United States
Environmental Protection
Agency
Environmental Research
Laboratory
Duluth MN 55804
Research and Development
EPA-600/S3-83-061 July 1984
Project Summary
A Simple Transmission
Network Planning Method:
Wisconsin Power Plant
Impact Study
Farrokh Albuyeh and James J. Skiles
This report describes a new model for
planning the expansion or modification
of transmission networks. The model is
different from traditional models which
employ mathematical optimization
techniques, in that it closely parallels
the logical steps followed in practice by
planning engineers. No claim is made
for the optimally of plans produced.
but they will be similar to those
developed by planning engineers on the
basis of their working experience with
the system.
The first step in analyzing a power
network is to formulate a model that
describes the components in the system
and how they are interconnected. A
classical network reduction algorithm
models the system by simple equivalents.
focusing attention on parts of the
system that are of interest. Reliability
criteria for the network are translated
into a series of contingency studies
which the algorithm treats as pass-fail
tests. Sensitivity matrices simulate the
experience of planning engineers. An
overload logic then ranks the branches
of the network according to their
expected effect on the system, and
performs a series of contingency
studies to find the least costly changes
that will alleviate line overloads in the
network. When no overloads remain,
the voltage correction logic checks for
deviations of the voltage from specified
limits and adjusts the bus reactive
power injections where necessary. The
program then advances to the next
planning period and repeats the entire
process. A line removal subroutine
checks the usefulness of lines after
passage of a number of planning
periods and removes unnecessary lines.
Sample planning studies indicate that
this method is applicable to practical
problems in large networks, and that it
will significantly shorten and simplify
the planning process.
This Project Summary was developed
by EPA's Environmental Research
Laboratory, Duluth, MN. to announce
key findings of the research project that
is fully documented in a separate report
of the same title (see Project Report
ordering information at back).
Background
One of the most important areas to be
considered in the planning of new or
expanded sites for generating electricity
is the accompanying modification of the
transmission network. The network must
be designed to carry electricity effectively
and economically, with a specified degree
of reliability, from the generating site to
the load centers. Constraints on the
network may limit or preclude develop-
ment of certain sites. Therefore, modifi-
cation of the transmission network must
be considered in evaluating alternative
plans for expansion.
This report describes a new model,
unlike earlier models employing optimi-
zation techniques, for planning the ex-
pansion or modification of transmission
networks. It closely parallels the logical
steps followed in practice by planning
engineers. The report contains the
following major parts:
1. Review of the basic concepts in
power systems.
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r
2. Review of load-flow studies and
methods.
3. Review of methods for network
reduction.
4. Review of methods for network
planning and expansion.
5. Description of the proposed method
and examples of systems studies
based on it.
6. Appendices: mathematical deriva-
tions for models, computer outputs
for sample studies, and listings of
programs for an AC model and a
DC model.
Planning expansion of the transmission
network is one of the most difficult parts
of an electrical network study. Mostofthe
problems relate to four factors:
1. The large numbers of possible
expansion alternatives.
2. The complexity of reliability criteria,
which vary with the system and the
utility company.
3. External cost variables, such as
environmental costs, that are
difficult to quantify.
4. Uncertainties in predicting future
power demand.
Traditionally, plans for network expan-
sion have been designed by the utilities'
planning engineers on the basis of their
work experience with the system. The
system is expanded to satisfy specified
reliability criteria. Outages are simulated
on critical branches, and for a predicted
load profile the network is expanded by a
standard procedure.
Most attempts to develop automatic
algorithms for planning network expan-
sion have treated the problem as one of
optimizing a performance index subject to
a set of equality and inequality constraints.
These techniques are difficult to evaluate
because few of them have been developed
beyond the experimental stage. Planning
engineers are reluctant to use the
automated algorithms. Not only do plans
produced by automated methods not
always match those developed by standard
engineering procedures, but "optimal
solutions" obtained from different models
and with different techniques differ from
each other. The method developed in this
report has been tested in several sample
cases and appears to be a practical tool
for the complex and lengthy process of
planning expansion of transmission
networks.
Review of Planning Models
A typical power system is composed of
generating stations connected to load
centers by a transmission network.
