Energy Systems manuscript No.(will be inserted by the editor)

Multiobjective evolutionary algorithm for long-termplanning of the national energy and transportationsystems

Eduardo Ibanez · James D. McCalley

Received: date / Accepted: date

Abstract The transportation and electric sectors are by far the largest pro-ducers of greenhouse emissions in the United States while they consume asignificant amount of the national energy. The ever rising demand for thesesystems, the growing public concern on issues like global warming or nationalsecurity, along with emerging technologies that promise great synergies be-tween both (plug-in hybrid vehicles or electrified rail), creates the necessity fora new framework for long-term planning. This paper presents a comprehen-sive methodology to investigate long-term investment portfolios of these twoinfrastructures and their interdependencies. Its multiobjective nature, basedon the NSGA-II evolutionary algorithm, assures the discovery of the Paretofront of solutions in terms of cost, sustainability and resiliency. The optimiza-tion is driven by a cost-minimization network flow program which is modifiedin order to explore the solution space. The modular design enables the useof metrics to evaluate sustainability and resiliency and better characterize theobjectives that the systems must meet. An index is presented to robustly meetlong-term emission reduction goals. An example of a high level representationof the continental United States through 2050 is presented and analyzed usingthe present methodology.

Keywords Energy · Transportation · Long-term investment · Multiobjectiveoptimization · Evolutionary programming

This work was supported in part by the U.S. National Science Foundation under Award0835989.

E. Ibanez · J. McCalleyDepartment of Electrical and Computer Engineering, Iowa State University, Ames, Iowa,50011, USAE-mail: eibanez@iastate.edu, jdm@iastate.edu

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1 Introduction

Most US energy usage is for electricity production and vehicle transportation,two interdependent infrastructures. The strength and number of the inter-dependencies will increase rapidly as hybrid electric transportation systems,including plug-in hybrid electric vehicles and hybrid electric trains, becomemore prominent. There are several new energy supply technologies reachingmaturity, accelerated by public concern over global warming. The U.S. En-ergy Information Administration [24] suggests that national expenditures onelectric energy and transportation fuels over the next 20 years will exceed $14trillion, four times the 2010 federal budget [27]. Additionally in 2008, electric-ity generation and transportation accounted for almost 60% of US greenhouseemissions[26]. Intentional and strategic energy system design at the nationallevel will have very large economic and environmental impact.

The proposed work is motivated by a recognition that tools, knowledge,and perspective are lacking to design a national system integrating energy andtransportation infrastructures while accounting for interdependencies betweenthem, new energy supply technologies, sustainability, and resiliency. This vi-sion is captured in Fig. 1, where the two systems are represented, along withtheir interactions.

Nuclear

Coal

Biomass

Wind

Solar

Petroleum

Natural gas

Hydro

Pri

mar

y En

ergy

So

urc

es

Electrical Network

Liquid Fuel Network

Transportation Network

Geothermal

Tr

an

sp

or

ta

tio

n

Natural Gas Network

Co

nv

er

sio

n

Fig. 1 Conceptual representation of the energy and transportation systems

This research is part of an ongoing project known as The 21st CenturyNational Energy and Transportation Infrastructures Balancing Sustainability,

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Costs, and Resiliency or NETSCORE-21, funded by the U.S. National Sci-ence Foundation. Our objective is to identify optimal infrastructure designsin terms of future power generation technologies, energy transport and stor-age, and hybrid-electric transportation systems, with balance in sustainability,costs, and resiliency. Special attention is given to characterizing interdepen-dencies between energy resource portfolio and energy/vehicular transportationsystems at the national level.

