Application of a multiobjective facility location model to power plant siting in a six-state region of the U.S.

APPLICATION OF A MULTIOBJECTIVE FACILITY LOCATION MODEL TO POWER PLANT SITING IN A SIX-STATE REGION OF THE U.S. JAREDL. COHON,*CHARLES S, REVELLET and JOHN CURRENTS Department of Geography and Environmental Engineering, The Johns Hopkins University, Baltimore, MD 21218,U.S.A. THOMASEAGLES$ and

RWELL EBER~AI@

Applied Physics Laboratory, The Johns Hopkins University, Laurel, Maryland, U.S.A.

and

Department of Civil Engineering, University of Tennessee, Knoxville, Tennessee, U.S.A. INTRODUCTION

AND BACKGROUND

Several models have been formulated to analyze national energy policy. Typically, these models, such as the U.S. ~pa~ment of Energy Project Inde~nden~e Evaluation System (PIES), are used to develop and to evaluate national energy supply/demand scenarios. National models are useful, but national-level projections of energy variables cannot completely characterize the chances of achieving a given energy supply/demand state, the possible ways to achieve it, or the environmental impact of achieving it. These questions require analysis at a finer geographic level such as a region[l-31. The rationale for regional energy analyses draws further support from the nature of the physical systems and institutions that control or are affected by energy supply systems. Physical resources often have dimensions which cover several states (e.g. watersheds), and this fact has given rise to a number of regional resource management organizations [4]. Similarly, the existing systems for energy production and distribution (e.g. power pools) often extend over several states, suggesting a regional approach to energy planning. The model presented in this paper locates facilities within cells, equal roughly in size to counties, so as to meet projected regional energy demands. In the past, multi-state regions have been the smallest spatial elements considered by the majority of other analysts (e.g. Refs. [ 1 and 2J), and facility locations have been specified as “within the region”. In order to deal with impact *Jared L. Cohon is an Associate Professor of Geography and En~on~n~l En~n~ri~ at The Johns Hopkins University. He received his Ph.D. in Civil Engineering at Massachusetts Institute of Technology in I973. He teaches and does research on systems analysis, particularly multiobjective programming, and its application to public decision making problems, particularly environmental and energy problems. He is the author of M&objective Ptwgramming and Planning, published in 1978 by Academic Press. From 1977 to 1978, Dr. Cohon served as Legislative Assistant for energy and environment to the Honorable Daniel Patrick Moynihan, U.S Senator from New York. He is also editor of Water Resources Research.

Xharles ReVelle is a Professor at the Johns Hopkins U~ve~ity and teaches in the Program in Systems Analysis and Economics for Public Decision Making. He has pub~s~ more than 40 papers in the fields of Operations Research, Water Resources and Regional ~ie~~~o~aphy. His principal research interests are in the application of mathematical programming to the location of facilities and to reservoir management. He is the author, with his wife Penelope, of Sourcebook on the Environment (1974) and Approaches to Environment problens (forthcoming). SJohn Current is a graduate student in the Department of Geography and Environmental Engineering at The Johns Hopkins University. Heis completing his Ph.D. dissertation on facility location problems. _ #Thomas Easdes is a member of Senior Technical StatI of The Johns HOD~~IISUniversitv Annlied Phvsics Laboratory. He is manager o~studies involving the appliition of M~~b~tive prognunm‘irgland Plann& to&vet plant siting problems, 9Russell Eberhart is a member of the Principal Professional StatI of The Johns Hopkins U~versity Applied Physics Laboratory. He is supervisor of Energy Facility Siting & Special Studies witbin the power plant sitif@ group. [Richard Church is an Associate Professor of Civil Engineering at the University of Tennessee. He received his Ph.D. in 1974from The Johns Hopkins University. His papers include several on facility location algorithms, formulations and applications. He has served as a consultant to Brookhaven and Oak Ridge National Laboratories. He is co-author, with Charles ReVelle, of &sign of Locational Systems, a monograph to be published by Pion, Ltd. of London. 107

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questions, however, an even finer geographic resolution is required; accordingly, this study had as its goal the development of a method which could be used to assign probable locations to large numbers of hypothetical energy facilities within a region. There are many possible uses for such a method, such as power pool long-range location planning, resource limitation studies, and cumulative environmental impact studies. These uses imply that the precision of the location predictions need not be high. Locating a facility within an area of, say 490 square miles (the average area of a county in the study region) might be precise enough. Fortunately, methodological considerations also point to county-level precision. Nothing like actual site suitability determination is possible for such a large number of facilities; the intent is to indicate areas with a relatively high probability of accepting facilities, based only on existing data (no field work) and interaction with decisionmakers.