Transport of electricity can also take place
or from other power systems. The
transmission system generally has a
multiple loop structure with several
multiple-interconnected voltage levels (in
contrast to the radial structure common
to distribution systems). The loop structure
permits flexibility in routing of energy on
various links and offers multiple path
combinations for contingencies.
The first step in analyzing a power-
network is to formulate a model which
describes the characteristics of individual
components in the system and how they
are interconnected. For computer appli-
cations, network matrices provide an
accurate and convenient way of repre-
senting network models.
Load-flow calculations are performed
during planning, operation, and control
phases of power system studies. Digital
computers have replaced the earlier
"network analyzers" in these studies.
The load-flow problem is solved with a set
of nonlinear equations that describe the
steady state performance of the system.
The principal information that such a
solution yields is the magnitude and
phase angle of the voltage at each bus
and the real and reactive power flowing in
each line. The report discusses several
so-called Y-bus methods for solving load-
flow problems.
The report also reviews four techniques
for network reduction. These techniques
simplify non-essential parts of the
network so that the planner may focus on
those parts of the network that are of
interest.
Planning studies for expansion of power
systems can be divided into four steps:
forecasting loads, planning generation
capacity, planning transmission networks,
and planning distribution networks.
Planning has traditionally been treated as
a problem in mathematical optimization.
The techniques employed include heu-
ristic methods, linear programming,
nonlinear programming, dynamic pro-
gramming, and integer programming.
The report describes the major features of
these methods. All of them require a
mathematical model of the system and a
statement of the problem in terms of
mathematical optimization of a perform-
ance index or cost function. The major
differences among present automatic
network planning techniques are in their
methods of optimization.
None of the earlier methods has so far
led to a practical solution. This failure
may be caused by the large number of
variables that are difficult to quantify and
predict, such as costs and environmental,
political, geographical, social, and tech-
nical constraints. The various methods
are nearly impossible to evaluate and
compare because few of them have been
developed beyond experimental stages
and the demonstrations that have ap-
peared represent systems of very limited
size.
The Proposed Model
The algorithm developed in this report
divides the problem into three parts:
modeling the network, contingency
analysis, and expansion logic. In modeling
the network, a classical network reduction
algorithm is used to model the external
system by simple equivalents and to let
the planner focus on the areas of interest.
Two different modeling techniques are
utilized: DC modeling and AC modeling.
In the DC model, the network is repre-
sented by a DC power flow method
whereas in the AC model the network is
modeled by a decoupled AC power flow
model. For contingency analysis an
automatic contingency selection method
using network sensitivity matrices is
developed. This technique selects only
the contingencies that are critical and
avoids having to simulate all possible
contingencies. The expansion logic is
composed of an overload logic and a
voltage correction logic. The overload
logic uses the sensitivity matrices to
identify the most economical set of
branch reinforcements and the voltage
correction logics determines that reactive
power adjustments at buses to correct
voltage level violations. The voltage
correction logic is used in conjunction
with the AC model only.
Before a planning study for the trans-
mission network begins, the sites, sizes,
and dates of future additions of generating
capacity will be tentatively planned. The
following data are needed:
1. Descriptions of the existing trans-
mission system.
2. Forecasted load profiles for the
entire planning period.
3. A list of potential rights-of-way,
specifying their lengths, constraints,
and the particular transmission
facilities they can accommodate.
4. Impedances, shunt capacitances,
and capacities of available new
transmission facilities, together
with data on their cost.
5. Operating constraints for the sys-
tem, which are strongly influenced
by limitations in transmission.
6. Legal, environmental, and political
constraints.
7. Reliability criteria.
Sensitivity matrix
The sensitivity matrix J is an r x r full
matrix, where r is the number of branches.
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Each element Ju is the ratio of the branch
phase angle difference Af, to the branch
capacity
Contingency analysis
The expanded network must satisfy
prescribed reliability criteria. In planning
studies, these criteria are translated into
a series of contingency studies and are
treated as pass-fail tests. The network is
to be designed to withstand any single
line outage with no cascading overloads
for the given load and generation profile.
Multiple contingency tests are made by
removing lines or generators one by one
and proceeding as with the single
contingency test.
An automatic contingency selection
method has been implemented to select
critical branches and thus reduce the
number of contingency cases studied.
For every branch, a number is calculated
showing the relative effect that removal
of Ymax units of susceptance from that
branch will have on the system.