2 Modeling Approach

The energy system is comprised of (but not limited to) electricity, naturalgas, liquid fuels, nuclear, biomass, hydroelectric, wind, solar, and geother-mal resources. Modeling of national freight and passenger transportation fo-cuses on state-to-state travel; we consider both infrastructures (rail, highways,locks/dams, roads, ports, airports) and fleets (trains, barges, trucks, personalvehicles, airplanes, etc.), and there may be different kinds of fleets for eachmode (e.g., diesel trains and electric trains or conventional and plug-in hybridelectric).

planning

operation

Energy

capacityfixed

demand

flowsenergy

prices

transportation

Transportation

capacityfixed

demand

flowstransp.

prices

rights of way, etc…investment investment

fuel demand

Fig. 2 Proposed model that integrates the energy and transportation systems at two levels:operation and planning

Fig. 2 captures the scope of the modeling effort. The transportation andenergy systems interact mainly at two different stages: operation and invest-ment. At the operational level each system needs to satisfy its demand with theexisting capacity. However, operation of the two systems, and ultimately in-vestment, are interdependent; while the transportation sector demands energyin the form of fuel, the energy sector requires the movement of raw bulk energysources (e.g. coal or natural gas for thermal power plants). At the same time,the cost of meeting those reciprocal demands has an impact on final prices for

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energy and transportation. The ever-growing public need for energy and trans-portation creates the necessity to invest in new capacity. Given the potentialfor increased coupling between energy and transportation, it is apparent thatbetter designs of both can be achieved if these designs are performed together.

Our modeling approach consists of two levels. The lower level performsa cost minimization on a 40 year infrastructure investment plan, constrainedby lower and upper limits on technology investments, and evaluates resiliencyand sustainability metrics. The higher level uses an evolutionary program toperform a multiobjective search for the Pareto optimal front in the space ofcost, resiliency, and sustainability metrics, by manipulating the technologyinvestment lower and upper limits. The remainder of this section, togetherwith Section 3, is devoted to describing the lower level. The higher level isdescribed in Section 5.

2.1 Energy systems modeling

A generalized network flow transportation model [9, 14, 13] is used to modelenergy systems, where commodity flow is energy, and transportation pathsare AC and DC electric transmission, gas pipelines (for natural gas and/orhydrogen), and liquid fuel pipelines (for petroleum-based fuels, biofuels suchas ethanol or biodiesel, and anhydrous ammonia). Energy transport by rail,barge, and truck is included in the freight transport model.

Each source node, specified with location, is connected to a fictitious sourcenode that supplies all energy. Arcs emanating from each source are character-ized by maximum extraction rate and extraction cost. Petroleum, coal, naturalgas, and uranium have finite capacities, while renewables have infinite capaci-ties. All sources have finite maximum extraction rates. Conversion and trans-portation are endowed with: capacity, efficiency, operational cost, investmentcost, lifetime, component sustainability metrics (e.g., CO2), and componentresiliency (e.g., reliability).

2.2 Transportation systems modeling

The freight transport system is modeled as a multicommodity flow networkwhere the flows are in the units of tons of each major commodity. A commodityis major if its transportation requirements comprise at least 2% of the nation’stotal freight ton-miles. Data available to make this determination [21] indicatesthis criterion includes 23 commodities that comprise 90% of total ton-miles(e.g., the top eight, comprising 55%, are in descending order: coal, cereal grains,foodstuffs, gasoline and aviation fuel, chemicals, gravel, wood products, andbase metals).

There are two fundamental differences between this formulation and thatof the energy formulation. Whereas the energy formulation must restrict en-ergy flows of specific forms to particular networks (for example, natural gas

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or hydrogen cannot move through electric lines or liquid fuel lines), commodi-ties may be transported over any of the transport modes (rail, barge, truck).Also whereas energy movement requires only infrastructure (electric lines, liq-uid fuel pipelines, gas pipelines), commodity movement requires infrastructure(rail, locks/dams, roads, ports) and fleet (trains, barges, trucks), and there maybe different kinds of fleets for each mode (e.g., diesel trains or electric trains).

To accommodate these differences, the transportation formulation is com-prised of two multicommodity flows [2], one embedded inside the other. Com-modities flow through the network formed by the different types of fleet avail-able. At the same time, the units in those fleets travel along the network formedby the different infrastructures. An easy way to visualize this is captured inFig. 3, where the flow from node A to node B is divided according to the typesof infrastructures first and then into the different types of available fleets.

Node A

Railway

Diesel

Train

Highway

Ethanol

Truck

River

Barge

Node B

Hybrid

Train

Diesel

Truck

Hybrid

Truck

Node A

Node B

Fig. 3 Decomposition of transportation arc in two steps: infrastructure and fleet.