THE MODEL

At the heart of the methodology is a multiobjective linear programming model which generates probable locations for energy facilities. As currently formulated, the model is limited to nuclear and coal-fired electric generating plants. Extension to other facilities such as oil-fired electric generating plants, coal conversion facilities, oil refineries, and liquified natural gas (LNG) importing facilities does not present major conceptual difficulties. The model was formulated to locate coal and nuclear power plants so as to minimize a vector of four objectives subject to constraints on regional energy demand, fuel mix, the availability of resources and air quality and thermal pollution standards. The four objectives are to minimize a transmission cost surrogate, a fuel transportation cost surrogate, population exposure to nuclear plants and water storage in reservoirs. Minimizing each of these objective functions would lead to a different set of locations because the objectives conflict. Using generating techniques[5,6], a noninferior set (NIS) of locations can be generated relative to these four objectives; this NIS can then be used to display trade-off information to decisionmakers-state and local government officials and public and utility representatives. Though the model form was developed with enough generality to allow it to be applied to any arbitrarily defined region, the Department of Energy’s Region III which consists of Delaware, Maryland, Pennsylvania, Virginia, West Virginia, and the District of Columbia was initially chosen as the development and test region. New Jersey was subsequently added to avoid dividing the Pennsylvania-Jersey-Maryland Power Pool. The model structure is applicable to any time horizon, depending upon the year used for population projections; projections for the year 2000 were used for this study.

Structure

Current research in the area of regional energy analysis has led to the idea of county-level resolution for location analysis, at least in the eastern United States[7-91. In our study region, there are 269 counties with an average area of 490 square miles. County-level analysis represents at least an order-of-magnitude increase in locational resolution over that afforded by previous energy supply models (e.g. Ref.[2]), and it is probably close to the limit of accuracy which can be supported by the spatial resolution of the input data. While county-level resolution (or something close to it) was desirable, a uniform grid was seen to be methodologically preferable because the associated cell centroids are well-defined, resolution is constant from cell to cell, and generalization to the rest of the United States is facilitated. A cell measuring 15 minutes (17.5 miles, in latitude by 15 minutes (13.5 miles) in longitude was chosen because it corresponds to the existing United States Geological Survey (USGS) 15 minute geographical classification system, for which USGS maps covering each cell are available. There are 622 cells in the region, shown in Fig. 1, each covering about 240 square miles. Facility location is defined to be within a cell, with no attempt to be more site-specific within the cell. Each cell is represented by its geographical centroid, and distances to and from the cell are measured from this centroid.

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Siting decision variable The basic decision variable is Sjk,the amount of new capacity of type &,in Gigawatts (GWe, where 1 GWe = 1 billion watts), located in cell j. The subs~~pt k defines power plant type as follows: 1, nuclear, once-through cooling; 2, nuclear, wet cooling towers; 3, coal, oncethrough cooling; and 4, coal, wet cooling towers. Additional plant types could be used to incorporate other facility characteristics that may influence plant location. Such characteristics may include air pollution control devices, e.g. scrubbers.

Required capacity. Required new generating capacity, representing projected demands for electricity as well as the nuclear/coal mix, must be met. NCELL

S, = DEMNK NCELL g

,&

s,

(2)

= DEMCL

where NCELL is the number of cells in the analysis, j is the cell index number, k E Nuclear indicates that the sum covers both nuclear types, k E Coal indicates that the sum covers all coal types, Sjk is the amount of generating capacity of type k located in cell j, and DEMNK and DEMCL, inputs to the model, are the required nuclear and coal generating capacities, NCELL

respectively. For compactness, in the rest of the formulas,

Z will be represented by Z. j=I ~~~~~ cell capacity. The model includes constraints on cell capacity to allow vaous dispersed and concentrated siting strategies to be analyzed.

