t·
ESTIMATION OF AGGREGATE MILES OF
EHV TRANSMISSION LINE NEEDS
L. C. Markel
Report
#MIT-EL 73-011
August 1972
ENERGY LABORATORY
The Energy Laboratory was established by the Massachusetts
of Technology
as a Special
Laboratory
of the Institute
Institute
for research
on
the complex societal and technological problems of the supply, demand
and consumption of energy.
Its full-time staff assists in focusing
the diverse research at the Institute to permit undertaking of long
term interdisciplinary projects of considerable magnitude.
For any
specific program, the relative roles of the Energy Laboratory, other
special laboratories, academic departments and laboratories depend upon
the technologies and issues involved.
Because close coupling with the nor-
.mal academic teaching and research activities of the Institute is an
important feature of the Energy Laboratory, its principal activities
are conducted on the Ins'titute's Cambridge Campus.
This study was done in association with the Electric Power Systems
Engineering Laboratory and the Department of Civil Engineering (Ralph
M. Parsons Laboratory for Water Resources and Hydrodynamics and the
Civil Engineering Systems Laboratory).
ABSTRACT
Regression analysis is used to develop models for the
total number of miles of EHV line needed in a power system.
These models are not meant to be used to design a transmission system but to examine existing EHV systems to see
if general patterns or relationships exist on a systemwide basis.
The U.S. was divided into regions and data on-regional
load and generation characteristics was obtained for the
years 1960, 1970, 1980, and 1990. Regressions were performed
on this combination cross-sectional and time-series data to
develop equations for circuit miles of EHV line and for
gigawatt-miles (miles of line X power-carrying capability)
of EHV line. t- and F-tests were used to determine the
statistical significance of the model parameters.
The independent variables (system characteristics)
found to be most significant in determining the miles of
EHV line include the generating capacity of the system,
the area (square miles) of the region, the percent of area
that is metropolitan, the number of generating plants in
the system, the percent of energy used for industrial
purposes, the percent of generating capacity which is hydroelectric, and the average distance between plants and load
centers.
-The equations developed are multiplicative, of the
form miles of line = KF X , where the Xi's are system
characteristics. "Expansion" models attempting to determine
the additions to the existing grid in a 10 year period were
also postulated. However, they are not as statistically
significant as the "static" models.
Methods of using the models to investigate new plant
siting strategies, such as power parks or offshore nuclear
plants, are discussed. Analysis of the effect of trends
in plant siting and construction, such as the growing
scarcity of potential plant sites near load centers,
is also mentioned. The limitations, uses, and possible
extensions of this type of model are also described.
ACKNOWLEDGEMENTS
I would like to express my appreciation to Professor Fred Schweppe who
supervised this work, for his support and guidance.
As well as by giving
suggestions and criticisms, he was invaluable in helping to put things in
their proper perspective, and it was a pleasure to work with him.
I'd also like to thank Dr. Martin Baughman for his advice with the
statistical and econometric aspects of this research.
Discussions with
him were always a great help.
The work described in this report was partly supported by a National
Science Foundation Grant(#GI-34936) as part of a research program at MIT
entitled "Dynamics of Energy Systems".
The report essentially constitutes a master's thesis submitted to
the Electrical Engineering Department.
Marilyn Pierce and Karen Keefe
spent many hours typing this thesis andi good-naturedly met deadlines and
made last minute changes.
TABLE OF CONTENTS
Abstract
Chapter
1:
Chapter 2:
Introduction
Data Used in Models
A. Division of the U.S. into Regional Systems
ndependent Variables for the Model
B. Selecting
6
12
12
14
Chapter 3:
Model Development
22
Chapter 4:
Limitations of Regression Models
64
Chapter 5:
Applications and Uses of Models Developed 71
Chapter
Conclusions
6:
Appendix I:
Description of EHV Transmission Line
Appendix II: Data: Description and Sources
EHV Grid Size
Appendix V:
79
82
Graphs of Generating Capacity vs.
Appendix III:
Appendix IV:
76
Regression Results
Determining the Significance of Model
92
113
135
Parameters
References
1443
Figures
145
Tables
148
Bibliography
161
-6-
CHAPTER
1
Introduction
With the demand for electricity growing at about
8% a year, the number of generating facilities and transmission lines to deliver this power to the users must also
grow accordingly.. As the number of plants and transmission
lines increases, and as the environmental protection
constraints on new construction become stricter, it is
becoming harder to site new plants and lines.
In any attempt to predict, model or plan the growth
of an electric power system, the characteristics of the
associated bulk transmission system are an important
factor.
A transmission system is shaped by the social,
economic, and political constraints of a region as well
as by load carrying, system stability, etc. constraints.
Urban areas, the load centers, are already overcrowded.
Land is at a premium, with both the economic and social
costs of clearing the right-of-way becoming larger.
New plants tend to be larger and farther from the
load centers.
Air quality standards make it difficult
to locate a large fossil steam plant near a city.
opinion is not
amenable to nearby nuclear plants.
Public.
Water
requirements can often only be met, especially for pumped
-7-
hydro plants far from a city.
This requires even more
high voltage line, often in wilderness, forest or parkland areas.
While a cleared right-of-way does have some
multiple purpose uses, such as bridle paths or bicycle
and hiking trails, it usually has significant adverse
aesthetic and environmental effects.
(A desciiption
of the costs and land requirements for EHV lines is found
in Appendix
I and Tables
1 and 3.)
Thus, an estimation of the additional line
requirements for various 10 or 20 year expansion
strategies could be useful in system planning.
This
study's purpose is to predict the miles of EHV transmission line needed to meet the growth of the electrical
system of the U.S.
type is to
One use for an explicit model of this
analyze the effects of different plant
siting or generation mix strategies or the growing scarcity
of new plant sites on the expansion of the transmission
grid.
Transmission line siting is a complicated trade-off
of engineering, economic, right-of-way, and environmental
considerations.
In a report to the FPC by the Advisory
Committee on Reliability of Electric Bulk-Power Supply,
the following recommendations on the design of bulk transmission networks were made: 1
-8-
1.
Maintain proper relationship between size and
capacity of all system elements, or between systems.
2.
Plan for adequate margins of transmission
reserve capability through EHV lines.
3.
Avoid excessive concentration of transmission
capacity on a given right-of-way.
4.
Maintain adequate interconnections among systems.
5.
Avoid concentration of critical circuits at sub-
station switching facilities.
6.
Use relay schemes of least complexity that pro-
vide the required protection with the
in the event of faulty
7.
least
hazard
operation or testing.
Examine proper transmission network contingencies
when investigating system performance.
These principles are not all quantifiable.
They involve
determining minimum levels of acceptance and involve many
trade-offs, especially economic.
The general models
developed here are not meant to locate lines on an individual basis or to take the place of the system planner
in planning grid construction.
Rather, this study attempts
to determine whether the present techniques used in planning
the transmission grid on a line-by-line basis can be
generalized or aggregated to give some system-wide conclusions, characteristics, or "rules of thumb".
The purpose
-9-
is to predict the number of transmission line miles, based
on such more easily predicted and measured qualities as
the generating capacity of the system, the physical area
covered by the system, the number of major load centers,
etc.
"EHV' line" for this study is taken to be line
at 230 KV and higher.
The years examined are 1960, 1970,
and projections for 1980 and 1990.
1955 to 1960 saw the
start of the present rapid growth in EHV line, with developing technology leading to the opening of the first 500 KV
line in 1964 and the first 765 KV line in 1968 (see figure
1).
Research on higher voltages is underway.
Although
costs and land requirements of line construction increase
with rated voltage, the power carrying capacity grows
even faster, roughly as the square of the rated voltage.
(See table 1 and Appendix I)
Thus, the models developed
here estimate two quantities:
the circuit miles of EHV
line (CM), and the power-carrying capability, or gigawattequivalent miles (EM), of a grid.
To develop a model of grid size, equations relating
miles of line to various system characteristics were
hypothesized.
Using multiple linear regression, the para-
meters -for the equations were estimated and t- and F-tests
-10-
(Appendix V has a description of these statistical
tests) were used to measure the statistical significance
of each parameter.
Those parameters which were found to
be statistically significant were incorporated in the
final model.
Those found not to have a high level
significance (i.e., the null hypothesis, that the coefficient of that parameter equals zero, could not be rejected)
were dropped from the model.
For each region of the country, data for the years
1960 and 1970, and Federal Power Commission projections
for 1980 and 1990 were taken as observations for the
regression.
Data from all four years could not be used
in each regression since it was not always available,
especially for the year 1960.
Chapter 2 and Appendix II describe the data used
for the models.
Chapter 3 gives the models developed.
(And Appendix IV contains some of the results of regressions on previous models leading up to the final ones.) It
was found that equations with a fairly simple structure:
Miles
of line =
K-r
Xi
a
X i = independent variables
gave good results.
Onlyacomparatively small number of
independent variables were needed to estimate the miles
of line to within 25% accuracy.
Generating capacity,
-11.physical area of a region, average distance between plants
and load centers, and per cent of metropolitan area were
found to be the most significant parameters.
Also, some models concerned explicitly with system
expansion were hypothesized and tested.
The results,
however, were a good deal less encouraging, and no
acceptable expansion models were developed.
From the first type, or "static,"models, some
generalizationScan be made regarding system growth
in the light of current trendssuch
as the increasing
rarity of sites, and for possible new siting strategies,
such as power parks.
Some of the results, and the limita-
tions, of the models developed are discussed in Chapter 4.
-12-
CHAPTER
2
Data Used in Models
A.
Division of the U.S. into Regional Systems
The entire country is interconnected; but, for the
purpose of this study, the U.S. can be viewed as a number
of fairly independent electrical regions connected by tie
lines.
Possible divisions are by power pools, FPC power
supply areas, reliability councils, census regions, etc.
The six FPC national power survey regions are used
in this study rather than the 50 states, since dividing
the U.S. into 50 states would result in areas too interdependent.
North Dakota, for example, has an extensive
230 KV network, but it is used to ship power out of the
state, to places such as Minneapolis.
Similarly, large
pumped hydro projects being planned in Maine or New
Hampshire are to be used to meet the peak of the Boston
area.
The FPC national power survey regions(figure 2)
closely follow the boundary lines of the reliability
councils (figure 3) of the country in most cases.
The
utilities comprising a reliability council cooperate in
system planning and dispatch, so they are fairly good
divisions of the country into electrical systems.
-13-
Of course, some of these regions are much more closely
bound than athers.
Region II, the East Central region,
follows the boundaries of ECAR, and it is a very closely
interconnected region.
Region IV, the South Central region,
includes ERCOT, which is practically unconnected with the
rest of the country, as well as the Southwest Power Pool.
The West region (region VI) combines the dissimilar areas
of the mountain states, a large, thinly settled region, with
the thickly settled, electricity-intensive Pacific states.
The Northeast region (region I) contains three smaller
power pools, New England Power Pool (NEPOOL), New York
Power Pool, and P-J-M (Pennsylvania-New Jersey-Maryland).
Because data for each of these smaller, well-defined regions
was available, the Northeast was divided into New England,
New York, and PJM for this study.
Since in the regression
models the Northeast then counts as 4 points (Northeast,
New England, New York, and PJM), the models' coefficients
and parameters are biased toward the northeast. However,
the three northeast subregions were used mainly to help
in model development, to decide which variables of the
models were statistically significant.
Also, the three
areas, while all are thickly settled, have many differences
in other system characteristics.
To develop a model, nine regions were used, the Northeast (NE), New England (ND), New York (NY), PJM (PJ),
the East Central (EC), the Southeast (SE), the South Central
(SC), the West Central (WC), and the West (W).
regions are shown in figure 2.
These
Data for these regions was
taken for the years 1960 and 1970, and FPC projections
were used for values for 1980 and 1990.
The projections
are valid data points as long as they are self consistent.
Knowing that, for instance, the East Central region will
require 58 new plants and 11508 more miles of EHV line by
1990 to meet a peak demand of 148,000 MW is valid as data.
If the peak in 1990 turns out to be 160,000 MW and construction delays result in only 50 new plants and of a different
generation mix than was originally planned, then obviously
the additional mileage needed might not be 11500 miles.
As
the system characteristics change, so do the transmission
needs.
The projections are accurate if, (if the projection
describes a viable system) should all the other projections
be fulfilled, the transmission grid size is as predicted.
B.
Selecting Independent Variables for the Model
Regression is used to determine the relationship
between one variable, the "dependent" one, and other variables
-15-
it is correlated with, the "independent" variables.
However,
correlation between two numbers does not necessarily prove
that a casual relationship exists between them.
In choosing
regional characteristics'as independent variables, an effort
was made to choose those which logically should
EHV grid size.
influence
The number and location of a region's load
centers is probably more of a determinant of the transmission network of that region than vice versa.
The load
characteristics can also be predicted fairly independently
of the planned electric generation and distribution system.
This independence, of course, is not always found.
Thus,
in predicting the number and location of future plants
and the reserve requirements of a system, implicit assumptions and decisions about the transmission system must be
made.
Nothing, of course, works out perfectly, so the
real world never matches exactly a mathematical model.
Some
interactions of the actual system can not be easily modelled.
Some obvious problems can be avoided, however,
The
circuit miles of line in a grid would no doubt prove to
be highly correlated with the number of transmission towers
in the system.
Telling a system planner that if his system
has "x" towers, it will require "y" miles of line is not
helpful, since he is more apt to estimate the second number
by first estimating the first.
The causal effect is clearly
reversed in saying "y" is a function of "x", but a correlation coefficient can not indicate thp.t.
The less obvious interactions are the ones which
in effect provide "spurious" correlations, since few
people would attempt to try to predict the line mileage
needed by the number of transmission towers planned to be
built.
In a model, a strong correlation may exist between
the.percent of generating capacity that is nuclear and
the miles of transmission line.
However, this might simply
be a coincidence, since developing nuclear technology,
stricter air quality standards, and fossil fuel shortages
are presently leading to a larger nuclear portion of the
generation mix.
At the same time, there is a trend towards
stronger transmission networks and greater interconnection.
Those regions increasing interconnection the most may also
be installing more nuclear plants.
The two trends may be
coincident but not related, and if for some reason no new
nuclear plants were constructed, the grid size might not
grow very differently from the present predictions.
