / Energy 32 (2007) 1676–1689 1685
and the Drawing Area such that clicking on one alternativeor component will highlight the respective component(s) inthe Drawing Area, making it easier to identify specificcomponents in a large energy system.
Both standard parameters embedded in the librarycomponents and case specific parameters entered by theuser are stored in an MS Access database linked to theGUI. When complete case data are input, the problem isexported to the COIN solver which performs the optimisa-tion. The results are returned to the database and displayedin the Result Window.
8. Model applications
Main applications of the eTransport model includeexpansion planning in local energy systems, optimisationof construction and operation of new DG plants subject tomultiple infrastructures as well as evaluation of up-streaminfrastructure for fuels (including truck, train and ship).The model identifies mutual influence and dependencebetween different energy systems, and can be used as ascenario tool to evaluate ‘‘threats’’ from other DER andsuppliers in the same area. The GUI is designed to enablean improved visualisation and communication of conclu-sions of complex problems.
The development of the eTransport model (2000–2006)has been organised around case studies submitted by theindustrial sponsors. For each case study new componentmodules and new functionality was implemented in themodel. During the course of the project the following casestudies have been made:
2002:
� Operation of district heating network with waste fuelledCHP [22].
2003:
� Municipal energy survey.� Operation of gas fuelled CHP and district heating
network as alternative to electricity grid expansion [23].� Operation of large-scale district heating network with
multiple fuels.
2004:
� Operation of district heating network with biomassfuelled CHP, incl. transport logistics of biomass.� Planning of gas pipeline, LNG ships or HVDC for bulk
transport of energy. This study was made both to verifythe operational model on large-scale energyinfrastructure and to test the first version of theinvestment model.
2005:
� Planning of local gas distribution versus district heatingnetwork.
� Optimal size of gas-fired CCGT with CO2 capture atindustrial site.� Expansion of existing district heating network with heat
pumps and biomass boiler; the biggest case tested so farwith more than 600 components in the network.
2006:
� Joint optimisation of bulk infrastructures for gas,electricity and CO2 in Norway; major extension of themodel by including mass flow of CO2.� Planning of alternative supply of electricity, gas or
district heating to residential and commercial areas [24].
Only a couple of these case studies are publishedinternationally, but further information about them isavailable in the open project report [25].
9. Case study
9.1. Case overview
To demonstrate the use of the eTransport model, asimplified version of the latest case study from a newdevelopment area in a Norwegian municipality is chosen[24,26]. The area of analysis is limited to a developmentarea outside the main city where 2–300 detached homes areexpected to be built over the next 30 years. The supply ofenergy to the rest of the municipality, including industrialgas demand, is omitted here to emphasize operating andinvestment costs directly related to the new area. Theperiod of analysis is set to 25 years (2008–2032), split intofive 5-year periods. Each year is further split into 3 loadsegments: peak load (29 days), intermediate load (243 days)and low load (93 days). The construction of new houses isassumed to happen at an even rate of 50 per 5 years,starting in 2013. Electricity demand in the area is assumedto increase with 1.2% per year throughout the analysis.
9.2. Technical alternatives
The different alternatives for energy supply are:(a) electric boilers, (b) ground source heat pumps, (c) gasboilers and (d) hydrogen/FC solution with electrolyser andwind power. Rather than using screen dumps like in Fig. 3,Figs. 4a–d show only the principal layout of the differentdesigns, omitting details of the specific networks. Addi-tional cases from the original study [24] including gas-firedCHP and district heating networks for a larger part of themunicipality are omitted for simplicity. There is noelectricity generation within the area, so all electricity isassumed to be purchased at the Nordic Elspot market.External electricity supply cost is in all cases assumed astypical Norwegian market prices for peak load, intermedi-ate load and low load, respectively.In alternative (a), electric boilers are used for space and
tap water heating (Fig. 4a). In the model 3 aggregated
ARTICLE IN PRESS
EL_SUP
EL_LOAD_MAIN
EL_LOAD_NEW
HEAT_LOAD_NEW
Electricity
Hot water
BOILER
EL_SUP
EL_LOAD_MAIN
EL_LOAD_NEW
HEAT_LOAD_NEW
KEROSENE
Electricity
Kerosene
Hot water
GS_HEAT
BOILER
HEATPUMP
STOR
EL_SUP
EL_LOAD_MAIN
EL_LOAD_NEW
HEAT_LOAD_NEW
GAS_SUP
Electricity
Natural gas
Hot water
BOILER STOR
EL_SUP
EL_LOAD_MAIN
EL_LOAD_NEW
HEAT_LOAD_NEWWIND ELECTR. STOR
Electricity
Hot water
Hydrogen
FC
STOR
KEROSENE BOILER
Kerosene
a b
c d
EL_NETWEL_NETW
E L_NETWE L_NETW
EL_NETWEL_NETW
EL_NETWEL_NETW
Fig. 4. (a) Energy supply with electric boilers, (b) energy supply with heat pumps, (c) energy supply with gas boilers, (d) energy supply with RES and
hydrogen.