(4)

C

sjk

s QMAX

Vi

(5)

where QMAXN, QMAXC and QMAX are the capacity limits for nuclear, coal and total cell capacity, respectively. Note that varying the upper limits from run to run and, perhaps from cell to cell, provides complete flexibility in modelling political or regulatory constraints on plant concentration. Upper bounds on bay. It is also possible to limit the total generating capacity sited in groups of cells. The model incorporates two such constraints, one each for the Chesapeake and Delaware Bays (see Fig. 1). The constraints are of the form:

(6) where jE Bay denotes the set of cells bordering a bay, and QBBYdenotes the generation capacity limit. This type of constraint was used to represent the widely held belief that the Bays, though large, are crucial and fragile ecological systems that have a limited capacity to assimilate the effects of shoreline power plants. Of course, the real challenge is in estimating Gay, a problem that is mitigated in the model by sensitivity analysis. Efectric power demand. This set of constraints takes the following form: (7)

Application of a multiobjective

facility location model to power plant siting

III

where 4 is the demand at load center I, pool 1 is the power pool in which load center 1 is located and Xj, is a decision variable denoting the amount of power (GWe) transmitted from cell j to load center 1. Though the definition of load centers is entirely general, we chose, for computational and analytical purposes, to represent load centers as the larger cities, with the population of each electric utility’s service area aggregated and assigned to the cities within the service area in proportion to the cities’ populations. Each cell was allowed to transmit power to each load center in the same power pool, a formal collection of utilities that operate their systems in a joint fashion. Power pools in our region are shown in Fig. 2. E/e&c power supply. Continuity of power generated at and supplied from j must be insured.

where pool j is the power pool in which cell j is located. This simply says that the power generated at cell j must equal the sum of the power transmitted from cell j to each load center 1 located in a common power pool. Coal supply. This constraint requires that the sum of the coal shipped to all cells from coal source i be less than or equal to the coal production Ri at source i. The decision variable, Cij,is defined as the tons of coal per year shipped from coal source i to cell j. The constraint has the form:

2 i

Cij 5 Ri

Vi.

(9)

Coal demand. This constraint requires that sufficient coal be supplied to coal plants sited in cell j. The constraint is written:

(10) where V is the coal required per unit of capacity (tons per year per GWe). V is calculated from V = 4380000 (HEATRT) (CAPFAC)/HEATVL where HEATRT is the plant heat rate in BTU per kilowatt hour, CAPFAC is the plant capacity factor, and HEATVL is the heating value of the coal in BTU per pound. Seven coal production centers [ IO] have been identified for the study region. If the total coal demand implied by DEMCL of equation (2) in a given run is greater than estimated 1985 coal production, then the extra production needed is distributed to the seven centers as “phantom mines” in proportion to their 1985 production shares. Implicit in the “phantom mines” approach is the assumption that sufficient coal reserves are available within the region to supply the total coal demand for any possible scenario. With 121.8 billion tons of coal reserves in the region [ 1l] this assumption appears reasonable. Water consumption. In an attempt to formulate a simple consumptive use constraint for use in site screening, the Nuclear Regulatory Commission (NRC) suggested that a reasonable consumptive allowance without augmentation would be 10% of the ‘I-day, lo-year low flow [ 121,but did not specify whether this should be applied site-by-site or by river basin. In the case where low flow augmentation is provided, the NRC[12] proposed that consumption be limited to 10% of the annual 20-year low flow, again not specifying whether by site or by basin. In the north-east, this flow is often an order of magnitude higher than the 7-day IO-year low flow and thus makes many more rivers eligible. In the model, an annual low flow consumption criterion was adopted as follows:

(11)

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Application of a multiobjective facility location model to power plant siting

where “j E Basini” indicates that the sum refers to those cells associated with rivers within a basin, @&is the consumptive water use in cubic feet per second (cfs) per unit of generating is the annual 20-year low flow in cfs measured at the most capacity of type k, Qannm,i downstream gaging station in basin i, and u is the fraction of Qannm,iwhich is allowed for consumptive use by the plants to be sited in the basin. In addition to (1 I), a second consumption constraint was imposed; this constraint is discussed below, after the presentation of withdrawal constraints. Water withdrawal. When the annual low flow consumption criterion was applied by basin, it became apparent that additional constraints were needed to limit withdrawal at each site (i.e. within each cell). The NRC[12] suggested a limit of 15% of the 7-day lo-year low flow in the no-augmentation case, but did not deal with withdrawal limits where reservoirs were involved. The basic problem was that, in general, some sites would need flow augmentation and some would not, and yet the NRC sought a single constraint that would apply to all situations. Moreover, it was thought desirable to let the model select the amount of augmentation (if any) necessary for each site. The solution chosen was to impose two types of withdrawal constraints, involving an augmentation decision variable, and to formulate an objective to minimize the amount of augmentation required. The objective is described later in this paper. The constraints have the form:

(12) F 5 Q7lOj Vi

(13)

where wk is the water withdrawal rate (cfs) associated with one unit of generating capacity, Uj is the set of all cells upstream of cell j, Q7iojis the 7-day, lo-year low flow in cfs at cell j, p is the fraction of Qioj allowed for withdrawal, and yi is the safe yield (cfs) from the reservoir assumed to be constructed to serve the generating capacity being sited in cell j. Several assumptions are implicit in (12) and (13). First, it was assumed that the entire reservoir safe yield would be used by the plant. Second, each reservoir’s size was assumed to be limited such that its safe yield was not greater than the natural 7-day, lo-year low stream flow for the river supplying it. This limit implies a small, single-purpose offstream reservoir, a kind of reservoir that is more likely to be built than the large, on-stream impoundments which are becoming increasingly unpopular. Finally, it was assumed that such a small augmentation reservoir was feasible where required; no attempt was made to assess physical feasibility. Additional consumption constraint. Another constraint was found to be necessary in order to cover the cases where little or no augmentation was developed in a basin. In such cases, the total consumption by newly-sited plants in the basin was limited by the NRC to a percentage of the 7day, lo-year low flow at the mouth of the basin (Qlom). In this study, such a limit was adopted in the case of no augmentation, and a variable limit was imposed on basin consumption based on the amount of augmentation provided. These limits were combined in one constraint as follows: (14) where Q710m, i is the 7-day IO-year flow measured at the most downstream gaging station in basin i. Water consumption values taken from a National Academy of Engineering Report[l3], are:

Nuclear, Wet Towers (1 GWe) Coal-Fired, Wet Towers (1 GWe)

Consumption (cfs)

Withdrawal (cfs)

26 21

33 27

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Statistical streamflow data were obtained from the U.S. Geological Survey (USGS), Office of Water Data Processing (OWDP) in Reston, Virginia. Low flows between gaging stations were obtained by interpolation, using drainage areas provided in Ref. [ 141. Air quality constraint. This constraint has the form,

(15) where E is the amount of SO, emitted per unit of coal-fired generating capacity, D is the dispersion factor which relates maximum ground level concentration (24-hour average) to emission, uj is the 24-hour average ambient SO, air quality standard at cell j, Aj is the measured ground-level ambient SO, concentration (annual maximum 24-hour average) at cell j, and yj is the fraction of gj - Aj which the sited plant is allowed to take up. Any attempt to characterize atmospheric dispersion in a general area-wide analysis is, at best, a gross approximation. Previous experience with such problems and a host of simplifying assumptions, many of which may be relaxed, led to the formulation presented. A detailed discussion of the assumptions and the problems of air quality representations is contained in Ref. [15]. Ambient air quality data were collected from the various energy and air quality control departments of the six participating states. These data were reduced to common units, and the annual maximum 24hour average ground-level concentration for SO, was encoded for each cell. Interpolated values were used for these cells for which no data was available. Area screening. It is possible to exercise the model using all 622 cells as potential locations for generating capacity. The resultant problem size, however, would be expensive to run, so there is substantial motivation to eliminate cells u priori by use of manual screening. The a prioti elimination of many cells is also supportable from a resource standpoint. For example, the model assumes that plants located in a cell draw their water from that cell, and not from nearby cells. Therefore, any cell which does not contain a water source with the required minimum flow may be screened out. In addition, it is reasonable to screen out cells with obviously low political potential for major facility location, such as those located in national parks and urban areas. For the initial model application, all but 169 of the 622 cells were screened out. Primary screening factors were the lack of adequate water, the presence of Federal and State dedicated lands such as national and state parks, and a population “constraint”, described in Ref. [ 151. Objectives The model includes four objectives involving transmission, coal transportation, low flow augmentation, and population impact (nuclear plants only). The first three objectives serve as surrogates for location-dependent cost components. Minimizing total cost is the traditional objective of linear programming formulations, but cost computations in quantifiable categories such as land, labor, and materials leave out the intangible costs of externalities, which have an increasingly annoying habit of showing up in legal and regulatory arenas long after plans for a facility have been made. Though an overall cost objective offers certain advantages of explication, in this study an attempt was made to construct physical objectives which incorporate fundamental cost-like attributes, hopefully including at least some of the intangible costs. The last objective (population impact) is completely divorced from dollar cost calculations, and reflects the component of regulatory and public opinion which favors sites remote from population centers. Transmission. The objective is written as Min MWMIS = c