Again,
a correlation coefficient does not imply causality.
Causality can be inferred only from knowledge of how
the system is planned.
Thus, fear of nuclear accidents
may necessitate locating nuclear plants farther from cities
than fossil installations, requiring more transmission line.
-17-
In this case, a correlation, and a causal relationship,
between the portion of generation that is nuclear and the
transmission requirements is to be expected.
In actuality,
a correlation in the model may represent a combination
of causal dependence, coincidence, and a third, often unquantifiable, factor or interaction.
There is no sure way
to separate one from the other.
Appendix II lists the independent variables investigated as possible components of a transmission model.
It also states the source of the data and reasons for investigating each variable.
Data for 1960 and 1970 and projections for 1980 and
1990 were compiled.
Some data for 1965 is given in table 5
along with the 1960, 1970, 1980 and 1990 data, but 1965
data was not used in any of the regressions.
The dependent variables, the quantities to be estimated, were circuit miles of EHV line, (CM), and gigawatt-equivalent miles of EHV line, (EM).
For each voltage class
of line there is a scaling factor, proportional to the square
of the rated voltage, which indicates the power-carrying
capability of that line.
are given in table 1.)
EM =
Li
i
CM
(The load scale factors (L) used
The derivation of EM is
i = 230 KV, 345 KV, 500 KV, 765 KV
-18-
The independent variables used to develop the models
were:
Symbol
Variable
A
area; the physical size (in square miles)
of a region
the generating capacity of a system (in
G
gigawatts)
the number of generating plants with a
p
nameplate capacity of 400 MW or above
LC-500
the number of load centers with a peak
and
demand of 500 MW or over and 1000 MW
LC-1000
or over
the percent of delivered power used for
I, R, and C
industrial, residential, and commercial
uses
F, H, and N
the percent of generating capacity which
is fossil fueled, hydroelectric, and
nuclear
FnewHnew
and
new
the percent of generating capacity built
within the last 10 years which is fossil
fueled, hydroelectric, and nuclear
METRO
the percent of land area included in
metropolitan areas
APL
the average plant to load center distance
between plants of 400 MW or over and load
centers of 1000 MW or over.
-19-
TPL
the total plant to load center distance
TPL = P
APL
NAPL and
APL and TPL for new plants, built within
NTPL
the last 10 years
OAPL and
APL and TPL for old
OTPL
10 years previously
AAPL
adjusted average plant to load center distance
AAPL 19 8
AAPL1 9 9 0
=
plants, built over 10
1 9 xAPLPL
7
ApL
APL 1 9 8 0
AAPL1 9 8 0
APL1 9 9 x
OAPL1990
APL
The purpose of this study was to predict EHV line
).-
needs on the basis of more readily predicted system
characteristics.
Therefore, the independent variables
picked were objective and easily computable and quantifiable.
Other system characteristics such as reliability also may
have a major influence on the size of the EHV grid.
It
would be very useful to be able to include a reliability
value in the model and thus determine explicitly the
tradeoff between reliability and grid size.
However, there
is no agreed-upon measure of a transmission system's
reliability, and little system-wide data on reliability is
available.
The number of customers per year who experience
-20-
an interruption or degredation (as in voltage reduction)
in service due to lack of adequate transmission facilities
is simply not an available datum.
Some characteristics are unquantifiable; environmental
constraints are an example of this.
Air quality standards
may result in more plants located far from the urban load
centers.
Court decisions on licensing may delay nuclear,
pumped storage, or transmission line construction, resulting in an increase in gas turbines on sites near the existing
grid.
However, a variable such as "maximum allowable S02
emission" or "average lead time for new plant construction"
would not be very practical.
Aside from the difficulty
in projecting federal standards or court decisions, the
impact of these "unquantifiable" developments is not known.
Strict air quality standards could lead to the use of low
sulphur fuels, the development of better air scrubbers, the
location of new plants further from cities, the encouragement of nuclear and pumped hydro technology or, more probably,
a combination of all of these.
Thus, the effect of stricter
environmental statutes on plant size, location, type and
number should be predicted, and the resulting effect on
EHV grid size can be determined from changes in these
parameters.
-21-
For ease in handling the data, data was divided by
various factors of 10 so that all variables would be of a
magnitude comparable to 10.
Thus,
or instance, per-
cents were actually expressed as "10's of percents" for the
regression
(58.6% would become 5.86).
Generating capacity
It
was expressed as "10's of gigawatts; miles of line was
expressed as "thousands of miles of line", etc.
scaling factors are given in table 6.
These
-22-
CHAPTER
3
Model Development
The purpose of this study was to estimate the total
number of circuit miles (CM) and gigawatt miles (EM)
of EHV transmission line in a system.
In general, miles
of line, M, is given by:
f (X1, X 2,
M
(1)
X i)
where the X's, the independent variables, are the system
characteristics,
G, A, F, I, METRO,
of this paper.
Chapter 2
APL, etc. listed
in
It was assumed that the general
model was multiplicative, that is:
M = eK '
i
(2)
fi (Xi)*
Each factor of the equation may be a function of several
variables, however:
fi = fi (Xi, X 1 ,' X 2,
..
)
The general model assumed was:
fi
=
X
o +
(aX)
(3)
To develop a workable model, an equation was postulated,
its parameters (K, b's, and a's) estimated by multiple
linear regression, and the statistical significance of
* eK was used as a constant instead of simply "K" for
ease of notation, since the logrithm of this equation
was used in the regression.
-23-
those parameters determined in order to include only
relevant variables in the final mode'.
Because linear regression was used, the general
model of equations (2) and (3) could not be used
immediately.
The number of possible parameters (a's and
b's) to be estimated was too large.
Also, in addition to
developing an accurate model, it was desired to include
as few independent
variables
as possible.
(Using
30
independent variables to estimate 36 values of M would
be highly suspect.)
Thus, the first equations examined were much simpler
than (2) or (3), while still within their general framework.
The IBM Scientific Subroutine Package
to perform the regression.
was used
The SSP programs also computed
t- and F-statistics in order to test the significance of
the estimated parameters.
tests
and their
A description of the t- and F-
meaning is given in Appendix V. These
tests were used to "weed out" the unrelated or nonsignificant
variab les.
While t- and F-tests may reveal whether a variable is
"significant" or not, a user of a regression model is also
interested in "how far off" the model
can be.
Thus, in
-24addition to using critical points in the t- and F-tables,
the percentage of error (l-predicted value/actual value)
for each region was computed.
The results of regressions done on some preliminary
models are given in Appendix IV.
The first type of model examined is a straight
multiplicative model of the form:
M= e
rX,
K.
ai
(4)
i
Logrithms were taken of both sides in order to perform
a linear regression:
in M = K +
ai
(5)
rn Xi
i
After eliminating non-significant variables (see Appendix
IV), the resulting equations are:
K
al
a3
a
a5
a 6 AAPLa 7
(6)
and
E MA 1
eK
E M= e A
G
2 METRO 33
METRO
AAPL
APL
The coefficients, statistics, and predictions of these
(7)
-25models are given in tables 3-1 and 3-2.
of the a's are as we would expect;
The signs
M is directly pro-
portional to A, I, G, METRO, H, and APL and inversely proportional
1.
to P:
The greater the physical area (A) a system serves,
the more line is needed to "cover" it.
2.
A larger percentage of industrial use (I) indicates
a concentration of demand in specific areas.
Higher
capacity line is needed to bring power to industrial than to
residential areas.
Conversely, the coefficient for
residential use, R, is negative.
(See Appendix IV,
Table IV-2.) (R and I are strongly correlated, so
both could not be used in the same equation.
Tables
IV - 3 & 4)
3.
The greater the generating capacity (G), the
more power has to be transported and the greater the
grid size needed.
4.
Metropolitan or urban areas (METRO) have greater
load concentrations than rural areas, so we would
expect the same relationship as in "2" above.
5.
Hydroelectric plants (H) are usually located
relatively further from load centers than steam
plants and thus require more line.
-26-
TABLE 3-1-A
CM - eK Aa
l
pa2 Ia3 Ga4 METROaS Ha6 AAPLa7
Degrees of freedom (Df)*:
7/17
Regions
(NE, ND, NY, PJ, EC, SE, SC, W) 70,
80, 90
Years used (R & Y):
(WC) 70
F-Statistic/Significance (F)*: 67.51/.01
Average % Error (AE):
Coefficient
K
Value (V)
15.6%
Standard Deviation (S)
t-value'
-1.946
a1
.583
.113
5.16/.01
a2
- .471
.280
1.68/.2
a3
1.325
.480
2.76/.05
a4
.756
.218
3.47/.02
a5
.566
.188
3.01/.05
a6
.223
.100
2.23/.1
a7
.341
.157
2.17/.1
* See Appendix V for definition of these terms.
(t)
-27TABLE 3-1-B
CM
Region
Actual Value
CM
Fitted Value
% Error
NE 70
7,452
6,502
13
NE 80
10,855
10,935
1
NE 90
15,610
14,326
ND 70
1,397
12,140
13
ND 80
2,580
2,608
1
ND 90
3,370
3,585
6
NY 70
1.600
1,981
24
NY 80
2,310
2,869
24
NY 90
3,595
3,480
3
PJ 70
4,455
3,832
14
PJ 80
5,965
6,070
2
PJ 90
8,645
7,673
11
EC 70
6,160
6,881
12
EC 80
13,730
11,661
15
EC 90
17,030
18,148
7
SE 70
7,160
10,417
46
SE 80
21,770
16,360
25
SE 90
30,340
25,746
15
SC 70
5,700
6,699
18
SC 80
12,780
14,311
12
SC 90
18,270
24,674
35
WC 70
8,770
6,149
30
W
70
29,280
28,355
3
W
80
42,910
37,455
13
W
90
51,970
.60,372
16
-28-
TABLE 3-2-A
EM = eK A
G2
METROa3 AAPLa 4
4/20
Df:
(NE, ND, NY, PJ, EC, SE, SC, W) 70, 80, 90; (WC) 70
R&Y:
F:
62.39/.01
AE:
23.2%
V
S
t
K
-1.384
a1
.502
, .128
3.91/.02
a2
.708
1171
4.15/.02
a3
.582
.251
2.32/.1
as
.490
.214
2.29/.1
-29TABLE 3-2-B
Region
EM
Actual Value
EM
Fitted Value
% Error
70
3,124
3,653
17
NE 80
5,331
8,019
50
NE 90
13,104
14,845
13
70
618
442
28
ND 80
1,328
1,284
3
ND 90
2,467
2,443
1
NY 70
561
834
49
NY 80
987
1,606
63
NY 90
3,411
2,772
19
PJ
70
1,945
1,713
12
PJ 80
3,016
3,433
14
PJ 90
7,226
6,261
13
EC 70
5,550
3,325
40
EC 80
13,818
6,592
52
EC 90
17,058
1,170
31
SE 70
2,529
4,'234
67
SE 80
9,385
9,033
4
SE 90
16,154
16,755
4
SC 70
3,778
4,067
8
SC 80
8,260
10,166
23
SC 90
15,011
19,317
29
WC 70
3,232
3,062
5
NE
ND
W
70
11,996
10,956
9
W
80
22,608
18,656
17
W
90
31,946
34,409
8
-30-
6.
It is expected that the greater the average
distance between generation an'.load centers (APL),
the more line will be needed to transport power to
the load.
7.
The more plants there are (P) for a given G,
the more dispersed the generation pattern is.
Thus,
plants are more likely to be located near load
centers.
The independent variables used in the equations are
not all uncorrelated, however.
In general, the larger the
physical area, the more generation which one can expect
to find in that area.
Likewise, the larger A is, the
larger the plant to load center distance can be (APL).
A larger percentage of metropolitan area (METRO) could
indicate higher load concentrations, and thus more generating capacity.
Thus, A, G, METRO, and APL are all inter-
correlated.
In addition, many variables are correlated with
time.
The number of plants, the percent of nuclear capacity,
the miles of EHV line, the generating capacity, and the
number of load centers all increase with time.
The per-
centage of hydroelectric and fossil fuel generation is
declining with time.
The data for equations (6) and (7)
was for 9 regions of the country for the years 1970, 1980,
-31-
and 1990; thus it was both cross-sectional and time
series data.
In an attempt to determine whether the
same variables were significant on a purely cross-sectional
bgis,
regressions using data for only a single year were
done.
(See Table IV-1-A.)
Some results are given in
Tables IV-- to 12 and in Tables 3-3 to 3-6.
The cor-
relation between A, G, METRO, and APL, as mentioned before,
is apparent here, as equations
with
several of these
variables show different ones as significant in different
years.
Because there were only
8 or 9 data points for each
year, fewer variables were used.
The results of the
final year-by-year equation:
CM
=e
K
A
G2
a
E M
eK A
(8)
G
(8)
a
G
(9)
are given in Tables 3-3 and 3-4.
The results for 1960 were not very accurate and the
parameters not very significant.
This is probably be-
cause EHV line was just beginning to be a major power
carrier in 1960.
Before that, grids of 115 KV, 138 KV
and 161 KV handled most of the bulk power transmission
-32C14
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-33-
TABLE 3-3-B
Region
NE 60
ND 60
NY 60
PJ 60
EC 60
SE 60
SC 60
WC
W
NE
ND
60
60
70
70
NY
70
PJ
EC
SE
SC
WC
W
NE
ND
NY
70
70
70
70
70
70
80
80
80
PJ 80
EC 80
SE 80
SC 80
WC
W
NE
ND
NY
80
80
90
90
90
PJ 90
ES 90
SE 90
SC 90
WC 90
W 90
CM
CM
Actual Value
Fitted Value
2,130
266
371
1,393
2,221
1,318
143
3,417
13,962
7,452
1,397
1,600
4,455
6,160
7,160
5,700
8,770
29,280
10,855
2,580
2,310
5,965
13,730
21,770
12,780
14,780
42,910
15,610
3,370
3,595
8,645
17,030
30,340
18,270
22,060
51,970
2,385
2,436
474
618
2,117
2,437
1,544
1,293
3,333
7,274
1,445
1,928
2,594
6,912
9,773
9,384
8,581
16,761
13,191
2,548
2,675
4,437
12,416
19,554
20,401
15,449
30,634
18,232
3,696
3,754
6,619
16,921
27,019
28,121
19,887
41,330
% Error
12
8
28
56
5
85
979
62
76
2
3
21
42
12
37
65
2
43
44
7
35
22
49
23
42
2
21
17
10
4
23
1
11
54
10
20
-34-
ri
o
('i -W
Ol
,n
,
r-I
all,
o
o
0
cC
tI
oj
I >I
.0
-H
'.