B.H. Bakken et al. / Energy 32 (2007) 1676–16891686
boilers of 100, 100 and 150 kW are used; but in reality anumber of smaller units would be installed. The efficiencyof the boilers is set to 90%. The model has the choice toinstall the boilers one by one during the period of analysis(in 2013, 2018 and 2023, respectively).
In alternative (b), large-scale ground source heat pumpsof 50 kW each are installed in a heat central (Fig. 4b).When using heat pumps one needs to consider whether touse them solely for space heating or for both space and tapwater heating. In the latter case, the output temperature ofthe heat pumps has to be higher, reducing overallefficiency. In this study, we assume an ambient heat sourceof 5 1C and an output water temperature of 65 1C.Assuming a thermal efficiency of 60% yields an annualheat factor of 3.4. Also in this alternative the model isallowed to install 3 such heat pumps during the period ofanalysis (in 2013, 2018 and 2023). Heat pumps aregenerally not dimensioned to cover all heat demand so a50 kW kerosene boiler is installed together with each heatpump to cover the peak load. The efficiency of the keroseneboilers is set to 80%. Hot water storage of 150 kWhcapacity is also included to level out diurnal variations inthe heat load.
In alternative (c), the heat pumps and kerosene boilersin the heat central are replaced by gas fuelled boilers(Fig. 4c). In this alternative, the model is allowed to installthree boilers of 100 kW rating in 2013, 2018 and 2023,supplying hot water for both space and tap waterheating. Efficiency of the gas boilers is set to 90%. Thehot water storage of 150 kWh capacity is also included. Gassupply is assumed to be handled by road transport, andis not included in this study. The original study [24]also includes a solution with gas distribution throughpipelines.
In alternative (d), a 750 kW wind turbine separate fromthe power grid supplies electricity directly to an electrolyserfor production of hydrogen that is fed into a genericstorage module (Fig. 4d). An aggregated fuel cell module of175 kWe supplies electricity to the grid and heat to a hotwater storage for domestic use. Both the electricity andheat recovery efficiency of the fuel cell are set to 35% [27].In this case a 150 kW kerosene boiler is added to cover thepeak load. This alternative is not very realistic in thepresent situation, but is added to the case to test theconcept in comparison with the more conventionalsolutions.The hydronic heat distribution systems within the
buildings are assumed the same in all alternatives. This isnot entirely correct, however, as some differences might berequired in the technical solutions due to storage options,temperature differences between the various sources, etc.The investment costs of the different alternatives are
calculated as shown in Table 2. The cost of kerosene isset to 0.42USD/litre (43.14USD/MWh) and natural gasto 0.31USD/Sm3 (29.58USD/MWh). Elspot market
prices for 2006 including transmission tariffs are used forelectricity imported to the area in the first period.The diurnal variation is between a minimum of57.42USD/MWh at low load night and a maximum of74.16USD/MWh at peak load day. It is assumed thatenvironmental taxes and costs of emission certificates arealready included in the Elspot market prices, so no specificemissions are related to the import of electricity. Duringthe period of analysis a flat 1% per year increase in theprices is assumed. In reality, Nordic Elspot prices mighthave large variations from year to year due to variations inhydropower availability, but this is not reflected in thepresent study.