i 7

dj/&

(16)

where dj, is the distance between the centroid of cell j and load center f, and Xrl is the power (GWe) transmitted from plants sited in cell j to load center 1. No specification was made as to

Application of a multiobjective facility location model to power plant siting

II5

how the power is transmitted. It was assumed that minimizing the transmission distance best captured both the dollar cost and the hidden, “hassle factor” cost of the trouble and delay associated with acquisition of transmission routes. Multiplying the distance by the power transmitted captures the fact that higher power (and the associated higher voltage) lines are more costly in all senses. In the model the transmission of power is permitted only from plants to load centers within the same power pool. This restriction was captured in constraints (7) and (8). Coal transportation. This objective has the form: Min TONMIS = 7 2 dii Cij i

(17)

where dij is the distance between coal source i and the centroid of cell j, and Cii is the amount of coal (tons per year) shipped from coal source i to cell j. Only those cells with rail access to the seven coal centers, described earlier in the coal supply section, were considered as potential coal-plant sites. The coefficient dij was taken as great circle distance, shown by Battelle Northwest[16] to be a relatively constant proportion to rail distance in the U.S. In the case of lower New Jersey and the Delmarva peninsula (the areas of Delaware, Maryland and Virginia between the Delaware and Chesapeake Bays), distance calculations were modified to account for railroad routing around the north end of the Chesapeake and Delaware Bays. It was assumed that no coal barging for electric utility use would occur on the Bays or on the Atlantic coast. Since freight rates are, to a large extent, functions of distance, this objective serves as a surrogate for coal transportation cost. It should be mentioned that the current representation of both coal transportation and power transmission are somewhat unrealistic. Improved formulations that include representations of existing railroad networks and transmission grids have been developed by Brookhaven[9] and the present authors. Low-flow augmentation. Providing augmentation means building reservoirs which are both expensive and environmentally undesirable. In addition, reservoir construction has come under increasing public attack. Thus, reservoirs carry high hidden costs associated with delay, contention, and uncertainty. For all these reasons, it was decided to incorporate an objective to minimize total new reservoir capacity within the region. Its form is very simple: Min MINRES = C Ujq i

(18)

where Yj is the safe yield of the reservoir constructed at cell j, and Uj is a weighting factor which is either 1 or the 7-day lo-year low flow at cell j. Setting Uj= 1 minimizes the total reservoir capacity over the region, while setting uj = Qrioj biases the objectives to favor reservoirs on small streams over those on large rivers, while still tending to minimize total capacity. Population impact. This objective is an outgrowth of one first proposed in a study performed for the Brookhaven National Laboratory[8], and is intended as a way to address nuclear safety issues in a way which goes beyond NRC’s constraints on population exposure, already taken into account during cell screening. The objective is written as follows: Min POP = x

j

z

PjSjk

(19)

kENuclear

where Pj is the population within a specified distance of cell j. The population of each county was aggregated at its county seat, except in cases where one large city exists within the county, which then received all its population. Where two or more large cities exist within a county, the county population was distributed among them in proportion to their populations. Pi was then calculated as the populations, represented by the population centers, within a specified radius of each cell.