Un
it
%.D
*c
o
uI
,-4
C4
C-
H
co
0n
N
CV4
-t
0
o
C
'.0
*'
o
0
cn
I
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t
'.
.N
0
a
en
r
MC
C
r-
on
'T
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%D
CN
..
rHq
w0)
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N
1-
p-
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-
c
En
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t
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Nt~~~
CC
,
%D~~~
%
r-
rCS
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00
I.
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C14
0
W
P'4
-I
,-4
W
.
z 0
0
>1
0
D
'D
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C4
1;
U
. --4
Ir'4
-35-
TABLE 3-4-B
Region
NE
ND
NY
PJ
EC
542
60
60
60
60
60
1,189
SE 60
SC 60
324
38
WC
W
NE
ND
NY
PJ
EC
60
60
70
70
70
70
70
SE 70
SC 70
1J
EM
Actual Value
WC
W
NE
ND
NY
PJ
EC
70
70
80
80
80
80
80
SE 80
SC 80
WC 80
W 80
NE 90
ND 90
NY 90
PJ 90
EC 90
SE 90
SC 90
WC 90
W
90
67
117
358
874
3,599
3,124
618
561
1,945
5,550
2,529
3,778
3,232
11,996
5,331
1,328
987
3,016
13,818
9,385
8,260
8,384
22,608
13,104
2,467
3,411
7,226
17,058
16,154
15,011
16,423
31,946
EM
Fitted Value
786
61
141
185
673
731
396
324
886
3,556
587
845
1,166
3,320
4,728
4,312
3,903
7,966
7,651
1,234
1,330
2,336
7,092
11,518
11,715
8,542
17,843
14,639
3,106
3,285
5,754
13,360
20,284
19,819
13,854
27,044
% Error
45
8
20
48
43
126
942
63
75
14
5
51
40
40
87
14
21
34
22
1
16
26
10
10
60
5
29
12
26
4
20
22
26
32
16
15
-36-
and continued to do so through 1960, especially in the
Southeast and South Central regions.
Another "year-by-year" regression with very significant
parameters was
a
C M = eK G1
a
(10)
APL2
aI
K
a2
(11)
E M = eK Gal APL
Equations (10) and (11) could tell a system planner more
about how his decisions will affect the system, as APL
is a variable dependent on plant siting policy while A
is a constant.
However, A and APL are obviously cor-
related with each other, as regressions using A, G, and
APL gave much poorer results than equations(8) - (11).
This makes sense,
(Tables IV-9 and IV-l0,for example)
since in regions of larger area, the distance between
plants and load centers can be larger.
Equations (8) and (9) were also used as a model for
the cross sectional and time series data.
While the
parameters were significant, two variables were not sufficient to estimate the 25 "regions" used with accuracy
comparable to equations (6) and (7).
(See Tables VI-5
and IV-6.)
_
I_
I
_____._____
-37-
0
Ln
a
0
o
4J-
I
P4
*
O0
0
Z
I
,
,I
I
Li-'
Fn* U)
Ln H
\
C-O
00
¢Q ^ O
I.
e o ^
ee
eeLl~
e
e
Ln
z
VI
o
L
oo
Lfl
aONi
c
O-..
4
I
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£
HI
0
co^w
_44 >
U
<
o
U
-38-
TABLE 3-5-B
CM
Region
Actual Value
CM
Fitted Value
% Error
NE 70
7,452
7,032
6
ND 70
1,397
1,552
11
NY 70
1,600
1,417
11
PJ 70
4,455
3,849
14
EC 70
6,160
6,362
3
SE 70
7,160
9,104
27
SC 70
5,700
9,539
67
WC 70
8,770
6,802
22
70
29,280
21,420
27
NE 80
10,855
16,622
53
ND 80
2,580
2,886
12
NY 80
2,310
1,965
15
PJ 80
5,965
5,884
1
EC 80
13,730
12,766
7
SE 80
21,770
20,342
7
SC 80
12,780
18,556
45
W
80
42,910
23,672
45
NE 90
15,610
22,267
43
ND 90
3,370
3,776
12
NY 90
3,595
3,289
8
PJ 90
8,645
7,181
17
EC 90
17,030
17,673
4
SE 90
30,340
26,957
11
SC 90
18,270
24,774
36
W
51,970
34,222
34
W
90
-39-
cN
o
I
0o
-*
I
CS
H
1P
I
Z;W
W
o
o
,n
CO
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C~)I
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00
.l
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I
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0
Un
0
"Pc3i
U
0'
(N
^
Ho
H
ON
c
co
(Nr
(,
Lrn
co
.
H
r-
CO *q - IL;
a 0'
I
4-
I
zX
CS
aOo
C,
CN
CN
.\
[m
W
1.4
H
'.D9
aV
PC-
ko
I.
cn
C14
H sz V)
sr
4.1]
4^
I_4
U
Ch
rcoN
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C)
1-
(/2
(N
a
r(~~~~~/ 4;
Z
Cd
C
0
-4
w
cC
I
(/2J
9i
CO
H
o
(N
-41
o
ON
a\
0
H)
C4
H
1
I
Hi
0l.
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o
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cn~
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M4
t4
co
Cu
~ t Cu
-40-
TABLE 3-6-B
.Regions
EM
Actual Value
EM
Fitted Value
% Error
NE 70
3,124
3,358
8
ND 70
618
640
4
NY 70
561
608
8
PJ 70
1,945
1,711
12
EC 70
5,550
3,004
46
SE 70
2,529
4,373
73
SC 70
3,778
4,472
18
WC 70
3,232
3,150
2
70
11,996
10,474
13
NE 80
5,331
9,581
80
ND 80
1,328
1,409
6
NY 80
987
962
3
PJ 80
3,016
3,092
3
W
EC 80
13,818
7,227
48
SE 80
9,385
11,914
27
SC 80
8,260
10,670
29
80
22,608
13,839
39
NE 90
13,104
16,660
27
ND 90
2,467
2,914
18
NY 90
3,411
3,113
9
PJ 90
7,226
6,229
14
EC 90
17,058
13,946
18
SE 90
16,154
20,536
27
SC 90
15,011
17,624
17
W
31,946
22,163
31
W
90
- 41-
Models of the type of equations (4) and (5) were
used to narrow down the number of relevant variables,
resulting in equations (6) and (7).
With the number of
independent variables to be examined decreased, a more
general model, of the type of equations (2) and (3),
could be developed.
The single most significant
variable was the generating capacity, G.
This makes sense
intuitively, as the transmission system is laid out to
"serve" the generation system, to be able to deliver power.
Appendix III consists of graphs of miles of EHV line vs.
generating capacity for the 9 systems used in the
study.
A strong correlation between the two can be seen.
Thus, it would seem to make sense to talk of grid
size depending mostly on
G, (i.e., of the function
fG (equation (3)) "dominating" equation (2)).
The result-
ing equation is:
M = eK
(
ai
i
+ i
bi Xi
i
ig(G
(12)
or, taking logrithms to linearize for the regression:
Ln M = K +
E
iG
ai
n Xi +btn G +
i
b
(Ln G' Xi)
i
(13)
-42After eliminating the non-significant variables (Appendix IV,
Table
IV-1-B), the resulting equations were
C M = eK Aal APL a 2 Ga3 Ga4METRO
or
CM =eK
or
C M = e
and
or
A1 AAPL 2
K
M = e
E M = eK
A
a
A
al
AAPL
Ga3I
a2
°
G
AAPL2
AAPL
2
(14)
(15)
Ga4"METRO
3METRO
METRO
(16)
a 3 METRO
(17)
G3
(18)
GaMETRO
(The coefficients are given in Tables 3-7 to 3-11.)
Equations (14) and (15) give comparable accuracy.
Equation
(16) is slightly less accurate, but it uses one less
independent variable.
Similarly, equation (17) is only
slightly less accurate than (18), but it has 3 independent
variables while (18) has 4.
Once again, the coefficients
of A, APL, AAPL, G, I and METRO are all positive as
expected; each of these characteristics tends to increase
the amount of transmission line needed in a system.
The
results of each model are summarized in Tables 3-7, through
3-11.
TABLE 3-7-A
CM = eK Aal Ga2 APLa 3 Ga4METRO
4/20
Df:
72.01/.01
F:
20%
AE:
V
S
t
K
-.185
al
.490
.129
3.81/.02
a2
.424
.248
1.71/.2
a3
.510
.195
2.62/.1
a4
.105
.046
2.30/.1
-44TABLE 3-7-B
CM
Region
NE 70
NE 80
NE 90
ND 70
ND 80
ND 90
NY 70
NY 80
Actual Value
7,452
10,855
15,610
1,397
2,580
3,370
1,600
2,310
SE 80
3,595
4,455
5,965
8,645
6,160
13,730
17,030
7,160
21,770
SE 90
30,340
SC 70
5,700
SC 80
12,780
SC 90
18,270
8,770
29,280
42,910
51,970
NY 90
PJ 70
PJ 80
PJ 90
EC 70
EC 80
EC 90
SE 70
WC 70
W
70
W
80
W
90
CM
Fitted Value
% Error
7,410
1
12,709
21,286
17
1,414
1
2,368
3,673
1,526
2,363
8
36
9
5
2
4,026
12
3,020
5,176
32
13
8,089
6
6,833
11,531
11
20,100
18
9,525
33
15,100
31
22,891
10,756
15,775
24,286
8,785
24,202
26,140
44,977
25
16
89
23
33
0
17
39
13
TABLE 3-8-A
CM = eK Aal AAPLa2 Ga3I Ga4METRO
4/20
Df:
70.81/.01
F:
AE:
20%
V
t
K
.219
al
.639
.095
6. 73/.01
a2
.301
.143
2.10/.2
a3
.0448
.0283
1.59/.2
am
.125
.036
3.52/.05
(
--t.h~
--
TABLE 3-8-B
Region
CM
Actual Value
CM
Fitted Value
% Error
NE 70
7,452
6,465
13
NE 80
10,855
11,321
4
NE 90
15,610
18,673
20
ND 70
1,397
1,560
12
ND 80
2,580
2,553
1
ND 90
3,370
3,361
0
NY 70
1,600
1,526
5
NY 80
2,310
2,439
6
NY 90
3,595
3,973
11
PJ 70
4,455
2,833
36
PJ 80
5,965
5,177
13
PJ 90
8,645
9,434
9
EC 70
6,160
6,720
9
EC 80
13,730
11,725
15
EC 90
17,030
21,399
26
SE 70
7,160
8,803
23
SE 80
21,770
14,422
34
SE 90
30,340
23,926
21
SC 70
5,700
10,736
88
SC 80
12,780
17,346
36
SC 90
18,270
26,416
45
WC 70
8,770
8,960
2
W
70
29,280
22,193
24
W
80
42,910
29,301
32
W
90
51,970
44,257
15
-4
7-
TABLE 3-9-A
CM = eK Aal AAPLa2 Ga3METRO
3/21
Df:
87.28/.01
F:
AE:
22%
V
S
t
K
.304
ai
.756
.063
12.08/.01
a2
.319
.148
2.16/.2
a3
.172
.021
8.24/.01
48 -
TABLE 3-9-B
CM
Region
Actual Value
CM
Fitted Value
% Error
NE 70
7,452
6,556
12
NE 80
10,855
11,796
9
NE 90
15,610
20,832
34
ND 70
1,397
1,608
15
ND 80
2,580
2,437
5
ND 90
3,370
3,080
9
NY 70
1,600
1,513
5
NY 80
2,310
2,550
10
NY 90
3,595
4,555
27
PJ 70
4,455
2,813.
37
PJ 80
5,965
5,207
13
PJ 90
8,645
10,121
17
EC 70
6,160
6,255
2
EC 80
13,730
10,770
22
EC 90
17,030
20,275
19
SE 70
7,160
8,604
20
SE 80
21,770
12,997
40
SE 90
30,340
20,468
32
SC 70
5,700
11,588
103
SC 80
12,780
16,334
28
SC 90
18,270
22,138
21
WC 70
8,770
9,860
12
W
70
29,280
26,422
10
W
80
42,910
32,698
24
W
90
51,970
43,025
17
TABLE 3-10-A
a
EM
AAPLa2
Ga3METRO
EMt=
= eK
e Aal
A
APL
z
3/21
Df:
89.00/.01
F:
24%
AE:
V
K
S
t
-. 936
al
.728
.070
10.44/.01
a2
.546
.165
3. 31/.05
a3
.242
.023
10.43/.Ol
-50-
TABLE 3-10-B
Region
,·
EM
Actual Value
EM
Fitted Value
% Error
NE 70
3,124
3,316
6
NE 80
5,331
7,971
50
NE 90
13,104
18,162
39
ND 70
618
654
6
ND 80
1,328
1,275
4
ND 90
2,467
1,816
26
NY 70
561
621
11
NY 80
987
1,355
37
NY 90
3,411
3,113
9
PJ 70
1,945
1,453
25
PJ 80
3,016
3,560
18
PJ 90
7,226
9,238
28
EC 70
5,550
3,014
46
EC 80
13,818
6,585
52
EC 90
17,058
16,140
5
SE 70
2,529
3,975
57
SE 80
9,385
7,229
23
SE 90
16,154
13,789
15
SC 70
3,778
5,328
41
SC 80
8,260
8,897
8
SC 90
15,011
13,687
9
WC 70
3,232
4,223
31
W
70
11,996
13,920
16
W
80
22,608
18,926
16
W
90
31,946
27,943
12
-51-
TABLE 3-11-A
EM
=
e K Aal AAPLa2 Ga3 Ga4METRO
4/20
Df:
72.44/.01
F:
AE:
21%
V
S
t
K
-. 999
al
.563
.123
4.59/.02
a2
.420
.177
2.37/.1
a3
.377
.234
1.61/.2
a4
.163
.054
3.02/.05
-52-
TABLE 3-11-B
EM
Region
EM
Actual Value
Fitted Value
%Error
3,124
5,331
10
NE 90
13,104
3,437
8,074
17,851
ND 70
618
593
4
ND 80
1,310
2,129
1
ND 90
1,328
2,467
14
NY 70
561
664
18
NY 80
987
39
NY 90
1,367
2,966
1,369
3,271
7,944
3,105
6,718
15,443
4,160
8,265
16,415
4,742
9,381
16,398
3,856
11,226
17,311
29,855
NE 70
NE 80
W
70
W
80
3,411
1,945
3,016
7,226
5,550
13,818
17,058
2,529
9,385
16,154
3,778
8,260
15,011
3,232
11,996
22,608
W
90
31,946
PJ 70
PJ. 80
PJ 90
EC 70
EC 80
EC 90
SE 70
SE 80
SE 90
SC 70
SC 80
SC 90
WC 70
52
36
13
30
9
10
44
51
9
65
12
2
26
14
9
19
6
23
6
-53-
As before, year-by-year regressions were done on the
equations
C M
and
eK aA l aG
E M = eK aAa
l
G
2
METR
(19)
2 METR
(20)
the results of which are given in Tables 3-12 and 3-13.