2.3 Review of other planning tools

There is a wide range of modeling tools that are used to study the energyand transportation systems, both together and independently. An extensivedescription of the issues related to modeling and more information on method-ology classification can be found in [3] and [12].

There are only a few planning tools that expand beyond one sector and aremost closely related to the scope of this work. The most prominent cases are theNational Energy Modeling System (NEMS) [22] and the MARKAL/TIMESsuite [6]. NEMS is an equilibrium model (it only evaluates proposed portfo-lios) which represents the petroleum, natural gas, coal, and electric supplyand transport/transmission sectors together with energy/economy macroeco-nomic interactions and international energy activity. MARKAL/TIMES, anoptimization model, represents resources associated with the petroleum, natu-ral gas, coal, and electric sectors but not the transport/transmission associatedwith these sectors. In addition, whereas NEMS iterates to equilibrium through

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sequential solutions of each sector, MARKAL/TIMES minimizes total cost ina single optimization and allows the usage of stochastic programming to ad-dress uncertainty.

There are two interesting tools developed by National Renewable EnergyLaboratory, the Regional Energy Deployment System (ReEDS) [18] and theStochastic Energy Deployment System (SEDS) [17]. ReEDS is a multiregional,multiperiod linear programming model of capacity expansion in the electricsector of the United States. The model performs capacity expansion but withdetailed treatment of the full potential of conventional and renewable electric-ity generating technologies as well as electricity storage. The principal issuesaddressed include access to and cost of transmission, access to and quality ofrenewable resources, the variability of wind and solar power, and the influenceof variability on the reliability of the grid. On the other hand, SEDS focuses ona more global approach, similar to that in NEMS, considering multiple energysectors and the inclusion of light and heavy duty vehicles. REDS is designedto be more flexible and easier to use than NEMS and, like it name suggests, isalso able to represent risk and uncertainty through stochastic programming.

3 General cost minimization formulation

The optimization problem associated with this model can be conceptuallydescribed by (1),

min CostOp + CostInv

subject to:

Meet energy demand,

Meet transportation demand,

Capacity constraints

Power flow constraints on electric transmission

(1)

The objective is to minimize the combined energy and a transportationcost with constraints of meeting demands on energy, and freight transportwhile following the capacity constraints. The operational characteristics of themodel provide additional constraints on the system, such as the inclusion ofpower flow relations for electric transmission lines (we used the so-called ”DC”power flow approximation for this purpose).

This section contains a rigorous description of the formulation needed toachieve the characteristics described above. The explanation of the formulationis preceded by an introduction to the nomenclature used.

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3.1 Nomenclature

3.1.1 Decision Variables

e(i,j)(t): Operational flow of energy arc from node i to node , j, for time stept (MWh)

eInv(i,j)(t): Capacity investment on energy arc from node i to node j, fortime step t. (MW)

f(i,j,k,m)(t): Operational flow of transportation arc from node i to node j forcommodity k using transportation mode m during time step t (ton)

fleetInv(i,j,m)(t): Fleet m capacity investment for transportation arc fromnode i to node j during time step t (ton/hour)

infInv(i,j,l)(t): Infrastructure l capacity investment for transportation arcfrom node i to node j for time step t (ton/hour)

θi(t): Phase angle at node i, used to model DC power flow (radians)

3.1.2 Sets and networks

NE : Set of energy nodesAE : Set of energy arcsAE

DC ⊂ AE : Set of AC electric transmission arcs, which satisfy DC powerflow equations

N T : Set of transportation nodesAT : Set of transportation arcsAT

j ⊂ AT : Subset of transportation arcs that create an energy demand atenergy node j

K: Set of commoditiesKc ⊂ K: Subset of commodities used by the energy system, e.g. coalM: Set of fleet or transportation modesMl ⊂M: Subset of fleet that can use transportation infrastructure lMj ⊂M: Subset of fleet that require energy from energy node jnE(i,k) ∈ N

E : Energy node that corresponds to the geographic location i andcommodity k in the transportation system