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DISCUSSION

OF RESULTS

The model application and results described in this paper were undertaken for proof-ofprinciple purposes only, and the results should be considered primarily as illustrative of the type of output which the model can produce, rather than as useful in themselves. Time constraints prohibited the collection of data in the desired amount and detail and limited input from regional decisionmakers to familiarization and first impressions. The value of the model as a decision-making tool is, however, demonstrated with these tentative results. For the first model runs, 50GWe of new generating capacity, 50% coal-fired and 50% nuclear, was selected as the input amount to be located. Thus DEMNK = 25 and DEMCL = 25. This represents a regional annual growth rate for electricity demand (1977-2000) of somewhat greater than 2.5%, depending on how much new cycling and peaking equipment is assumed to be installed in addition to the 50 GWe base. An arbitrary upper bound of 4GWe was set as the maximum allowable nuclear capacity allowed in each cell (QMAXN); this corresponds roughly to the capacity of four large nuclear units. Likewise, a limit of 3.2GWe coal-fired capacity per cell (QMAXC) was imposed, corresponding to four typically-sized new coal-fired units. In addition, an overall limit of 4 GWe was imposed on total new capacity in each cell (QMAX). Existing capacity (as of 1977)in a cell was accounted for by subtracting it from the amount which could be located in that cell, In the previous presentation of the model, several other parameters were defined which could be set by the user. For the initial runs, Table 1 gives the values used, and shows the equation number in which the parameters appear. All of these parameters and the cell capacity limits may be varied, affording the user the capability of doing parametric analyses involving total demand, fuel mix, degree of capacity concentration, coal heating value, plant efficiency, capacity factor, water use, emission standards, air quality guidelines and Bay siting limits. The number of constraints in the model varies with the number of cells included in the analysis. For this application only 169 cells survived manual screening. This resulted in a linear program with 886 constraints, one solution of which (with a starting basis) required between one and three minutes on an IBM 360/91 computer, using the IBM-MPSX package. Because it utilizes linear programming, the model locates generating capacity in a continuous fashion. Therefore, the amount of capacity located in a given cell normally does not correspond exactly to a typical “real-world” unit size. or even a multiple thereof. This problem becomes most troublesome in those instances where the model-sited capacity is much less than the smallest practical unit size. For the relatively low-growth scenario used in the initial exercise of the model, 83% or more of the 50GWe capacity was sited in “plant sizes” of 0.5 GWe or greater in all cases studied. The resultant number of locations was always between 23 and 30, with plant sizes ranging from 0.5 to 4 GWe, the assigned upper limit. The remaining Table 1. Parameter values Parameter

Value

Equation

10GWe

6 6

10GWe BTU 8900KWH HEATVL CAPFAC ;

D E*

12250E LB 1 0.10 0.15 PPMS02 2’52x 1°-6(LB/HR)S02 lo 680(LB/HR)SOz GWe

Yj

0.5

%

1

11,14 12 IS 15 15 18

*E is based on the assumption that coal plants emit SO*at the rate allowed by the Federal New Source Performance Standard of 1.2LB per million BTU. All State standards agree with this except Delaware’s which is 0.8 LB per million BTU. Accordingly, Delaware’s E was 7120(LB/HR)SOdGWe.

App~i~tion of a m~l~iobjectivefacility location model to power plant siting

I17

portion of the 5OGWe (always less than 17%, and as low as 2%) was distributed in small sizes (0.015-0.499 GWe). Further improvement in the small unit problem could be effected by further aggregation of the smaller load centers. The use of mixed-integer programming would completely eliminate the problem by forcing the unit sizes to be uniform and realistic. The usefulness of both of these approaches will be explored in future work. In Figs. 3 and 4, location maps are presented which corresponds to optimal solutions for the transmission, and population objectives, respectively. Only those locations with 0.5 GWe or greater are plotted; the remaining 2%-17% of the total sited capacity (see preceding paragraph) was ignored; it could be allocated among the mapped locations, if desired. There is little loss of information from ignoring this small, scattered percentage of total capacity, and the relatively uncluttered maps are more easily used for analyzing location patterns. Notice in Fig. 3 that the plants are clustered near the cities (load centers) of the region, while in Fig. 4 the plants are farther away from the cities and are larger, to minimize population impact. Location maps similar to Figs. 3 and 4 were also generated for the optima of the coal and reservoir objectives and for intermediate noninferior solutions. Such solutions were presented to decisionmakers during workshops held in the six states of the region, and the following preliminary generalizations about the objectives emerged: (1) Minimizing MWMIS was seen by the utilities as a viable surrogate for the costs associated with bulk electric power transmission at this gross geographic scale, and should be afforded a high weight. (2) Minimizing TONMIS was not seen as a strong locational determinant, but it does play a role in some cases; (3) Minimizing required flow augmentation was favored by State officials and river basin commissions; (4) There was no discernible desire to minimize population proximity beyond the NRC guidelines. In an additional effort to gain insight into the relative importance of objectives, the model-produced locations were compared with regional utility expansion plans. The modelgenerated solution showing the best agreement with utility plans from Ref. [17] is presented in Fig. 5. This solution can be produced by assigning relative weights of 2.1, 1.0, 0.1, and 0 to MINRES, MWMIS, TONMIS, and POP, respectively. The solution was actually found by constraining all objectives except MWMIS to arbitrarily selected upper bounds; the weights correspond to the dual variables associated with each objective constraint. Over two-girds of the model-generated locations in Fig. 5 are within three cells (a m~imum of about 50 miles) of an actually planned unit; 70% of these are of the same type (coal or nuclear) as the planned units, In six cases, the model located capacity in cells containing planned units; four of these also matched by fuel type. It is reassuring to note that the solution of Fig. 5 also corresponds with the generalizations obtained in the workshops; that is, ~n~zing Bow au~entation and transmission are important objectives, while minimizing coal shipment is much less important, and minimizing population proximity (beyond NRC guidelines) is not considered at all. GRAPHICAL