Equations (19) and (20) were used for the entire data set,
too, with results similar to those for equations (8)
and (9):
Two independent variables, though significant,
were not as accurate for estimation as equations (14) (18).
The previous equations have been static ones;
that is, they estimate the miles of lines in a system
without any knowledge of that system at a prior time.
was desired to determine whether a model for system
expansion could be developed.
Such a model would use
knowledge of the state of the system at time to
and the values of certain system characteristics (the
independent variables) at time t > t
miles
of line at time t.
to predict the
It
ul
r
ON
H
e'
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-55-
TABLE 3-12-B
Region
NE
ND
NY
PJ
60
60
60
60
EC 60
SE
SC
WC
W
NE
ND
60
60
60
60
70
70
NY
PJ
EC
SE
SC
70
70
70
70
70
WC 70
W 70
NE 80
ND 80
NY 80
PJ 80
EC
SE
SC
WC
80
80
80
80
W
NE
ND
NY
PJ
EC
80
90
90
90
90
90
SE 90
SC 90
WC 90
W 90
CM
Actual Value
2,130
266
371
1,393
2,221
1,318
143
3,417
13,962
7,452
1,397
1,600
4,455
6,160
7,160
5,700
8,770
29,280
10,855
2,580
2,310
5,965
13,730
21,770
12,780
14,780
42,910
15,610
3,370
3,595
8,645
17,030
30,340
18,270
22,060
51,970
CM
Fitted Value
% Error
3,815
238
392
692
2,053
1,793
1,364
1,265
3,742
8,302
1,272
1,874
2,990
7,273
8,386
8,792
7,930
19,040
12,828
2,183
2,965
5,059
13,160
16,102
18,435
15,341
37,139
16,583
3,095
4,448
7,208
18,658
22,307
25,612
20,626
48,903
79
11
6
50
7
36
854
63
73
11
9
17
33
18
17
54
10
35
18
15
28
15
4
26
44
4
13
6
8
24
17
10
26
40
6
6
-56-
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-57TABLE 3-13-B
Region
NE
ND
NY
PJ
EC
EM
Actual Value
EM
Fitted Value
% Error
60
60
60
60
60
542
67
117
1,251
131
64
114
5
358
1,189
208
SE 60
SC 60
324
38
505
42
48
56
834
62
72
32
17
46
29
37
56
WC
W
NE
ND
NY
60
60
70
70
70
PJ
EC
SE
SC
WC
70
70
70
70
70
W
NE
ND
NY
70
80
80
80
PJ 80
EC 80
SE 80
SC
WC
W
NE
ND
NY
PJ
80
80
80
90
90
90
90
EC 90
SE 90
SC 90
WC 90
W 90
874
3,599
3,124
618
561
1,945
5,550
2,529
3,778
3,232
11,996
5,331
1,328
987
3,016
13,818
9,385
8,260
8,384
22,608
13,104
2,467
3,411
7,226
17,058
16,154
15,011
16,423
31,946
622
355
328
1,011
4,118
511
818
1,372
3,507
3,948
4,009
3,575
9,244
7,474
1,020
1,495
2,732
7,641
9,234
10,393
8,420
2,226
13,753
2,399
3,919
6,485
15,463
16,791
17,706
13,909
32,251
2
6
11
23
40
23
52
9
55
2
26
0
1
5
3
15
10
9
4
18
15
1
-58Taking the derivative of equation (4),
K
dM
Xi aJ)
Xi
i
(21)
(7Txj
a
de
j
By approximating X by Xt - Xo and dividing by Mo,
equation (19) becomes
( Xit - Xio
M
Mt
(22)
)
i
M
Xio
Similarly, the derivative of equation (12) was taken
K
dM
dt-
i
('I
e
X
[
i
a
ai
Xi
(
X
i Xi j i
( b
i
X)
G
aj)]
G
Z biXi
+(nG)G
+
biXi
ii b
i i
Xi)
i
(23)
Again, approximating X by X t - Xo and dividing by equation
(12) gives
-59-
Mt-M
t- M
=
0o
z (a
X
i
-
io)+
Xi
Git
(E
Go
i
biXit)+
nGC bi(Xit-Xio)
i
(24)
Regressions were performed on these equations (Table
IV-I-C);
however, no set of independent variables was found to be
statistically significant.
The average % error in estimating the amount of line
added to the system in the previous 10 years varied from
67% to 52%, with F-values from 0.1 to
for EM.
1.5for equations
Some equations for CM did have significant F-
values, such as
CMt-CM0
t
K+
a
CMt
AAPL -AAPL
Ia METRO tETRO
AAPLo
0
+a 3
METRO
P
P
+a 4 It-Io
I
(25)
with an F-statistic of 11.70. For equation 25, the regression results are given in Table 3-14.
However, the
average % of error was 38%, the same percentage as for
other equations with low F-values.
The % of error is
about the same (11%) for total' line in the system
the "static" models used earlier (15%).
as for
No significant
improvement was made in model accuracy by these "expansion"
model equations.
-60-
TABLE 3-14-A
CM -CM
t
CM
o
AAPL -AAPL
= K + al
o
t
I
AAP
AAPL
o
0
to
a2
+ a3
METRO
to
P
0
o
4/11
11. 70/.01
Df:
F:
(NE, ND, NY, PJ, EC, SE, SC, W) 80, 90
R&Y:
AE in Line Added in last 10 years:
38.0%
AE in Total Line:
10.5%
V
S
t
K
- .508
al
- .549
.325
1.69/.2
a2
2.391
1.285
1.86/.2
ia3
1.626
.444
a4
-3.537
1.517
3.66/.05
2.33/.1
to
I -I
P -P
METRO -METRO
+
a4
+O
0
-610)
a,
$4
N
--4
r
r-
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om
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CO 0
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CM
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>
-62-
One reason for this may be the approximation of the
derivative of the variables.
A derivative was approxi-
mated by
X
(Xt - Xo ) /(t-t
o
)
where (t-0) is 10 years; in a 10 year period, most systems
approximately double their generating capacity and grid
size.
Thus, the incremental change a
is not what is being described.
derivative describes
If the growth rate is
exponential (as in curve b, figure
the derivative
fig.
fig. 3-1
I
J70
At 7
1 1
7' IR
9 O
approximation for a 10 year
be quite wrong.
o'70
7i
71 ;6
-2
s 30
t (curve a, figure 3-1)
may
Using a smaller time period, such as 2
years, will result in a much more realistic approximation
(figure 3-2).
A workable system expansion model may result from
regressing (Milest - Mileso ) for two-year intervals and,
-63-
to estimate the state of the system 10 years from the
present, the "output" or estimate for the equation
for
(Mt - Mo ) could be used as input for the equation for
(Mt+l - Mt).
This will, of course, necessitate more
detailed predictions for growth of generating capacity,
number of plants, plant sites, load classification,
metropolitan area, etc.
The result would be a more
dynamic model of transmission expansion as compared to the
relatively static models developed here.
The results of
these "expansion" models will be discussed in greater
detail in Chapter 4.
-64-
CHAPTER
4
Limitations of Regression Models
Regression anslysis can be a useful tool, but the
models developed here do have shortcomings and limitations.
The most important limitation of a regression model has
already been mentioned:
it is no proof of causality.
The correlation of two variables may be the result of
causality, coincidence, or common correlation with a
third variable.
A regression coefficient has no "sign";
even in a causal relationship it does not indicate which
variable is the dependent one.
This must be inferred
from theory and knowledge of the system being modeled.
Even "causal" correlations, however, may have many
factors.
"METRO" influences the size of the EHV grid
because of its connection with land use and availability,
load characteristics, or the "energy-intensiveness" of
a region.
These factors can not be separated out.
The
fact that the variable METRO affects the number of miles
of EHV line in a system can provide insight into what
determines the size of the EHV grid of a region, but it
does not give a definitive causal relationship.
The data used in the regressions was both crosssectional and time-series data.
As was mentioned previously,
-65-
regressions using data for only one year were done for the
more important variables.
It was seen that such variables
as G, APL, and METRO were indeed "significant" and not
Just related to CM and EM through a common correlation with
time.
(In addition, regressions were performed using
the 1970 value of METRO for all years, and METRO was
still found to be significant.)
AAPL is much more time-
correlated than APL, but both have about the same significance
and result in models with silar
ever,
in all the models,
parameter values.
the parameters
do reflect
Howa
certain amount of time correlation which can not be separated
from their other casual relationship to miles of EHV line.
Factors not included in a model can drastically change
the results.
For example, EHV line was not used in the
South Central region until later than most of the rest of the
country; 115 KV and 161 KV line continued to handle the
majority of bulk power transmission.
for the region "SC
EHV mileage.
Thus, predictions
60" are much higher than the actual
The effects of this "low" data point on
the model are shown in tables 4-1, and 4-2, where the
K
same regression
equation,
CM = e
A
a1
G
a2
METRO
, was
used for data with and without the SC 60 region.
The
-66TABLE
Model:
4-1
EI = eK Aal Ga2 METRO
Regions & years used: a) (NE, ND, NY, PJ, EC, SE, SC, WC,
b) Same
as (a) except
for SC
) 60,70,80,90
60
c) (NE, ND, NY, PJ, EC, SE, SC, WC, W) 70,80,90
2/33
Degrees of freedom*:
a)
F-Statistic/Significance*:
a) 34.45/.01
Average % of Error:
a)
Coefficient
a)
K
al
a2
b)
c)
Value
c)
2/24
b) 59.05/.01
c) 85.18/.01
b)
c)
67.3%
31.5%
t-value/c<*
Standard Deviation
.855
.399
- .887
.943
a2
.359
K
2/32
-1.077
al
K
189.6%
b)
al
- .032
.867
a2
.235
.160
.060
5.34/.05
6.71/.05
.117
.044
8.03/.02
8.18/.02
.075
11.60/.01
8.19/.02
.029
TABLE 4-2
Model:
,·
CM = eK Aal Ga2 METR O
Regions & years used: a) (NE, ND, IY, PJ, EC, SE, SC, WC, W) 60,70,80,90
b) Same
as (a) except
for SC
60
c) (NE, ND, NY, PJ, EC, SE, SC, WC, W) 70,80,90
Degrees of freedom*:
a)
F-Statistic/Significance:A
a) 32.31/.01
b)
Average % of Error:
a)
b)
Coefficient
a)
2/32
77.81/.01
Standard Deviation
47.5%
c) 116.97/.01
c)
t-value/o< *
.040
.826
.293
.133
.050
.087
.032
10. 47/.01
a2
.214
.907
.256
K
.830
al
.835
.168
.058
.022
14.52/.01
7.62/.02
K
a2
* See Appendix V for definition of these terms
2/24
c)
al
al
c)
140.5%
b)
K
a2
b)
Value
2/33
6.20/.05
5.92/.05
7.91/.02
25.7%
large errors when including SC 60 "weakenTi the entire model
and bias all other regions' predictions.
This comes about
because regression, using a least squares cost criterion,
penalizes the rest of the data points a little in order
to prevent the error due to incorrectly estimating SC 60
being too large.
This large error comes about because
no provision for the late introduction of EHV line, a
technological factor, was incorporated in the model.
Mine-mouth coal plants are another important factor
not included in the models. "Improvements in high voltage
transmission generally tend to improve the competitive
position of coal" l
This facilitates the development of
inaccessible or mine-mouth reserves.
The amount of coal-
fueled generating capacity was not incorporated in the
model due to lack of data.
(There were no "% generating
capacity using coal" predictions for 1980 and 1990 for most
of the regions.)
However, further research along these
lines should attempt to include coal use.
As was mentioned, a correlation between two numbers
may be a combination of causality, coincidence, and correlation with a third variable.
Thus, the coefficients for the
same variables in tables 3-1 and IV-13 are different, although the 2 regression equations,
-68-
a
CM = e
a
A l
a2
a3
a4
a 2 Ia3 G4
a5
METRO
5
a6
aa
7
Ha6 AAPL
(26)
and
a
a2
a
CM = eK A a l Pa2 I
al
3
G
4
a
a
METRO 5 Ha 6 APL
a
7
(27)
differ only by using AAPL or APL.
For example, the value
of a2 , the coeffieient for P, the number of plants, is
-.471 in equation (26) and -.586 in equation (27).
These two values of a 2 reflect varying degrees of the three
"factors" of a correlation, and using APL instead of AAPL
in the equation changes the "proportions" of those factors.
Thus, in comparing two systems or strategies, the -. 471
and -.586 coefficients are both equally valid to use in
determining the effect of changing the number of generation
sites, (as in building a power park instead of 7 or 8
separate plants).
An examination of the results of
regressions show that one exact number can not be assigned
to each variable; you can not say with certainty that,
7
for instance, CM is proportional to p-.4 1.
However,
the variance of the coefficients is such that you can say
CM is proportional to p-X, where X is between .45 and
.60; in other words, you can get an approximate relationship
-69-
or a range of values; (i.e., saying, for instance,"changing
the number of plants from 40 to 50 will change the amount
of EHV line needed by between 5 to 7%.")