ARTICLE IN PRESS
Table 2
Investment costs
Total (1000USD)
Alt. (a) Electrical boilers (distributed) 460
� 2300USD� 200 houses
Alt (b) Heat pumps (centralized) 720
� Heat central: 3� (50+50) kW� 861USD/kW
� Distribution: 1500m� 308USD/m
Alt (c) Gas boiler (centralized) 646
� Heat central: (3� 100) kW� 615USD/kW
� Distribution: 1500m� 308USD/m
Alt (d) Wind/hydrogen 3220
� Wind turbine: 750 kW� 1230USD/kW
� Electrolyser: 750 kW� 2090USD/kW
� Hydrogen storage: 24 kg� 517USD/kg
� Fuel cell (PEM): 175 kW� 3700USD/kW
� Kerosene boiler: 150 kW� 461USD/kW
Table 3
Ranking of investments
Year Annuity (1000USD/year)
1. Ground source heat pumps 2013 1260
2018
2023
2. Gas boilers 2013 1263
2018
2023
3. Electrical boilers 2013 1269
2018
2023
4. Hydrogen FC with wind power 2013 1318
B.H. Bakken et al. / Energy 32 (2007) 1676–1689 1687
9.3. Ranking of investments
With numerical assumptions as presented above, and adiscount rate of 5%, the resulting ranking of thealternatives is given in Table 3 where the annuity is givenas the sum of operating and investment costs. Sinceoperating cost during the 25 years dominates the costs,there are relatively small differences between the annuitiesof the alternatives.
The best alternative is to install heat pumps with peakload kerosene boilers in 2013, 2018 and 2023, respectively.The gas boilers come in second place, while increasedoperating cost puts the electrical boilers as third alter-native. Due to the high investment cost, the hydrogenalternative is the last one in the ranking. Even though thedifference between the annuities in Table 2 seems rathersmall, the gas price must be reduced by more than 25%before the gas boiler alternative becomes the most cost-effective one.
9.4. System operation
As shown in Fig. 2, the model optimises the operationof the system hour-by-hour in all load segments andyears to calculate annual operating costs. This makes itpossible to study the diurnal behaviour of the systemfor each configuration alternative and load level. Withthe technical alternatives shown above, a number ofdetails regarding the operation of the various designs canbe analysed in the model. All variables can be displayed inthe analysis window of the user interface. In this paper,selected results are presented by Excel graphs ratherthan using screen dumps to increase the readability ofthe paper.
Fig. 5a shows the diurnal operation of heat pumps,kerosene boiler and storage during peak load in 2013when the first 50 houses are constructed. The boiler isnot used during intermediate and low load level in thisperiod. Jumping to peak load 2028 in Fig. 5b, all threeheat pumps are constantly in operation during most of theday, and the kerosene boilers are also run for longerperiods at rated capacity 3� 50 kW. The boilers are usedat all load levels, indicating that the heat pumps areunder-dimensioned for this period. Looking at the alter-native with gas boilers at peak load 2028 in Fig. 5c, wefind that the boilers are used in merit order to cover theheat demand. The operation of the electrical boilers is notshown here, as they merely keep track of the diurnalvariations in the load. Fig. 5d shows the operation ofthe wind/hydrogen alternative at peak load 2028. Theelectrolyser is operating at constant level, feeding theintermediate hydrogen storage. The fuel cell is alsooperating mostly at rated level, with the boiler coveringthe peak load during morning and afternoon. Compared tothe heat pump alternative in Fig. 5b, also here the boilersare needed most of the day during peak load. During lowload periods the fuel cell sells surplus electricity to thespot market.
9.5. Emissions
Fig. 6 shows the CO2 emissions from the fouralternatives (similar graphs can be shown also for CO,NOx and SOx emissions). Naturally, the alternative withgas boilers dominates the picture, but the use of keroseneboilers to cover peak load causes emissions also from theheat pump and wind/hydrogen alternatives. Especially inthe last period (2028–2032) the emissions from the heatpump alternative increases dramatically to 45,600 kg/year.The reason for this can be seen directly from Fig. 5b: theheat pumps are not able to cover the load in the last periodand the kerosene boilers have to run most of the time.Installing a fourth heat pump in 2028 would mitigate thisproblem.