3.1.3 Energy Parameters

η(i,j)(t): Efficiency of arc (i, j) during time t (unitless)lbe(i,j)(t): Lower bound for flow in arc (i, j) for time t (MWh)ube(i,j)(t): Upper bound for flow in arc (i, j) during time t due to the initial

existing infrastructure (MW)lbeInv(i,j)(t): Minimum allowed capacity increase in arc (i, j) at time t (MW)ubeInv(i,j)(t): Maximum allowed capacity increase in arc arc (i, j) at time t

(MW)costOp(i,j)(t): Operational cost for flow in arc (i, j) during time t ($/MWh)costInv(i,j)(t): Investment cost for capacity increase in arc (i, j) in network l,

at time t ($/MW)

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heatContentk(t): Heat content of commodity k, at time t (MWh/ton)dEj (t): Fixed energy demand at node j during time t (MWh)

b(i,j): Susceptance of transmission line between nodes i and j (Ω−1)

3.1.4 Transportation Parameters

ubFleet(i,j,m)(t): Upper bound for total transportation flow for fleet m in arc(i, j) during time t due to the initial existing fleet (ton/h)

lbFleetInv(i,j,m)(t): Minimum allowed capacity increase in arc (i, j) for fleetm at time t (ton/h)

ubFleetInv(i,j,m)(t): Maximum allowed capacity increase in arc arc (i, j) forfleet m at time t (ton/h)

ubInf(i,j,l)(t): Upper bound for total transportation flow across infrastructurel in arc (i, j) during time t due to the initial existing infrastructure (ton)

lbInfInv(i,j,l)(t): Minimum allowed capacity increase in arc (i, j) for trans-portation infrastructure l at time t (ton/h)

ubInfInv(i,j,l)(t): Maximum allowed capacity increase in arc arc (i, j) fortransportation infrastructure l at time t (ton/h)

costOp(i,j,k,m)(t): Operational cost for transportation flow in arc (i, j) in fleetm, commodity k and time t ($/ton)

costFleetInv(i,j,m)(t): Investment cost for capacity increase in fleet m for arc(i, j) and time t ($ h/ton)

costInfInv(i,j,l)(t): Investment cost for capacity increase in transportation in-frastructure l for arc (i, j) and time t ($ h/ton)

fuelCons(i,j,m)(t): Fuel consumption for transportation mode m for trans-portation arc (i, j) during time step t (MWh/ton)

dT(i,j,k)(t): Fixed transportation demand of commodity k for arc (i, j) during

time t (ton)

3.1.5 Auxiliary parameters

These parameters are calculated as a combination of decision variables andpredetermined parameters.

costOpE : Operational cost from the energy system ($)costInvE : Cost due to the investment upgrades on the energy system ($)costOpT : Operational cost for transportation system ($)costFleetInvT : Investment cost on transportation fleet ($)costInfInvT : Cost on transportation infrastructure ($)dETj (t): Energy demand at node j during time t due to the transportation ofcommodities (MWh)

3.1.6 Other parameters

r: Discount rate∆t: Length of time step t (h)

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3.2 General formulation

The following formulation (2) incorporates the modeling capabilities that havebeen previously described in this paper.

The energy sector is represented by a set of nodes NE and arcs AE . Eachnode represents an energy subnetwork in a geographic location. For example,for a particular location, there might be three energy nodes; one for electricity,one for gas, and one for petroleum. Energy arcs link these various nodes, bothwithin same subnetwork (representing transmission lines, natural gas pipelines,or petroleum pipelines) or different, where conversion takes place (e.g., powerplants).

The flow across these arcs, e(i,j), are part of the decision variables of theproblem. These flows must be such that they satisfy the demand for energy(2b), part of which is due to the energy required to perform the movementof commodities in the transportation system (2n). Energy flows are also re-quired to meet lower and upper bound constraints (2c). The upper boundis determined by the capacity of the existing energy infrastructure and is acombination of the initial capacity, ube(i,j)(t), and investment on upgrades,eInv(i,j)(t). The first is a parameter while the second is another decision vari-able, with its corresponding lower and upper bound (2p). Energy flow mustalso satisfy other constraints, such as DC power flow equations for electrictransmission (2d).