The "expansion" type models did not provide any
improvement over the more "static" models.
This may be
because the 10 year period used was too large.
Possibly
the information gained in knowing the line mileage 10
years previously was offset by the inaccurate derivative
approximation.
The models for EM (the best is given in
table IV-20) did not have significant F-values.
Even
with the models for CM, the difference in accuracy (Average
%Error) between equations with high and low F-values was
small.
These models were dependent on the structure already
postulated for the models:
M=K
'·
7
Xi
(28)
and
M= K G
b
X
a
Xi ii
(29)
A derivative approximation of these equations was used
for the expansion models.
Cutting the 10 year At into 2
year periods may improve the derivative approximation,
but an entirely different type of expansion model, such
as
-70-
Mt
Mo
K
Xt
ai
Xoi
(30)
may give better results.
The models of equations 1 through 20 were multiplicative.
Taking
the logrithms of these equations
gives equations
linear in logs of the variables, and therefore
for multiple linear regression.
suitable
A more complicated, non-
linear model is possible, but another computational tool
would have to be used to estimate its parameters.
On
the basis of the research so far, there is no other form
which, a priori, appears to be better than a multiplicative
model.
However, it is possible that a better form exists.
For the expansion type models aimed at determining the
additions to the existing grid, models not of the "derivative" form of equations 22 and 24, such as equation 30,
should be investigated.
-71CHAPTER
5
Applications and Uses of Models Developed
This study has shown that predictions can be made of
the EHV transmission grid size of a system from information about other system characteristics.
Accuracy is
almost always to within 50% and usually within 25% of the
actual values.
A relatively small number of system variables
were found to be relevant.
Changes in technology, laws,
and siting strategies can be related to these variables
(generating capacity, number of plants, average plant to
load center distance, etc.).
Together with predictions
on the character of the load (% industrial) and the
characteristics of the
area served (% metropolitan area),
the size of the transmission grid can be predicted.
As mentioned before, however, this study is not an
attempt to decide where the transmission line goes, so
its "absolute" numbers of EHV line miles are not accurate
enough for a "hard" prediction to be made.
The models
can give estimates to within a factor of two, but it is
as a "relative" comparison or ranking that they may be
most useful.
The models quantify some of the tradeoffs
involved in system planning.
Thus, the economies of scale
of building larger plants (and, therefore, fewer total plants)
-72-
can be compared with the cost of the extra transmission
needed (equation (6) and table 3-1).
To meet air quality
standards, the difference in transmission between continuing
the present generation siting strategy (using low sulfur
fuel or air scrubbing equipment) and a new policy of
locating the power plants far from the cities or using
offshore nuclear plants (thus increasing APL) can be
examined.
Specifically, a power park, in reducing
of plant sites, is expected
transmission line needed.
the number
to increase the amount of
Using equation (6) and table 3-1,
a system with, for example, 60 plants in 1980 may decide
that its generation needs in 1990 can be met by building
20 new plants or 9 plants and a power park (with a capacity
of about 11 plants.*) From table 3-1, comes the relationship:
C strategyl
80-
471
)_1'
e .94
(31)
CMstrategy2
or 6% more line will be needed for the power park.
In
addition, the effect on the average plant to load center
These numbers (one power park -11
separate plants, etc.)
are used for illustrative purposes and are not necessarily
indicative of the actual size of a power park.
-73-
distance (APL) must also be included.
From table 3-1
comes:
CMstrategy
1
-471
P1
~~CM
2
CMstrategy
AAPL1
(
)
.341
P2AAPL
(32)
2
Chapter 4 brought out the fact
that table IV-13
(equation (27)) gives -.586 as a value for the coefficient
of P.
Using equation (27) for the basic model, equation (32)
becomes
1strategy
CM
=
CM
strategy
2
-.586
1)
(
P2
.392
AP1
)
APL
(33)
However, the difference between (P1 /P 2 )- 471 and (P1/P2)- 586
is .94 and .925.
Thus, the "extra" line needed for a
power park is between 6 and 8%, the range given by using
equations (26) and (27). In examining any alternative,
"hard" predictions can not be made, but a range of possible
effects
(as in "about
6%" or " 1 0 to 15%"; etc.) can be
determined.
The effect of the growing scarcity of acceptable
power plant sites on P and APL can be estimated.
Then the
-74-
resulting effect on EHV line needs can be calculated using
the preceding procedure.
In similar manner, the effect of building offshore
nuclear plants on the plantto load center distances can
be determined and the relative "cost" in transmission line
estimated.
However, the transmission line carrying power
from an offshore plant may have relevant characteristics
not included in this study.
Because of special reliability
problems, several lines may be laid.
A variable, "% of
capacity in offshore plants", may be what is lacking to
describe the special characteristics of these plants,
as "% hydroelectric capacity", (),
was used in this study
to indicate the role of hydroelectric plants.
The results of this study are limited in that
offshore plants and power parks were not in the data
used.
Thus, a relationship which may be valid for the
tradeoff between 3 400
lWplants or 2 600 MW plants may
not be valid for the tradeoff between 15 600 MW plants or
a 6000
W
power
park and 3 1000 MW plants.
The
6% in-
crease in line from the example of using the power park
strategy should be taken with "a grain of salt".
The
6 to 8% difference between using a power park or not is a
-75-
hypothesis resulting from this model.
Extensive analysis
of system alternatives, such as planing
the system with
and without power parks and comparing the two, will be
needed to determine the validity of this application of
the model.
-76-
CHAPTER
6
Conclusions
The models developed in this paper are summarized
in Table 8.
While the limitations of regression models
must be kept in mind, the equations of Table 8 do
represent relationships for estimating EHV transmission
line needs using a relatively small number of system
characteristics as independent variables.
In addition to determining a region's EHV line needs,
these models can also be used to evaluate different
generation construction and siting strategies or predict
the effect of trends in technology,
or environmental constraints.
site availability,
The effect of a particular
"strategy" or "trend" on the independent variables of
the models can be estimated, and the difference in transmission line needs computed from the changes in those
variables.
However, it must be kept in mind that there
may be other relevant variables (
coal generation, number
of offshore nuclear plants, etc.) which are not included
in these models.
Two other aspects of transmission lines not covered
in this research are reliability and cost.
Reliability
data was simply not adequate enough to assign a reliability
-77-
"value" to a transmission system.
If such a number could
be developed, however, the information on the tradeoff
between reliability and line mileage could be quite
useful.
Costs of transmission line, both right-of-way and
construction costs, depend quite a bit on the characteristics
of the surrounding area.
A study similar to this one
attempting to estimate EHV line cost may be fruitful.
The degree of settlement or urbanization of the area in
which the line is built would be expected to be the most
significant parameter of such a model.
In general, the models developed here show that
different plant siting strategies don't have radically
different effects on the EHV needs of a region.
Things
"beyond the control" of the system planner, such as load
size and characteristics, metropolitan area, etc. seem
to be more important.
A more useful tool might be an
improved expansion model, concerned more directly with
the additions to the power system and the changes in load
and regional characteristics.
Further research along this line could consist of
examining other possibly significant variables, developing
a model concerned explicitly with additions and expansion
-78-
of an existing transmission grid, developing a model
for transmission line costs, or exploring other forms
of a transmission model than the multiplicative ones
developed here and using other curve fitting techniques
to compute the model parameters.
-79-
APPENDIX
I
Description of EHV Transmission Line
EHV line, for this paper, is defined as transmission
line with a rated nominal voltage of 230 KV or higher.
The National Standards Institute, Inc., has established
standard voltage levels for transmission systems.
Standard
nominal voltages include 230 KV, 345 KV, 500 KV, and
765 KV.
Associated with each standard nominal voltage is
a standard maximum voltage, the designed limit at which
the system can operate.l
EHV construction rapidly increased starting about
1957, as 345 KV line was introduced, followed by 500 KV
line in 1964 and 765 KV line in 1968.
The amount
of EHV
line in the U.S. for the years
1940 to 1990 is given
table
the rise in 345, 500, and
2.
Figure
1 illustrates
765 KV line mileages.
in
Research to develop higher rated
voltages is currently underway.2
As the nominal
voltage
of a line increases,
the
power carrying capability of that line grows approximately
as the square of the voltage.3
Construction costs and
right-of-way requirements also increase with voltage.
These characteristics are summarized in tables 1 and 3.
Construction and right-of-way costs vary greatly according
to the existing
uses of the land, as shown in table
4;
-80-
right-of-way costs are as much as $60,000
per mile in
urban areas and as low as $2,000 per mile in desert areas.
Construction costs are higher in urban areas, too, because
of the larger number of towers required, increased clearance
requirements, foundation problems, and aesthetic considerations..
Table 4 is meant to be illustrative, and no
attempt to estimate costs of line is made in this paper.
Representative costs are roughly proportional to rated
voltage for lines 230 KV and above.5
The maximum plant size is constantly increasing,
from 208 MW in 1950 to 1068 MW in 19696, and.that growth
is continuing.
As generation is concentrated in one
place, so transmission is being concentrated in large
corridors.7
One 765 KV line has the power capacity of 5
345 KV or 30 138 KV lines. The equivalent reactance of a
765 KV line is about 1/5 that of a 345 KV line, effectively
cutting the "electrical" distance between the ends of the
line by 1/5 and thus decreasing resistance losses.
Also,
while one 765 KV line requires about 200 feet of right
of way, 5 345 KV linesrequire
lines require
3000 feet.8
750 feet, and 30 138 KV
Thus, with the increase in the
amount of electric generation in the U.S., and with land
available for power facilities becoming scarcer, EHV line
is becoming more and more widely used.
-81-
Presently, EHV line is used in 3 cases:
1.
Long distance energy transfer from remote generating
sources to load centers.
2.
Interconnection between areas previously isolated
from each other to achieve economies in utilization
of available
3.
generation resources.
Higher voltage overlay of an existing well-
developed lower-voltage system so as to allow such
an overlay to take over the major tasks of bulk power
transfer between generating points and load centers
within the system and to permit the continued integrated
operation of the overall system in an economical and
reliable manner.
An example of the first use is the 735 KV line of Hydro
Quebec to deliver power from the planned northern hydroelectric plants to load centers 380 miles away in Quebec
City and Montreal.
is exemplified
The second type of use, interconnection,
by the 850 mile + 400 KV DC and 500 KV AC
lines comprising the Pacific Northwest - Southwest intertie.
AEP's 1200 circuit mile 765 KV grid overlays an extensive
existing 345 KV grid in the east central.region.
-82-
APPENDIX II
Data:
Description and Sources
The variables chosen for the regression models are
described in this section.
The data used to estimate the
model parameters are listed in table 5
Data was assembled
for the years 1960, 1965, 1970, 1980 and 1990.
However,
data for each year was not used in all the regression models.
Two measures of EHV transmission line mileage were
used as dependent variables.
The first, circuit miles of
EHV line (CM), is the total number of circuit miles of line
at a nominal voltage of 230 KV and above.
The second
measure is that of the power carrying capability of the
line.
The capacity of a line increases as the square of
the rated voltage.
Thus, the number of miles of each voltage
class of line was multiplied by a load factor.
NEMA 1
load scale factors were used to determine the "gigawatt"
equivalent miles" of EHV line (EM).
The load factors
for each voltage class are given in table 1.
one mile of 230 KV line quals 0.25
For example,
GW-equivalent miles,
one mile of 500 KV line equals 1.2 GW-equivalent miles, etc.
Data for the years 1970, 1980 and 1990 were obtained from
the 1970 National Power Survey.
Data for 1960 was obtained
from the FPC Statistics of Privately Owned Electric Utilities
in the U.S., Statistics of Publicly
Owned Electric Utilities
-83-
in the U.S., Electrical World's Directory of Electric
Utilities, the 1964 FPC National Power Survey, and FPC
"Principal Electric Facilities" maps.
The population of each region was taken from the
1960 and 1970 Censuses and the 1970 National Power Survey
The regional advisory committees for the most part assumed
a 1.5% per
year growth of population, and this was used
to project future population for 1980 and 1990.
-The physical area (A) of a system may have a large
effect on grid size.
In a larger area, generation sites
and load centers are usually scattered more widely, and
there are usually longer plant to load center distances.
The generating capacity (G) of a system obviously
is an indication of the power needs of that region.
Since
the purpose of transmission line is to transfer and distribute
the generated power, the generating capacity was expected to
be a significant input to the model.
Appendix III contains
graphs of generating capacity vs. miles of line for the
regions studied.
A strong correlation is seen to exist
between them.
Sources for data on generating capacity were the
FPC Statistics of Privately Owned Electric Utilities in the
United States - 1960 and Statistics of Publicly Owned
Electric Utilities in the United States - 1960 for the year
The generating capacity for 1965 and 1970 and
1960.
projections for 1980 and 1990 were tken
from the 1970
National Power Survey.
The number of generating plants and the number of load
centers were investigated as possible model inputs.
Be-
cause the study was concerned with EHV line, only large
plants and load centers were considered, as small plants
and loads might only require 115 KV or lower line.
The
variables used were the number of plants over 400 MW (P),
the number of load centers over 500 MW peak load, (LC-500),
and the number of load centers over 1000 MW peak load,
(LC-1000).
These sizes were used mainly to facilitate data
collection, as the FPC National Power Survey
those classifications.
maps included
Data for 1965, 1970, 1980 and 1990
were taken from the 1970 National Power Survey, from plant
and load listings for regions when available and from
regional maps when not.
The number of load centers for the
East Central region in 1960 was also given in the National
Power Survey.
The West Central region did not include a plant list or
map, but rather a list of "generation areas".
These
included zero, one, or several plants with capacities over
400 MW.
The capacity for each generation area was broken
down to peaking units, hydroelectric units, fossil units,
-85-
and nuclear units.
Where any of these subdivisions was
in excess of 400 MW, a plant over the minimum size was
assumed to exist.
This approximation yielded fairly
accurate results for 1970, the only year it could be
checked, as the above method yielded 25 plants, and the 1971
FPC Principal Electric Facilities
in July,
maps showed 28 plants
1970.
The load classification was also investigated for
possible significance.
Of the yearly generation (in
gigawatt hours) actually delivered to the customer (losses
were not included) the percentage in each of three classification was computed.