REPRESENTATION

OF THE NONINFERIOR

SET

Due to time limitations, only a very coarse approximation of the noninferior set (NIS) was generated. The constraint method was used15 and 61 to generate tradeoffs between the transmission (~MIS) and coal shipment (TONMIS) objectives for several fixed values of the population proximity (POP) and flow augmentation (MINRES) objectives. In all, 24 solutions were generated, spanning the extremes of the four-dimensional NIS. In this application, the actual objective values were not of great interest, since they are only rough surrogates for supposed locational influences. Figure 6 shows four “slices” of the four~imension~ NIS corresponding to the four combinations of the population and transmission objectives-(POP, MINRES) = (26.4, 1150), (26.4,0), (5, 1150), (5,O). Figures 7 and 8 are slices orthogonal to the plane of Fig. 6 represented in Fig. 6 by the dotted line passing through point A. The solution, mentioned previously, which most clearly matches utility plans is represented by point A in all three figures. The large

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Application of a multiobjective facility location model to power plant siting

5ooo k

Point A corresponds to the solutlon depicted in Fiq.5

1000

5000

3000

Fig.

9000

7000

TONMIS

(millions

of

11000

ton-miles

13000

15000

per year)

6. MWMIS vs TONMIS for two extreme values of POP and two extreme values of MINRES.

2500

2000

I

I

-

3 .:

To”‘-lo2og,

5

f g

.H

1500

-

\

,o

\

” I 5 I

,%,,==26.q

‘4

\ 1000

500

-

L

0

I ..-_-__I_ 1500

1000

500 MINRES(cubic

feet

per

second)

Fig. 7. MWhUS vs MINRES for fixed values of POP, TONMIS. CAOR Vol. 7. No. I-2.4

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1000 -

I

I

I

I

I

0

5

IO

15

20

25

POP (millions

30

of people x gigawatts)

Fig. 8. MWMIS vs POP for fixed values of MINRES, TONMIS.

dotted lines in each figure represent weighted objective function contours through point A; the slope of this line is the negative reciprocal of the ratio of the relative objective weights associated with solution A. The slopes are:

d(~MIS) = 0.1=_. d(TON~S)

1.0

4MWMW _ 2.1= d(MINRES)

1.0

1

(Fig. 6)

f

(Fig. 7)

.

2

*

d(M.WMIS) 0 d(POP) = -1.0 = ’

(Fig. 8).

The coarseness of the NIS approximation shown here precludes a final judgement about the stability of the solution relative to changes in the weights. From Fig. 6, it appears that large changes in the relative weights on MWMIS and TONMIS (and thus large changes in the slope of the weighted objective function contour) would not change the solution from point A. However, a finer rendering of the NIS would show more solutions in the neighborhood of point A. The resulting corner at A would be less sharp, and less change in objective line slope would be required to move the soIution away from point A.

CONCLUSfONS

A mode1 has been developed which locates variable amounts of electric generating capacity in a six-state region. The model is suitable for extension to other geographical regions. Initial test runs produced variable location sets which reflected postulated locational influences and subjective evaluations of their importance, The locational influences and importance evaluations were obtained in part through interactions with regional decisionmakers. More input from decisionmakers and a more realistic assessment of the most important parameters are necessary before the model output can be considered dependable.