The transportation system is also formed by a set of nodes N T and a setof arcs AT , although the nomenclature is slightly different. Here, each noderepresents a unique geographic location, while the transportation flows arereferred to as f(i,j,k,m), where (i, j) represent the origin and destination nodes,k the commodity that is being transported and m the mode of transportationused.

These flows must satisfy the transportation demand, which is predeter-mined (2e) for all commodities except for those that are energy related (e.g.,coal, uranium). In that case, the transportation demand depends on the use ofthat commodity in the energy system (2f). Transportation flows are limited bythe capacity of the available fleet (2g) and transportation infrastructure(2h).Both can be increased by the their respective investments, fleetInv(i,j,m)(t)and infInv(i,j,m)(t), which have upper and lower bound constraints (2r,2s).

min costOpE + costInvE + costOpT + costFleetInvT + costInfInvT (2a)

subject to:

Meet energy demand at every node∑k

η(j,k)(t)e(j,k)(t)−∑i

e(i,j)(t) = dEj (t) + dETj (t) (2b)

Energy flow lower and upper bounds

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lbe(i,j)(t) ≤ e(i,j)(t) ≤ ube(i,j)(t)∆t+

t∑z=0

eInv(i,j)(z)∆z (2c)

DC power flow equations

e(i,j)(t) = b(i,j)

(θi(t)− θj(t)

), ∀(i, j) ∈ AE

DC (2d)

Transportation demand for non-energy commodities∑m

f(i,j,k,m)(t) = dT(i,j,k)(t), k ∈ K\Kc (2e)

Transportation demand for energy commodities∑m

f(i,j,k,m)(t) = heatContent−1k (t) e(nE(i,k)

,nE(j,k)

)(t), k ∈ Kc (2f)

Fleet upper bound for transportation flows∑k

f(i,j,k,m)(t) ≤ ubFleet(i,j,m)(t)∆t+

t∑z=0

fleetInv(i,j,m)(z)∆z (2g)

Infrastructure upper bound for transporatation flows∑k

∑m∈Ml

f(i,j,k,m)(t) ≤ ubInf(i,j,l)(t) +

t∑z=0

infInv(i,j,l)(z)∆z (2h)

where:

costOpE =∑t

∑(i,j)

(1 + r)−tcostOpE(i,j)(t) e(i,j)(t) (2i)

costInvE =∑t

∑(i,j)

(1 + r)−tcostInvE(i,j)(t) eInv(i,j)(t) (2j)

costOpT =∑t

∑(i,j,k,m)

(1 + r)−tcostOpT(i,j,k,m)(t) f(i,j,k,m)(t) (2k)

costFleetInvT =∑t

∑(i,j,m)

(1 + r)−tcostFleetInv(i,j,m)(t) fleetInv(i,j,m)(t) (2l)

costInfInvT =∑t

∑(i,j,l)

(1 + r)−tcostInfInv(i,j,l)(t) infInv(i,j,l)(t) (2m)

Energy demand from the transportation system

dETj (t) =

∑(a,b)∈AT

j

∑m∈Mj

fuelCons(a,b,m)(t)∑k

f(a,b,k,m)(t) (2n)

Decision variables:

Energy flows: e(i,j)(t) ≥ 0 (2o)

Energy capacity inv.: lbeInv(i,j)(t) ≤ eInv(i,j)(t) ≤ ubeInv(i,j)(t) (2p)

Transportation flows: f(i,j,k,m) ≥ 0 (2q)

Fleet inv.: lbFleetInv(i,j,m)(t) ≤ fleetInv(i,j,m)(t) ≤ ubFleetInv(i,j,m)(t) (2r)

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Infrastucture inv.: lbInfInv(i,j,l)(t) ≤ infInv(i,j,l)(t) ≤ ubInfInv(i,j,l)(t) (2s)

Phase angles: − π ≤ θi(t) ≤ π (2t)

3.3 Compact notation

A more compact version of (2) can be produced using vectorial and matrixnotation. First of all, the vector capInv includes all capacity investment vari-ables, while the operational variables are grouped in vectors called flowst.The subscript t in this section represents the operational year to which avariable belongs. When using this notation we can reduce the model to theexpressions (3).

min[CostInv> CostOp>1 CostOp>2 . . .