% Industrial ( I ),
Those classifications were:
including industrial use and
electric transportation;
% Residentual and Rural ( R),
including residential,
rural, agricultural (irrigation) and street and
highway lighting;
and
% Commercial (C), consisting of commercial use.
All three variables were not used at the same time in a
regression, since any one can be expressed as a function
of the other two.
This linear dependence would cause the.
data matrix to be singular.
Since matrix inversion is
used in multiple regression, a zero determinant would
result.
Thus, only the variables R and I were used.
-86-
Sources for the data were the 1970 National Power
Survey for the years 1965, 1970, 1980 and 1990
and EEI's
Statistical Year Book of the Electric Utility Industry
for the year 1960.
Another characteristic of each region which was
examined was the generation mix of the system.
a number of
1.
There are
ustifications for this:
Hydroelectric and pumped storage plants tend to
be located farther from major load centers than
fossil plants simply because the necessary water
resources and land required to develop them are seldom
found near cities.
2.
Because of public opinion, nuclear power plants
are usually not located in metropolitan areas because
of the chance of a radiation accident.
Thus, they
are often farther from the load centers than conventional plants.
3.
Nuclear plants are often being planned in con-
Junction with pumped hydro-peaking plants.
The
pumped hydro plant is run by the nuclear plant at
night.
Thus, there must be a strong tie between
the two.
More EHV line is often required.
Also,
the nuclear plant may be located near the pumped
storage plant, and thus farther from the load center.
-87-
Information on the generation mix is in the form of % of
capacity fossil fueled (F), % of capacity hydroelectric (H),
and % of capacity nuclear (N).
The makeup of generation
additions (per cent F, H, and N) in the 1971-1980 and 19811990 periods was also calculated.
Sources for the data
were the FPC's 1970 National Power Survey for the years
1970, 1980, and 1990 and EEI's Statistical Year Book for
1960 and 1965.
As with the load characteristic variables
(I, R, and C), any variable can be determined if the other
two are known.
Because of this linear dependence, only
2 of these 3 variables could be used in any regression.
Also, since N was zero for many cases, it was not used
as an independent variable in models where its logrithm
would be used, as its log would be infinite.
Urban areas provide unique problems in EHV line
construction.
In addition to the ever-present problem of
minimizing environmental impact, the right-of-way and
construction costs are highest in urban areas, with typical
costs of $330,000/mile line near an urban center as opposed
to $12 6 ,000/mile in a desert area. 2
Thus, the percent of
land area occupied by urban settlements was investigated
as a possible parameter for the model.
The variable used was % of area of a region that is
included in the Census Bureau's Standard Metropolitan
Statistical Areas with over 100,000 population.
The
-88-
definition of percent metropolitan area (METRO) is arbitrary,
but was designed to be more easily and objectively measured
and predicted.
The census defines 243 Standard Metropolitan
Statistical Areas (SMSA's) in the U.S. in 1970.
Except in
New England, a SMSA is a county or group of contiguous
counties which contain at least one city of 50,000 or more
or "twin" cities with a combined population of 50,000 or
more.
Contiguous counties are included if they are socially
and economically integrated with the central city.
England, SSA's
In New
are towns and cities instead of counties.
Urbanized areas are the thickly settled core of SMSA's.
However, the land area of urban areas was not given in the
census, so SMSA's were used.
A further qualification
imposed for this study in order to
help "weed out" the
"less urban" SMSA's was that a SMSA, to be included, must
have a population of 100,000 or more.
Source for the 1960
data was the 1960 Census of Population, Volume 1:
acteristics of the Population, Part 1:
34 and 36.
Char-
U.S.Summary, tables
1970 data was taken from the 1970 Census of
Population, Volume 1:
Number of Inhabitants, Part 1:
U.S. Summary, tables 35 and 36.
Projections for 1980 and
1990 were made by linear extrapolation of the 1960 and
1970 values.
Projections were also made by calculating
-89-
the yearly growth rate from 1960 to 1970 and assuming that
rate of growth would continue.
The yearly growth rates
calculated were:
North East
1.9%
New England
1.9%
New York
2.2%
P J M
1.7%
East Central
3.9%
South East
3.8%
South Central
$.1%
West Central
2.2%
West
1.6%
Regressions were done using both the linear and exponential
projections, and no significant difference was found in
the resulting models.
is given in table 7.
A comparison of two such regressions
For the other models presented in
this paper, the linear projections for 1980 and 1990 were
used.
Because transmission line's ultimate use is to bring
the power from the plant to the load center, two variables
dealing with plant to load center distance
were used.
The
first is the average plant.to load.center distance (APL), and
is the average distance between plants of over 400 MW
capacity and the nearest load center with over 1000 MW peak
-90-
load.
The second variable, total plant to load center
distance (TPL),
is the sum of the distancebetween
plants
over 400 MW and load centers over 1000 MW.
Because the number of load centers of over 1000 MW
is increasing, the yearly average plant to load center
distance for both new and old.plants is decreasing.
HIow-
ever, it was desired to compare the APL and TPL of existing
plants with those of new plants, to see if new plants
were being located in relatively more or less remote areas
than existing plants.
Thus, for the year 1980, for instance
the APL and TPL for plants constructed before 1970 was
calculated, as was the APL and TPL for plants between 1970
and 1980.
The APL for "old" plants in 1980 (Old APL) was
compared with the APL for 1970, and all 1980 values were
scaled up accordingly to give adjusted APL (AAPL)
adjusted TPL (TAPL).
scaled to 1970.
AAPL
=
1980
and
Thus, AAPL and TAPL represent values
The relationship used was:
APL1970
Old APL
x APL
1980
AAPL1980
1990AAPL
Old APL 1 9 90
1990
-91-
The values of APL and TPL were obtained by measuring
the distance, on maps in the 1970 National Power Survey,
between plants and load centers.
In many cases, this
necessitated making a composite map showing both plants
and load centers.
The West Central region, as was mentioned
previously, did not include a plant list, but rather a
"generation area" list.
Thus, actual plant sites could not
be located to obtain the values of APL and TPL for the
West Central region; the 1971 "Principal Electric Facilities"
maps were used.
Thus, the only values of APL and TPL for
the West Central region is for the year 1971.
For the East Central region, some generation addition
sites-weren't specified exactly, but an area in which they
would be located was given.
In this case, the center of
the proposed area was used as the plant location.
-92-
APPENDIX III
Graphs of Generating Capacity vs. EHV Grid Size
The graphs in this section are of circuit miles of
EHV line (CM) and gigawatt-equivalent miles of EHV line
(EM) vs. gigawatts of generating capacity (G).
Nine regions .of the country are plotted, and in graphs
1 through 10 the symbol for each section is used for the
plot.
The regions and symbols used are:
1.
Northeast
A.
New England
B.
New York
C.
P J M
2.
East Central
3.
Southeast
4.
South Central
5.
West Central
6.
West
Subregions
of the,
Northeast
The graphs are log-log graphs with thousands of
miles of line on the vertical axis and gigawatts on the
horizontal axis.
For each region, there are 4 points on
graphs 9 through 19.
These points are for the years 1960,
1970, 1980 and 1990, with CM, EM and GW all increasing
-93-
with time.
Graphs 11 through 19 use the following notation:
- thousands of circuit miles of line (CM)
x
= thousands of gigawatt miles of line (EM)
Data for this section was obtained from the 1970 National
Power Survey, 1960 Statistics of Publicly Owned Electric
Utilities in the U.S. and 1960 Statistics of Privately
Owned Electric Utilities in the U.S. and the Directory of
Electric Utilities.
Values for EM under 100 miles are not plotted in graphs.
,
4
9 l1_
3
L?5
6
7
8 9 1
2
3
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6
7
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.- ........
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:-,
,-..
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.-.. ,."
.. -.L ,.:. :, : ___ ,.--:., :_ " -,.-:1 ...
.;
T
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1-1.4-1I.III..4.
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I:...
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i.. : .I- I... 7.:1
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m:. _..: -.. .:-:_,:.--. .'
i..,
, -I,_. .- ..
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-1:
:..-:A."..:_.
- ... . - .- .-...
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IIL-
.,,.
7-7....I.I-I
,,.
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t!.--- . .... '. -TI:.-...
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I. I....i:i.
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.-- -...0:,.I.I...--.
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:. ...
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I...i_..I.. ...!.... .:
.-. :-,.--,.. .+..:m,..I
:-,-,:,I,-- -_,.,...
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I_... .".,-.-.-.
.- ...
.. .
47-'- -,-.-,-----,
__.i. .- , --...----.: -.. -. __. -..--..--,-,-.
_. __. _.- _. . ....-.r..
. _....
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. .___.
.___ ____..._4
-..---.-.--.-.- - -.....' -, _:. I _.
. __,.
:._._ -_...:...-_.
- ..-. -,-:: _:
..- " :_: --- -_= - __-I
-- 1 - - T-- ------.. .f,__.._._ ._.. L . -.- . ...
_..
- ..
.-._._
_j
- - - __1 -_ - -.----.
:.I
-"-"'--'
- -'-"'T : -'
'. __',----.., ..,.
__ . -. -_.. _. -;---...-:
__ -. .. -_ ._..
_: ....
_..
.--- - "' ---.
r -'--,7" : '_
.... - __._._..._.7___A
--. 7--.--.-j
_. +_ ; -.-. ,-4-- ---- - -, ...
. -I-.--. _.;Ir
- -- - - -. ; _ _. ._I. . __ 7-r..-.- ... -.
7_.-.
....
__.__ __-. :- I
__ . ._.___:_._
____...
- ..- -. ; ------._-.I-"__
7 .. i
.....
. _..
_..
.- ..
.-;-..-.-.-.-f
!I..
-].1.3-
APPENDIX IV
Regression Results
This section contains the results of some of the
regressions performed.
The results of the final models
are given in Chapter 3.
Chapter 3's tables also include
the predicted or "fitted" values of CM or EM for each
region.
Table IV-1 lists all the regressions which were
performed in the study.*
For ease in reading, the coa
efficients and constants are left out (M = e
A
a2I
G
becomes M = A GI ) and abbreviations are used for all
variables.
(Lists of the abbreviations are given in
Table 6; the end of Chapter 2, and Appendix II.)
To perform multiple linear regression, logrithms
,;.
were taken of both sides of each equation of Table IV-1-A
and IV-1-B.
The table entries relating to statistical tests
(F-statistic, t-statistic,
p"t, degrees of freedom,
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..
~f~wt
deviation) are defined in Appendix V.
*Complete results of all regressions listed in Table IV-1
are available from the author or Professor F. C. Schweppe,
M.I.T., Room 3-137, Cambridge, Massachusetts.
-114Table IV-1
Regressions Performed
a
i
X
ii
Miles = eK
A.
M=
M=
M =
M=
M=
M=
M=
M=
M=
M=
M =
M=
M=
M=
M =
M=
M=
A
I
A FH
G
M
G
M= A G METRO
A LC-500
A LC-1000
A
P
By Year
i
G
G
G
A LC-500
R G METRO H
A P LC-1000
R G METRO
A R G METRO H
H
A P LC-1000
R G METRO
H APL
A P I
A P I
H AAPL
H APL
G METRO
G METRO
(
GLC
-
G
i
500
GR GMETRO
500
GR GMETRO GN
GN GAAPL
TAPL
M
GR G ETRO
M = A AAPL
GI
M =
A AAPL
G M ETRO
M
=
A
AAPL G GETRO
M =
A
APL
M =
A
M =
A
APL G GMETRO
GMETRO
M =
A APL
GMETRO
M = A G GETRO
M = A GMETRO
G M ETRO
METRO
Expansion Model for
AM/MO = AD/D
AM/M = AD/D
o
0
AM/M = AD/D
AM/
= AD/D
0
AG
X
i)
Xi
M = A G TAPL GLC
C.
A G TPL
APL
AAPL
A R G METRO
A I G METRO
A P R G METRO
A AAPL
A G H
M =
M=
A G METRO
A G METRO
M = A G AAPL
M =
M =
A G AAPL
G TPL
M= G APL
H TAPL
a
!
A G I
M=
METRO
Miles = eK
B.
M=
M =
R G METRO H AAPL
G
A G METRO
M= A G APL
M= A G TAPL
A P LC-1000
A
=
0
Mt - M
M
14
(
)
AM/Ma~0
+ AG/G + A°METRO/METRO + AH/H +AP/P
+ AG/G + A METRO/METRO
0
0
+ AG/G
+ METRO
AG/G
+ n G * AMETRO
0
0
0
+AI/I
APL
-115-
Table VI -
continued
AM/M = AD/Do + METRO
=Do
0
0
AM/M o = AD/D + METRO
0
AM/M =0~~~ AG/G
AM/M= METRO
AM/M O0 =
~~~~o
AG/G
AG/G + AG/G + n G AMETRO
0
0
o
AG/G + Io AG/G +Zn G AMETRO+ZnGo AI
o0
+
0
0
n G o AMETRO
+ AG/G 0 + AP/P 0 + A/I 0
AM/M= AD/D
AM/Mo
AD/D0 + AMETRO/METRO 0 + AP/P 0 + AI/I
AM/MO = AD/D 0 + AG/G 0 + AI/I 0
AD/D
where four values were used for AD/D :
0
(TPLt - TPL o )/TPLo
(APLt -APLo ) /APLo
(AAPLt - AAPL o )/AAPLo
(NAPLt - OAPLt)/OAPLt
00
-11.6-
TABLE
CM = e
A
l
Pa2 Ra3 Gat METROaS
IV-2
a 6 AAPLa7
Degrees of freedom (Df)*:
7/17
F-Statistic/Significance (F)*:
57.67/.01
Average % error (AE):
16%
Coefficient
K
Value (V)
Standard Deviation (S)
t-value/o * (t)
1.378
al
.707
.113
6.26/.001
a2
- .436
.302
1.44/.2
a3
-1.219
.597
2.04/.1
a4
.628
.231
2.72/.05
as
.603
.201
2.99/.05
a6
.0968
.0873
1.11/.3
a7
.429
.182
2.36/.1
* See Appendix V for definition of these terms
-11 7-
TABLE
IV-3
CM = eK Aal Ia2 Ra3 Ga4
4/31
Df:
33.87/.01
F:
V
K
S
t
-2.574
a1
.229
.141
1.62/.2
a2
- .051
1.230
. 04/--
a3
1.878
1.356
1.38/.3
a4
1.193
.141
8.44/.