ARTICLE IN PRESS
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
1 3 5 7 9 11 13 15 17 19 21 23
Hours
Heat
(MW
h/h
)
Heat load
Boiler output
HeatPump output
Heat storage
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
1 3 5 7 9 11 13 15 17 19 21 23
Hours
Heat
(MW
h/h
) Heat load
Net Boiler output
Net HP output
Heat storage
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
1 3 5 7 9 11 13 15 17 19 21 23
Hours
Heat
(MW
h/h
)
Heat load
Gas Boiler 3
Gas Boiler 2
Gas Boiler 1
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
1 3 5 7 9 11 13 15 17 19 21 23
Hours
MW
h/h
Heat load
Boiler output
Electrolyser
FC heat output
a b
c d
Fig. 5. (a) Operation of first heat pump and boiler at peak load level 2013, (b) operation of heat pumps and boilers at peak load level 2028, (c) operation of
gas boilers at peak load level 2028, (d) operation of electrolyser, FC and boiler at peak load level 2028.
0
50 000
100 000
150 000
200 000
250 000
300 000
350 000
2008-
2012
2013-
2017
2018-
2022
2023-
2027
2028-
2032
Year
CO
2 (
kg
/ye
ar) 1. Heat pumps
2. Gas boilers
3. El. boilers
4. Wind/Hy
Fig. 6. CO2 emissions for the different alternatives.
B.H. Bakken et al. / Energy 32 (2007) 1676–16891688
10. Summary
This paper has presented a novel optimisation model‘eTransport’ for expansion planning in local energy supplysystems with multiple energy carriers. The model minimisesenergy system costs (investments, operation and emissions)of meeting predefined energy demands of electricity, spaceheating and tap water heating within a geographical areaover a given planning horizon, including supply infra-structures for electricity, natural gas, LNG, oil, biomass,waste and district heating. Many topographical details canbe accounted for, and this makes the model especiallyappropriate for local energy planning e.g. in municipalitiesor cities. The model offers a systematic approach to meetthe challenges of planning future energy supply systemswith competition between multiple energy carriers. The
current version finds the best solution(s) from on a user-defined set of investment alternatives. In the future,functionality to enable the model to optimise the size ofspecific components should be included.The model currently employs a nested optimisation of
mixed integer programming and dynamic programming,calculating both the optimal diurnal operation of thecomplete energy system and the optimal expansion plantypically 20–30 years into the future. In the next version,stochastic optimisation will be implemented to handleuncertainties in energy prices, demand and investments.A full graphical user interface is also developed to increasethe user friendliness of the model.The main user group for the eTransport model are
decision makers involved in planning of local energyservice systems including new DG plants. The model isalso useful for local authorities (e.g. municipalities) thatneed to analyse the local energy system because they havesome authority with respect to concessions and/or energyplanning. It is also useful for utilities that do regionalenergy studies, including large energy suppliers that mustfind the least-cost option for their supply. Governmentalagencies that give investment subsidies on basis of socio-economic efficiency can also use the model to analyse theeffects of the support.
11. Further work
There are currently a number of research activitiesrelated to the further development of the eTransportmodel. These include both addition of new technology
ARTICLE IN PRESSB.H. Bakken et al. / Energy 32 (2007) 1676–1689 1689
modules and improved decision support algorithms. In thefirst category, work is underway to develop modules forcooling/low-temperature systems and biomass/biofuelstransport and conversion processes. In the latter category,the first step will be to implement stochastic optimisationto enable handling of uncertainties. For future develop-ments, also algorithms for LCA [28] and multi-criteriadecision-making algorithms [29] are under consideration.Further improvement of the graphical user interface is alsoincluded in the continuation of the work. Several M.Sc.and Ph.D. students at the Norwegian University of Scienceand Technology (NTNU) are involved in these activities.
Acknowledgements
The authors gratefully acknowledge the support fromthe Research Council of Norway and from the industrialsponsors of the project.
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