]

capInvflows1flows2

...

subject to:

−I 0 0 . . .I 0 0 . . .0 A1 0 . . .0 −I 0 . . .L1 I 0 . . .0 0 A2 . . .0 0 −I . . .L2 0 I . . ....

......

. . .

capInvflows1flows2

...

≤

−lbInvubInv

d1

−lb1

ub1

d2

−lb2

ub2

...

(3)

The objective value is (2a), which is developed in expressions (2i-2m). Thefirst two rows in the constraints are directly related to the minimum andmaximum investment allowed (2p, 2r, 2s).

Following that there are three rows that are repeated for each year. The firsttwo correspond to operational constraints, such as demand balances (2b,2e,2f)or DC power flow constraints (2d). Such expressions are summarized in thematrix At and the vector dt. The next two lines correspond to the minimumand maximum operational flows from (2c,2g,2h). The matrix Lt accounts forthe fact that only investments done prior to the operational year can accountfor available capacity.

Inspection of (3) reveals an underlying structure (4) that would allow theuse of Benders decomposition methods [8]. This approach is not new to thefield and it has been implemented, for instance, in EGEAS [4], a very extendedinvestment software used in the electric industry. This special structure could

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be used to reduce the complexity of the linear problem and to increase solutionspeeds, an issue we are currently studying.

min[CostInv> CostOp>1 CostOp>2 . . .

]

capInvflows1flows2

...

subject to:

C0 0 0 . . .C1 D1 0 . . .C2 0 D2 . . ....

......

. . .

capInvflows1flows2

...

≤

b0

b1

b2

...

(4)

4 Emission index for greenhouse emissions

The previous sections, a modular methodology to optimize future investmentportfolios in terms of cost, resiliency and sustainability is presented. We can usethis multiobjective approach to find solutions which minimize both costs andgreenhouse gas emissions, while maximizing resiliency. Other studies [7, 11, 16]rely on the evaluation of social costs associated with these emissions as wellas trying to capture the time value of carbon.

We have developed an index that compares solutions to projected trends.Let us define a pessimistic scenario in which nothing is done to palliate green-house gas emissions and an optimistic case in which an aggressive reduction isaccomplished. Other emission forecasts can be compared to those referenceswith the following metric (5).

IGHG =1

n− k

n∑t=k

ActualEm(t)− LowEm(t)

HighEm(t)− LowEm(t)(5)

where k and n are the first and last year considered for the index, ActualEmis the emission forecast, and HighEm and LowEm are the yearly emissions forthe pessimistic and optimistic cases, respectively. Because of lead times fornew infrastructures, the first k years are not considered in the calculation ofthe index.

In Fig. 4 we can see a representation of this approach. The top continuousline represents the pessimistic scenario, with emissions increasing at the samerate as electric demand. The bottom line represents the optimistic case, withreductions in greenhouse emissions every year comparable to proposed bills inthe U.S. House and Senate[15]. In between those lines we can see how the indextakes different fractional values. The index is not limited to values between 0and 1 because emissions could go beyond the reference cases.

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0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

2.25

1 5 9 13 17 21 25 29 33 37

Emis

sio

ns

com

pa

red

to

ye

ar

1

Year

Optimistic scenario, I=0

Pessimistic scenario, I =1

I = 0.8

I = 0.6

I = 0.4

I = 0.2

Fig. 4 Greenhouse emission index for best, worst scenarios and fractions in between

5 Multiobjective optimizer

NETPLAN, an energy and transportation investment multiobjective evolu-tionary algorithm is proposed as an approach to efficiently solve the problemdescribed above and produce an approximation to the Pareto front. It hasbeen conceived in a modular fashion, to allow the independent development ofeach one of its components. Figure 5 introduces the block diagram behind theorganization of the different parts that form the multiobjective optimization.