Ol
-11.8-
TABLE IV-4
EM = eK Aa
1 Ia2
Ra3 Ga4
)f :
4/31
F:
42.49/.01
V
K
S
t
-5.379
al
.019
.155
.12/--
a2
.400
1.346
.30/.9
a3
.258
1.485
1.74/.2
a4
1.636
.155
1,o.57/.01
-119-
TABLE IV-5
CM = eK Aal Ga2
2/24
Df:
11.8.32/.01
F:
d'::
31.1%
V
sK
S
t
-. 431
a,
.075
.108
a2
1.156
.098
.69/.7
11.83/.01
-120-
TABLE IV-6
a2
EM = e K Aal
A
Ga2
2/24
Df:
F:
95.60/.01
41.8%
AE:
V
S
t
K
-1.711
a,
- .093
.151
.62/.7
a;
1.562
.136
11.49/.01
-121-
TABLE IV-7
CM = eK Aal Ga2METRO
Df:
F:
AE:
2/24
116.97/.01
25.7%
S
t
.835
.058
14.52/.01
.168
.022
7.62/.02
V
K
a2
.830
-122-
TABLE
EM
=
eK Aal Ga2METRO
Df:
F:
AE:
2/24
85.18/.01
31.5%
V
K
a2
,*
IV- 8
S
t
-.032
.867
.075
11.60/.01
.235
.029
8.19/.02
-1 23-
Lr
ful
i-
.i .
r-
,-I
0
y
-
oC' ,
%N
*
CO
',U' -It
cn
\>
*- c
-
N
00
= * 0'
m
r0i ·
4
I
o
<t
c
*N
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o
c.'J
rc
-H
LfC
C
*
O
T
<C
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co
C)
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9-4
Ew
0
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C
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co
t-
1
9-4
03
9-I
* -*
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1
Ln
co
o
L(1
aN
Un o
C)
(-N
9-4
(N
.
-
e
en
0
H
o
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>1
o
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*
Vo4
¢aH
II
n
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*-4
a
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(
m'
00
u-I
u-I
c
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9- 0
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14-4 p,
9-4
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C'C
)
0'C'IUn
n
c,~
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ON
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c
CS
cH
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crs
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cY)
cn
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Ln
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HI
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V-4 %o
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cN
CN
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co
r-.
S.t
C)
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Ln
C',
0H
rm
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cn
r-.
cn
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H-
c
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:
11
H-
H-
C
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%
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C "4
d
s
co
co
K
-125-
'41
o
N
oi
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N
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.
>I
0
m
TEN
.
'-~N
01
(3
m
Un
Ch
N
Lr~
ZI
CD
N·
c
o
co
ea:
N
Loo
a
'I
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co
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co
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r-f
O0
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cn
N
O0
CN
~Lr
·
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C\)
U)
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r4
v-I1
--4-~'
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(441
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0
2-4
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--
Ch
/
Hi
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f
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I4-
O U)
041
CC
n
<4
LPn
*
o
c
0'
Ho
Lt
Cn~
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C *z d
JI
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cn
co
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v-I
036,
<0
* I,-4
¢
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Cl
H~
-:-I
m
Ln
#
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Ln
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H~~~~
co
'.0 cn con
-It
o
*·
ao H
Lf')
-:r
--T
-~r
1
9*
-4Cd
Cd
Cd
,
O7%
C
-126-
H
Cl
*
o
H
OI
I
co o
I
cc
L·
·.
-·
Ln
H
r-4
H~~
C~~
--
H
o*
-
* Im
L)
C4
Cl
co
Hr-
H-
V)
Cl4
uL,
H-
Lf)
En,-I
or-i
Cl4
fl-i
Ln
tn
C4
I
0O
H
oo'
*.
1
C!
H*
Cl4
1
in
o
H
H-
C)
'.
Cl
-1J
Cl
H-
'l
u'l
H
C
'IO
cl
l--
*
H
0l
I
'-4
1.0
'N)
0
C4
Ln
'.
,o*
C
H-
'.0
-11
%-t
c
cCl
Unr
en
C-'
*
-.
4
H
U)
I
0
a)
U
'
L
H
a
0
Cl
-4
Cl
cr'o
I
I
1H
'.0 ~~~~~~~~~~~
* J
I¢
CU>
Cl)
inl
U,00Cl~~~~~~C,1
Un
i.n
I
H
cc
J >I
I4
c4
H-
Cl Lt~~~ r-I
0
oI
c
H4
L()
H
-1
).
tn
0
Le)
~
0m
cc
H-
.- 1
Lr)
r~~~~~~
044.4
H
oo
'o
o
o
H,0--i o4
*~) *
*-
o
Cl
oo
o4
l*
N
H
,
0-I
i
-127-
TABLE IV-13
CM
e K Aal pa 2 Ia3 Ga4 METROaS Has APLa?
7/17
Df:
63.34/.01
F:
AE:
15.1%
V
K
S
t
-1.778
al
.460
.125
3.69/.02
a2
- .586
.281
2.09/.1
a3
1.060
.497
2.13/.1
a4
1.091
.195
5.61/.001
a5
.481
.180
2.67/. 05
a6
.217
.104
2.08/.1
a7
.392
.212
1.85/.2
-128-
TABLE IV-14
EM
Aal
e
Ga2 METROa3
3/23
Df:
F:
(1970, 80, 90 data)
75.93/.01
AE:
29.5%
V
K
S
t
-.693
a,
.405
.130
3.12/.1
a
.952
.146
6.51/.01
.191
.207
.92/.5
a
2
3
EM = eK Aa
Ga2 METROa
3/32
Df:
F:
(1960, 70, 80, 90 data)
46.66/.01
AE:
86.6%
V
K
S
t
-1.769
aI
.211
.223
.95/.5
a.
1.465
.221
6.64/.01
a3
.235
.378
.62/.7
2
-129-
TABLE IV- 1 5
CM
=
Aal Ga2 METROa3
e
103.72/.01
F:
AE:
22.3%
V
_I
EM =
80, 90 data)
(1970,
3/23
Df:
S
t
K
.370
al
.610
.100
6.13/.01
a2
.573
.112
5.10/.02
a3
.338
.159
2.13/.2
K Aa
_
_
_
_
I_
Ga2 METROa3
(1960, 70, 80, 90 data)
3/32
Df:
39.85/.01
F:
AE:
71.6%
V
S
t
K
-. 511
a
.481
.197
2.44/.1
.961
.195
4.92/.02
.443
.335
1.32/.3
a
1
2
a3
-130-
TABLE IV-16
EM = e K Aal Ga2 METROa3 APLa4
4/20
Df:
55. 87/.01
F:
25.8%
AE:
V
K
S
t
-1.639
a1
.275
.155
1.78/.2
a2
1.080
.176
6.15/.01
a3
.378
.229
1.65/.2
a4
.540
.321
1.68/.2
-131-
TABLE IV-17
CM = eK Aal AAPLa2 Ga3R Ga4METRO
4/20
Df:
F:
62..59/.01
21.4%
AE:
V
t
.299
K
a
S
1
a2
a3
am
-.
.780
.109
7.14/.01
.350
.203
1.75/.2
020
.072
.27/.9
.183
.045
4.06/.02
-132-
TABLE IV-18
CM
eK Aa
l
Df:
APLa2 Ga3MtETRO
3/21
F:
73.27/.01
AE:
24%
V
S
t
I ....
K
.434
al
.778
.075
10. 31/.01
a2
.248
.270
.92/.5
a3
.195
.034
5.69/.02
-133-
TABLE IV-19
EM
e K Aal APLa2 Ga3M ETRO
3/21
Df:
58.63/.01
F:
AE:
31%
V
K
S
t
-.543
al
.785
.094
8. 37/.01
a2
.310
.336
.92/.5
a3
.271
.043
6.36/.01
-134-
TABLE IV-20
EM -EM
t o
= K + al
EM
0
AAPL -AAPL
t
AAPL
P -P
G -G
o
t o
+ a2
G
+ a3
_
_
P
O0
0
t o+
I -I
a4
0
4/11
Df:
2.73/--
F:
AE in Line Added in last 10 years:
52.7%
AE in Total Line:
18.6%
V
K
- 1.096
al
- 2.039
a2
1.753
a3
2.085
a4
-13.243
S
t
.776
2.63/.1
1.493
1.17/.5
..820
4.645
2.54/.1
2. 85/.05
t o
I
0
-135-
APPENDIX V
Determining the Significance of Model Parameters
As was mentioned previously, correlation and regression
can not be used as proof of cause and effect.
these techniques are useful in two ways:
However,
they may provide
further confirmation of a relation that theory tells us
should exist, and they may suggest casual relationships
not previously suspected (such as when cigarette smoking
was found to be correlated with lung cancer).
Thus, the
"statistical significance" of a parameter is indicative
of its correlation with the dependent variable.
It is
no guarantee of causality.
Two statistics were computed for the parameters
estimated by regression:
the t-statistic
and F-statistic.
The t-statistic can be used to compute a confidence interval
for the estimated coefficient or to test the null hypothesis.
A confidence interval gives the limits within whichwith
a certain probability,
be estimated
lies.
the true value of the parameter
Thus, a 95% confidence
interval
to
for a
coefficient, b, (which is an estimate of the true value (B)
of the coefficient) is defined by upper and lower limits,
u and
, such that with a probability of .95 the following
is true:
-136-
u
< b
<
Z
If the dependent variable is normally distributed, then
the regression
coefficients,
b, have a t-distribution,
as
shown below:
fig. V-1 ____
b(estimate of B)
confidence interval
To
test the null hypothesis, the t-statistic indicates
the probability that the null hypothesis will be incorrectly
rejected;
that is, the probability that a nonzero estimate
b of the true value
(B) will be made
if B is indeed
zero.
This method of testing the null hypothesis will be described
later in this section.
The F-statistic is an alternative method of testing
the null hypothesis. 2
The equations used in the calculation of these
statistics and the regression coefficients are given
below:
Xij is
input
data
i =
1,2
... N observations
J = 1,2,... M variables
There are M-1 independent variables and one dependent variable,Y.
-137-
N
E
The means X
=
X
il
i
are calculated.
N
The sums of cross products of deviations from the mean
are calculated.
Sjk =
4
N
N
N
- z (Xi-X j )
i=( (Xij-X
133 ) (Xik-X
iRk k ) j=
ij
i=1(Xik--k)
kk
N
The correlation coefficients are
rjk = Sjk/(~
sjju 0 VS k
)
The standard deviations of the variables are
Si
sj J ~N-1
With "Y" indicating the dependent variable, the regression
coefficients are
M-1
bj =
(
s
riy / r
)
Y
sj.
The intercept is
-138M-1
bO = Y-
b ,;
'
j-lE
Xj
A
This gives the fitted equation for Y, the estimate of Y.
M-1
A
Y = b
0
b
+
i=l
Xi
ii1
To obtain the t- and F-statistics, the correlation
coefficient, R, is first computed.
M-1
M-1
R
=
(riy
i=l
E- rjY/ ri) )
' (
Let Dyy = the sum of squares of deviations from the mean
for the dependent variable:
Dyy
=
N
i
i=l
(Yi
-
Y
)2
The sum of squares of deviations from regression (SSDR)
and the sum of squares attributable to regression(SSAR) are
SSAR
= R2
D
yy
and
SSDR = Dyy - SSAR
The F-statistic is
SSAR/(M-1)
SSDR/(N-M-2)
with (M-1)/(N-M-2) degrees of freedom.
-139-
To obtain the t-statistic, we first define
2
SSDR
y
1,2,
-' M-1 =
N-M-2
N-M-2
and
N
=
i=l
(Xij - xj)
2.
Then the standard deviation of the regression coefficients
is given by
Sb = Y1,2 'M-1
/(rjDjj 1)
The t-statistic is
tj
= bj/Sb
and it has M-1 degrees of freedom.
The t-distribution is shown below:
cal
fig. V-2
S
t-distribution
(1-c) confidence
interval
For the t-distribution to be valid, it is required
that the distribution
of Yi (or Yi
Y) is normal.
The
M
"residual variance" is s
N=2
N-2
it1 (Yi - Yi)
where
--1410A
Yi = the estimated value of Y
i
for each observation.
If
i
B = the true value
of the regression
coefficients
and b =
their estimated values, then the t-statistic is given by
b
tj =
L- B1
N
2
2
ij
i=l
The equation for a 95% confidence interval is5
s2
N
Bj
=
j+
t.
02 5
=1l
This means that
Pr(-t
025
b -B
<
2/E
where t
025
<
t
25
"025
)
=
.95
x2
is found in a standard table of t-values.
To test the null hypothesis, substitute B
into the above
equation:
,
tj
= b/
.~~~~
.
i/
If b, the estimated
(xij2)
value of B, is positive,
distribution for b is shown in figure V-3.
the
The midpoint
of the distribution is the estimated value b.
The standard
-141-
deviation of the regression coefficient b determines how
"spread
out" the curve is.
fi9 . V-3
to
fig. V-4
J
b
L
(l-R) confidence
(1-X) confidence
interval
interval
If the point b=o lies outside the confidence interval, that
is, in the shaded portion of the curve of figure V-3, then
the probability that B is indeed zero (the null hypothesis
is true but has been rejected) is given by the shaded area
of the curve.
Thus, if a/2 = .025, then the confidence
interyal checked is the 95% confidence interval (-a)
if b, the estimated value of B
b=0 lies in
and
is positive, and the point
he shaded portion of the figure V-3, then the
probability that B=0 is a/2 or .025.
(For a calculated b
less than zero, the appropriate curve is figure V-4 above.)
The significant number given after t-statistic in
Chapter 3 and Appendix IV of this paper is
a.
Using a,
the probability of a false rejection of the null hypothesis
can be calculated.
That probability is a/2.
The level of the confidence interval which includes
the given regression coefficient, b, is (l-a).
Thus,
for an a of .1, the probability that the null hypothesis
-142-
has been falsely rejected is .05 and b lies within the 90%
confidence interval.