Application of a multiobjective facility location model to power plant siting

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The model is a flexible tool for policy analysis. Among the issues that may be analyzed with the model, in addition to the problems of plant location mentioned previously, are air pollution control policies, limits on water withdrawal and variations in federal guidelines on population proximity to nuclear power plants. Certain modifications of the model may be required for these policy analyses. The locations generated by the model are not suitable for plant siting purposes. The model is designed to yield consistent location patterns which are physically feasible and which reflect regional values as much as possible, for use in studies assessing the cumulative environmental impact of energy supply scenarios. Acknowledgements-The work upon which this paper was based was supported by the Electric Power Research Institute, Inc. (EPRI). EPRI makes no warranty or representation, express or implied, with respect to the accuracy, completeness, or usefulness of the information contained in this paper, or that the use of any information apparatus, method, or process disclosed in this paper may not infringe privately owned rights; nor does EPRI assume any liabilities with respect to the use of, or for damages resulting from the use of, any information, apparatus, method or process disclosed in this paper. The authors wish to acknowledge the contribution of Dr. Peter Meier, Brookhaven National Laboratory, in providing the population projections used in this study. The authors also wish to thank an anonymous reviewer for many helpful comments.

REFERENCES 1. Batelle Pacific Northwest Laboratories Report, Regional Analysis of the US Electric Power Industry, Vol. l-6, BNWL-B-415,Richland, Washington, July (1975). 2. M. Carasso, J. M. Gallagher, K. J. Sharma, J. R. Gaylor and R. Barany, The Energy Supply PIarming Model, Vol. 1and 2, Bechtel Corporation, San Francisco, California, NTIS Nos. PB-245382and PB-245383(1975). 3. E. A. Cherniavsky, Energy systems analysis and technology assessment program. Topical Rep. BNL 19569, Brookhaven National Laboratory, Upton, New York (1974). 4. M. Derthick, Between Stare and Nation. The Brookings Institution, Washington, DC. (1974). 5. J. L. Cohon, Muhiobjectiue Programming and Planning. Academic Press (1978). 6. J. L. Cohon and D. H. Marks, A review and evaluation of multiobjective solution techniques. Water Resources Res. (1975). 7. Applied Physics Laboratory, The Johns Hopkins University, A Regional Pilot Study for the National Energy Siting and Facility Report. CPE-043, Laurel, Maryland (1976). 8. R. L. Church and J. L. Cohon, Muhiobjectiue Location Analysis of Regional Energy Facility Siting Problems. BNL 50567,Brookhaven National Laboratory, Upton, New York (1976). 9. P. Meier, B. Hobbs, M. McCoy and R. Stern, The Brookhaven Energy Facihfy Siting Model, Brookhaven National Laboratory, Upton, New York (1978). 10. B. E. Rifas and S. J. White, Coal transportation capability of the existing rail and barge network, 1985and beyond, EPRI EA-237, Final Rep. Electric Research Institute, Palo Alto, California (1975). Il. Battelle Pacific Northwest Laboratories Report, Regional Analysis of the U.S. He&c Power Industry. Volume 4A, Coal Resources in the United States, Report BNWL-B-415,V4A, Richland, Washington (1975). 12. Nuclear Regulatory Commission, Nuclear Energy Center Site Suruey--1975, Part V, Resource Availability and Site Screening, NUREG-0001, Part V of V, Washington, DC. (1976). 13. National Academy of Engineering, Engineering for the Resolution of the Energy-Environment Dilemma. Washington, D.C. (1972). 14. U.S. Geological Survey, Surface Water Supply of the LIniredStates, 196&65.Reston, Virgina (1971). IS. Applied Physics Laboratory, Probable distribution of effluent sources from energy supply and conversion. The Johns Hopkins University, Final Rep. CPE-7701, Laurel, Maryland (1977). 16. Battelle Pacific Northwest Laboratories, Regional Analysis of the U.S. Electric Power Industry. Volume 4B, Coal Supply Function, Rep. ENWL-R-415, Richland, Washington (1975). 17. Federal Energy Administration, Inventory of Power Plants in the United States, FEA/G-77/202, Washington, D.C. (1977).