Cost Minimization

Sustainability

Metrics

Resiliency

Metrics

Multiobjective algorithm

Select front of solutions

Generate new generation

Search and selection

Investment

Portfolio

Evaluation

(fitness functions)

Fig. 5 NETPLAN multiobjective approach

The popular NSGA-II algorithm [5] is used in the search and selectionstage, while the evaluation of the different candidates is based on the mini-

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mum cost formulation described in Section 3 and resiliency and sustainabilitymetrics, such as the one in Section 4.

The process is carried out through the following steps:

1. The NSGA-II algorithm proposes a number of candidates to the multiob-jective optimization problem. Each one of these candidates is characterizedby a vector of minimum investments. So, for instance, we could have a vec-tor with high investments in wind energy and low investments on pulverizedcoal plants.

2. For each of the candidate, the minimum investments are coded into con-straints and they become the lower bound for capInv in (4).

3. The minimum cost optimization (with the minimum investments enforced)is performed. As a result, the investment portfolio and operational flows forthe candidate solution are found, as well as the operational and investmentcosts.

4. Metrics for sustainability are calculated, based on the minimum cost solu-tion. In this paper, the emission index in Section 4 is used.

5. Resiliency calculations are performed. In this case, the average reservemargin for each electrical region is considered as a measure of the strengthof the system.

6. For each candidate solution the objective values for cost, sustainability andresiliency have been found. These values are returned to the NSGA-II al-gorithm, which will take them into account in the creation of subsequentgenerations. The algorithm is returned until the maximum number of iter-ations is reached.

In the current implementation, the use of minimum investment vectorsfacilitates shifting from the minimum cost solutions to others with better per-formance in terms of sustainability or resiliency. This approach is very simpleto implement but, if needed, could be complemented with other methods suchas subsidies for clean alternatives, taxes for polluting technologies (e.g., carbontax) or preventing certain technologies to be used in favor of others. Similarly,the metrics for sustainability and resiliency metrics are linear combinationsof the arc flows and investments. More computationally demanding metricscould include, for example, the simulation of large-scale failures in the energyand transportation systems [10].

6 Numerical example

6.1 Example description

A small numerical example is presented in this section and uses the method-ologies presented in this paper. The continental US is divided into 5 regions asshown in Fig. 6. Data for this example was obtained from [1, 19, 20, 23, 25].

We assume that the electricity demand for each region is known with anannual growth forecast of 2%. Initially, the demand is satisfied by the existingpulverized coal (PC) installed capacity. Data can be found in Table 1.

15

13

4

5

2

Fig. 6 Nodal representation of the Continental United States

Table 1 Electricity demand by region

Region Avg. demand (GW) Peak demand (GW) Initial PC capacity (GW)1 148 230.9 318.82 159 248.0 342.53 25.8 40.23 55.64 68.7 107.1 147.95 87.6 136.7 188.8

The increasing demand and the the continuous retirement of PC plantsalong the 40 years of the simulation creates the need to invest in new genera-tion. Four technologies are considered: pulverized coal, integrated gasificationcombined cycle (IGCC), wind and solar. Table 2 summarizes the characteristicsof these technologies. The efficiency of wind and solar generation is consideredto vary geographically as shown in Table 3. Each year, up to 4 GW of eachtechnology is allowed to be invested in each region.

Table 2 Generation technology data

Technology PC IGCC Wind SolarLife span (years) 40 30 20 25Operational cost ($/MWh) 2.95 2.84 0 0Investment cost (million $/GW) 4262.2 3725.9 2176.2 7603.7Operation CO2 (lb CO2e/MMBtu) 206 206 0 0Investment CO2 (lb CO2e/MMBtu) 2.33 0.79 14.9 32.1Heat rate (MMBtu/MWh) 9.2 8.8 - -Capacity factor 1 1 0.2 0.15

The arcs shown in Fig. 6 represent electrical transmission lines between thedifferent regions. Each arc has a maximum capacity of 15 GW, which remainsconstant throughout the simulation. Regions are also interconnected by rail,

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Table 3 Wind and solar efficiency by region

Region 1 2 3 4 5Wind 0.3 0.3 0.35 0.35 0.31Solar 0.11 0.18 0.12 0.17 0.2

which allows coal to be transported. Transportation is not constrained in thisexample, but we account for energy consumption (341 Btu/ton mile), dieselcost (20.6 $/Btu) and CO2 emissions (0.2 lb CO2e/ton-mile).