The F-test similarly tests the hypothesis that
B1 = B 2
...
BM
1
0.
The significance number given
after the F-statistic is the probability that this hypothesis
has been falsely rejected by assigning non-zero values to the
b's.
However, as in all probabilistic functions, it must
be remembered that a low t- or F-statistic does not mean
that B=0.
Rather, it indicates that the hypothesis that B
does equal zero can not be rejected.
Similarly, a high
t- or F-statistic means only that we probably will not
wrongly reject the null hypothesis.
-143-
References
Chapter
1.
1
Transmission Technical Advisory Committee
for the National Power Survey, "The Transmission of
Electric
Chapter
p.
89.
3
IBM , System/360, SSP, Version III
1.
Chapter
Power,t
4
1.
Appendix
1.
FPC, National Power Survey
1970, p. I-4-26.
I
Transmission Technical Advisory Committee,
op. cit., p. 6.
2.
Federal Power Commission, National Power Survey
3.
Transmission Technical Advisory Committee, op. cit.,
p. 11.
p. 23.
4.
Ibid.,
5.
Ibid.,p.
6.
Ibid.,
p. 11.
7.
Ibid.,
p.
8.
Ibid.,
p. 12.
9,
Ibid,
24.
11.
p. 7.
- 1i4-
Appendix II
1.
National Electrical Manufacturers Association,
"Second Biennial Survey of Power Equipment Requirements
of the U.S. Electric Utility Industry1".
2.
p.
Transmission Technical Advisory Committee, op. cit.,
23.
Appendix V
1. Wonnacott, R.J., and Wonnacott, T.H., Econometrics,
p. 125.
2.
Ibid.,
p.
3.
IBM, op. cit.
4.
Wonnacott
and Wonnacott,
5.
Ibid.,
25.
p.
119.
op. cit. p. 25.
-145GW-MI
60000 .
4000 0
2000 0
115-230KV
I
I
58 60
n
56
I
62
!
64
I l I
66 68
I
72
70
I
74
I
76
J
78
I
I
Transmission Capability
GW- MI
tau
6UUV
r
4000
2000
I
I
I
56
58
60
n
I
I
I
I
62
64
66
68
I
I
I
70 72
---
74
76 78
Transmission Capability Additions
GW-MI
2000
1500
1000
5 00
'Transmission
Figure 1.:
Capability by Voltage Class
Growth of EHV Line
Source: NEMDIA,"Second Biennial Survey,"p. 10 & 12
-1 46-
t,
0:
/·
Figure
NATIONAL
3
ELECTRIC RELIABILITY
COUNCIL
REGIONS
WSCC
WesternSystems
Coordinating
Council
NPCC
Northeast
Power
Coordinating
Council
MARCA
AreaReihbil;ty
Mid-Continent
Coordination
Agreement
MAAC
Mid-Atlantic
Area
Coordination
Group
SPP
Southwest
PowerPool
ECAR
EastCentralAreaReliability
Coordination
Agreement
ERCOT
ElectricRehliability
CouncilOfTexas
SERC
MAIN
Mid-America
InterpoolNetwork
Southeastern
Electric
Reliability
Council
Source: FPC, National Power Survey 1970, p.
-17-16
-1 18-
a)
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-150-
Table
3
Costs of EHV Line
Average Total Costs/Mile* in 19641
230 KV:
$60,000
345 KV:
$77,000
500 KV:
$99,000
700 KV: $143,000
*Costs have since risen
for 1968 in the Northeast
Costs/Mile
Regtrion(in thousands
of $)
New England
Right-of-Way
Line
345 KV
765 KV
$30- $60
$50-$85
$40-$80
$200
j'-tIi r) Ar,vVr
$10
$100-$220
500 KV
765 KV
$50
$75
$200
$200
$ 10-$100
$120-$200
New York
J"'
,
"~
')
}
r-
'vre~
P J M
500 KV
765 KV
$lo-$ oo
$200
Northeast Region
$10-$60
$10-$100
$10-$100
345 KV
500 KV
765 KV
Sources:
$50-$220
$120-$ 200
Power Survey, Vol. I, pp.
1
FPC, 1964 National
2
FPC, 1970 National Power Survey, pp. II-1-63
$200
151
Table 4
Actual AC Line Costs, Nominal 500 KV and 700 KV
Cost per mile
Conductors
Eastern area-500
R, W and clearing
Line Construction
Total
kV:
2-2037 ACSR ............................
2-2493 ACAR ............................
2-2049 5005 ..............................
3- 971 ACSR .............................
4- 583 ACSR .............................
2-2032 ACSR .....
$30,700
.
.......................
.
2-2490 ACAR .............................
2-2490 ACAR .............................
2-2500 ACAR ............................
3- 954 ACSR .............................
Central area-500 kV:
3- 954 ACSR ...........................................
3-1024 ACAR .
...........................
Western area--500 kV:
2-1780 ACSR ............................
...
i 3,500
16,700
12,400
10,000
17,000
'Latest data-otler
data prior to 1969.
2 Line near urban center.
128,500
85,800
65,300
95,500
98,000
$111,500
142,000
102,500
77.400
10:51,500
'115,000
20,000
59,000
142,000
272,000
1 162,000
1,2331,000
22,000
118,000
1140,00
12,000
95,000
107,000
24,000
84,200 ........................
95,600
119,600
7,100
2-1852 ACSR...........................................
2-2156 ACSR .............................
2-2156 ACSR .............................
700 kV:
Average of 735 kV and 765 kV lines...........
$ 80,800
72,200
79,300
82,000........................
25,000
2,000
93,900
124,000
118,900
1.3126,000
18,700
146,300
4 165,000
Desert construction.
I Includes line sections built over 4-year span.
3
Source: Transmission Technical Advisory Committee,
The Transmission of Electric Power, p. 23
--7.52-
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-155-
Table 5-B: Data
REGION
EM
CG
POPULATION
P
LC-500
LC-1000
(millions)
NE60
NE70
NE80
NE90
3,124
5,331
13,104
ND60
ND70
ND80
ND90
618
1,328
2,467
542
67
2,130
7,452
10,855
15,610
41.3
46.9
53.0
60.0
266
1,397
2,580
3,370
60
17
9
88
105
32
44
17
31
3
1
10
17
3
11
21
27
9
NY60
NY70
NY80
NY90
561
987
3,411
1,600
2,310
3,595
24
30
34
PJ60
PJ70
PJ80
PJ90
358
1,945
3,016
7,226
1,393
4,455
5,965
8,645
25
37
44
EC60
EC70
EC80
EC90
1,189
5,550
13,818
17,058
2,221
6,160
13,730
17,030
28.3
30.2
54
12
33
36.2
91
112
50
63
11
28
44
SE60
SE70
SE80
SE90
324
2,529
9,385
16,154
1,318
7,160
21,770
30,340
27.8
31.4
35.4
39
40.1
105
33
62
71
16
33
61
SC60
SC70
SC80
SC90
38
143
21.5
3,778
8,260
15,011
5,700
12,780
18,270
24.4
28.3
33.1
42
81
116
25
46
66
9
25
45
WC60
WC70
WC80
WC90
874
3,232
8,384
16,423
3,417
8,770
25
41
14
16
22,060
25.7
28.1
32.4
37.8
60
19
17
13,962
29,280
42,910
51,970
27.7
34.7
43.4
52.4
45
75
27
36
42
15
28
36
W 60
W 70
W 80
W 90
117
3,599
11,996
22,608
31,946
371
14,780
40.9
77
103
5
3
7
5
9
7
9
5
15
18
15
9
5
-156Table 5-C: Data
REGION
)
TPL
APL
AAPL
NTPL
NAPL
NAAPL
OTPL
OAPL
OAAPL
NE70
1,992
33
33
NE80
2,636
30
55
1,556
55
101
1,080
18
33
NE90
2,526
24
69
828
49
142
1,698
19
55
ND70
438
40
40
ND80
891
42
93
573
48
106
198
18
40
ND90
1,212
45
120
471
79
210
741
35
93
NY70
474
20
20
NY80
578
19
32
290
49
82
288
12
20
NY90
534
16
37
126
32
73
408
14
32
PJ70
1,080
43
43
PJ80
467
32
57
693
69
124
594
24
43
PJ90
780
18
68
231
33
124
549
15
57
E.C70
1,816
34
34
EC80
2,440
27
40
1,180
32
47
1, 260
23
34
EC90
2,260
20
42
553
26
54
1, 707
19
40
SE70
1,664
42
42
SE80
2,388
31
50
1,354
36
58
1, 034
26
42
SE90
2,100
20
53
619
22
58
1, 481
19
50
SC70
2,720
63
63
SC80
3,175
39
85
1,965
50
108
1,210
29
63
SC90
3,405
30
87
1,020
31
90
2,385
29
85
WC70
1,368
49
49
W 70
4,315
96
96
W 80
3,253
43
103
1,346
48
115
1,738
40
96
W 90
4,461
43
106
1,515
48
118
3,115
42
103
-157-
Table 5-D: Data
-0
% HYDRO new
REGION
% FOSSIL new
NE80
18.7
14.6
66.7
NE90
7.3
6.2
86.5
ND80
19.6
16.9
63.5
ND90
4.6
8.3
87.1
NY80
-10.8
23.7
87.1
NY90
4.8
11.9
83.3
PJ80
32.4
8.8
58.8
PJ90
10.0
2.1
87.9
EC80
61.2
10.1
28.7
EC90
42.1
2.4
55.5
SE80
42.0
8.2
49.8
SE90
42.3
8.9
48.8
SC80
79.7
6.3
14.0
SC90
58.1
5.7
36.2
WC80
31.4
0.1
68.5
WC90
19.9
0.6
79.5
W 80
37.6
25.3
37.1
W 90
26.2
13.5
60.3
% NUCLEAR new
-158-
6
Table
Data and Scale Factors Used in Regressions
Symbol
CM & EM
Variable
Scale Factor
Miles of Line
10- 3
Pop
Population
10-6
A
Area
- 5
lo0
P
Number of Plants
LC
Number of Load Centers
101
I,R & C
% of GWH for Industrial, Residential,
101
(sq. miles)
101
400 MW
or Commercial Users
G
Generating Capacity (MW)
lo0
METRO
% Metropolitan Area
10-
F, H &
% Generating Capacity
10-1
1
Fossil Fueled, Hydroelectric or Nuclear
TPL
Total Plant to Load Center Distance
10- 2
(Miles)
APL
Average Plant to Load Center Distance
101
(Miles)
AAPL
Average Adjusted Plant to Load Center
101
Distance (Miles)
NTPL
TPL for Plants Built within Last 10
10- 2
years
NAPL
APL for Plants Built within Last 10
lo1
years
NAAPL
AAPL for Plants Built within Last 10
l0o1
years
OAPL
TPL for Plants over 10 Years Old
APL for Plants over 10 Years Old
10- 2
10- 1
OAAPL
AAPL for Plants
10 -1
OTPL
Fnew
over 10 Years
Hnew & Nnew
Old
10
% of Generating Capacity added within the
Last 10 Years that is Fossil Fueled, Hydroelectric or Nuclear
-1
-159TABLE
7
COMPARISON OF LINEAR AND EXPONENTIAL PROJECTIONS OF VARIABLE METRO
A.
Model:
CM = eK Aal pa2 pa3 Ga 4 METROaas Ha6 AAPLa7
Regions
and years
used:
(NE, ND, NY, PJ, EC, SE, SC, W) 70, 80, 90
(WC) 70
7/17
Degrees of freedom*:
F-Statistic/Significance*:
Linear
Exponential
67.51/.01
65.61/.01
15.6%
15.6%
Average % Error:
Coefficient
K
.583
a2
a3
a4
aS
a6
- .471
1.325
Model:
.... ..
..e.
Std. Dev. t-valu/_*
-1.946
at
a?
B.
n
Value
.756
.566
.223
.341
.113
.280
.480
.218
.188
.100
.157
.
Std. Dev.
Value
5.16/.01
1.68/.2
2.76/.05
-1.938
.594
- .449
1.335
3.47/.02
3.01/.05
.685
.577
2.23/.1
2.17/.1
.120
.283
.486
.228
.199
.099
.163
.249
.358
t-value/s<*'
4.96/.01
1.59/.2
2.75/.05
3.00/.02
2.89/.05
2.53/.05
2.20/.1
EM = eK AalAAPLa2Ga3METRO
Regions and years used:
(NE, ND,
Y, PJ, EC, SE, SC, W) 70, 80, 90
(WC) 70
Degrees of freedom*:
3/21
Linear
F-Statistic/Significance*:
Average % Error:
Coefficient
ialue
Exponential
89.00/.01
91.02/.01
23.6%
Std. Dev.
22.3%
t-value/o<* Value
t-valueb*"
-. 869
K
-. 936
a1
.728
.070
10.44/.01
.546
.242
.165
.023
3.31/.05
.696
.572
10,43/.01
.202
a2
a3
Std. Dev.
*See Appendix V for dei4nition of these terms
.069
.163
.019
10. 13/.01
3.50/.05
10.56/.01
-1!60-
TABLE
8
Summary of Models Developed
Model #
1
CM = e
A a l pa2
2
EM = e
A a 1 Ga2 METROa3 AAPLa4
3
CM = eK Aa l
a2
4
CM
APLa2 Ga3IGaMETRO
5
CM = eK A a l AAPLa2 Ga3IETRO
6
EM = eK Aa 1 AAPLa2 Ga 3METRO
7
EM
eKAal
a3 Ga4 METROas ua6 AAPLa7
APLa3 Ga4M ETRO
e K Aal AAPLa2 Ga3 Ga4METRO
=
Model
1
K
3
4
5
6
7
-1.946
-1.384
-.185
.219
.304
-. 936
-.999
.583
.502
.490
,639
.756
728
.563
471
.708
.424
.301
.319
. 546
.420
.172
242
.377
a,
a2
2
#'s
-
a3
1.325
.582
.510
.0448
a4
.756
.490
.105
.125
aS5
.566
a6
.223
a7
.341
Average
% Error:
15.6%
23.2%
20%
3-1
3-2
3-7
20%
.163
22%
24%
3-9
3-10
21%
See
Also
Table:
3-8
31
BIBLIOGRAPHY
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