Coal is produced is regions 2, 3, and 5 (Appalachia, Illinois basin, and West-ern regions, respectively). The coal from each region is treated as a separatecommodity and their characteristics are summarized in Table 4.

Table 4 Coal production parameters

Region 2 3 5Annual Capacity (million short tons) 534 125 651

Avg. price ($/short ton) 30.2 22.7 10Avg. heat value (MMBtu/ton) 25.03 22.73 17.45

All costs are subject to a 2% annual inflation rate and a 7% discount rate.Salvage values are assigned for the investments close to the end of the sim-ulation period. The objective functions used are operational and investmentcost, the greenhouse emission index presented before and the average reservemargin at electrical nodes. This margin is defined as the difference between theavailable generation capacity at an electrical node (weighted by the capacityfactor) minus the peak demand, divided by the peak demand. For the green-house gas index the pessimistic scenario is defined as a geometrical 2% annualgrowth (equal to the demand growth) and the best scenario as a constant 3%annual reduction.

6.2 Results

The multiobjective algorithm is executed for 200 generation with 20 indi-viduals each. Each cost minimization program has 9020 variables and 6360constraints and its solved in 0.12 seconds using version 10 of CPLEX, runningon 3.6 GHz Pentium 4 processor with 2 GB of RAM.

Cost estimates for the Pareto front range from 4.9 to 6.2 trillion dollars,which is a low estimate compared to the 14 trillion dollars over 20 years pro-jected by DOE-EIA [24]. This difference is mainly due to the simplicity ofthe example in terms of granularity as well as the lack of more expensivegeneration technologies such as gas turbines.

Fig. 7 represents the average electricity generation by source for the bestcase scenario. We notice that even in this case renewables take an important

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role, especially in areas where their efficiency is best. Also, it is not surprisingto find that IGCC becomes almost the only coal-fired generation, since itshigher efficiency than pulverized coal reduces its overall cost and emissions.

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Fig. 7 Average electricity generation for least cost solution by type and region over simu-lation time

In Fig. 8 the most sustainable solution is compared to the absolute bestcost solution in terms of annual greenhouse emissions. The most sustainablesolution returns an average index of 0.15, due mostly to a very aggressive re-duction of emissions in the first half of the simulation, well below the referencelow case. This trend is not continued in the second half of the simulation dueto the fact that renewables have a shorter life time (20 and 25 years) and coalbased generation comes into play in the final stages. The lowest cost solutionrelies heavily on carbon-based generation and presents an emission index of1.23, which is above the pessimistic reference case. This is due to the factthat apart from the operational emissions that grow proportional to the load,we are also considering the emissions associated with the construction of newinfrastructure.

Finally, all the candidate solutions tested by the multiobjective optimizerare plotted in Fig. 9. The final Pareto Front of solutions identified by theNSGA-II algorithm are represented with red stars.

7 Conclusions

A new multiobjective approach to analyze long-term investment portfolios forthe national energy and transportation systems has been presented. It features

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Fig. 9 3D representation of candidate solutions (blue dots) and Pareto front solutions (redstars)

a modular design with a fast linear program model for cost minimization andsustainability and resiliency metrics. We have also presented a new metricthat accounts for time value of green-house emissions and compares trendsover time.

Finally, a small numerical example has been developed and tested usingthe approach presented in this paper. Although this example utilizes a highlyaggregated model of the United States, the approach may be applied usingsignificantly more granular models by increasing the number of regions, energynetworks, means of transportation and time steps used.

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The NETPLAN tool performs long-term, multi-sector, multiobjective in-vestment planning at the national level. This tool uniquely addresses a seriousneed today in that it provides a basis for setting long-term policy associatedwith supplying economic energy and transportation services while reducinggreenhouse gas emissions and maintaining a resilient system.

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