The Effect Indices are then used to rank
branches according to their expected
effect on the system. The magnitudes of
the Effect Indices indicate the expected
effect that the removal of the largest
capacity line from the branch may have
on the system. For contingency studies,
the branch with the largest Effect Index is
outaged first. The results of the load flow
are checked for overloads. Then, the
branch with the next largest Effect Index
is outaged. This process is repeated until
no overloads are observed over several
successive contingency cases. Different
stopping criteria may be used. Tests on
the IEEE 14 Bus Test System and the
Wisconsin Upper Michigan System's
reduced network show that with the
stopping criterion of "no overloads over
four successive outages" the results are
identical to those obtained using an
exhaustive contingency checking ap-
proach.
Cost vector
The total cost of adding capacity on a
branch is a function of capital cost,
operating cost, and environmental cost.
Because many environmental (including
social and political) costs cannot be
quantified, the environmental cost is
usually treated as a "go" or "no go" type
of factor. It can be assigned an arbitrarily
large value for a particular right-of-way in
order to exclude that right-of-way from
consideration by the automatic expansion
algorithm. Methods are needed for
assigning realistic dollar values to
environmental costs so that the model
can treat these costs as it does conven-
tional capital and operating costs.
The expansion logic
The planning logic is divided into two
parts:
1) The Overload Logic
2) The Voltage torrection Logic
The overload logic utilizes the sensitivity
matrices to find the least costly network
changes to alleviate line overloads. This
is a simple approach and can be classified
as a heuristic method that treats the
problem as a sequence of unconstrained
minimization problems.
There are two assumptions made:
1) Transmission capacity of a branch
can be increased by adding lines
only.
2) Only specific type of lines or
voltage levels that are provided to
the program can be used in ex-
panding the system.
In the absence of an input table
containing types of lines to be chosen
from, the line types already existing on
rights-of-way are used during the line
• selection process.
The voltage correction logic
The voltage correction logic is initiated
after all line overloads are alleviated. The
steps are as follows:
1) The contingency tests are carried
out and a vector is formed that
shows the largest voltage magni-
tude deviations from the specified
limits for every bus during the
contingency tests.
2) From the reactive power flow
equation, the adjustments to the
bus reactive powers needed to
bring the voltage magnitudes
within the specified limits are
calculated.
Line removals
As the network is developed through
successive planning periods, lines added
in earlier periods may become unneces-
sary. Therefore, a subroutine was devel-
oped to test the possibility of removing
lines from the system. A line removal
program checks the usefulness of lines
after passage of a number of planning
periods and removes unnecessary lines.
This algorithm may be viewed as the
reverse of contingency analysis, in that it
tests the results of removing branches
having the least effect on the system.
Planning studies
Several sample planning studies were
carried out using network data for a
model of the Pacific Northwest System,
the IEEE 14-Bus Test System, and a 26-
bus model of part of the Wisconsin Upper
Michigan System. These are presented in
the Appendices of the full report. Where
real data were unavailable, arbitrary
values were assumed. In practice, the
planning engineer would have access to
the necessary data and would be able to
use the computer programs developed
here to solve real, practical problems.
Conclusions and
Recommendations
1. A simple automated method for
network expansion has been devel-
oped. It is especially suited for studies
of alternative schedules for expanding
the generation and transmission of
electricity.
2. The steps in the algorithm follow the
logical steps carried out in practice by
planning engineers.
3. No claim is made for the optimality of
the plans produced by this method,
but they will be similar to those
obtained by planning engineers and
the automated method will shorten
and simplify the planning process.
4. The method has three new features:
a. A network expansion technique
which uses sensitivity matrices
to obtain economical plans.
b. Use of the "B" matrix from the
fast-decoupled load-flow algorithm
in an iterative procedure for
adjusting bus reactive power to
bring voltage within specified
limits.
c. An automatic contingency se-
lection procedure that ranks
branches according to their
expected effect on the system,
thus reducing the number of
contingency studies required.
5. Of the two models developed, the
non-iterative DC model is simpler
and faster and convergency difficult-
ies do not occur with certain ill-
behaved networks. The AC model is
more realistic and more flexible. It
uses a more accurate network model
and it provides information on voltage
magnitudes as well as on load flows.
6. Interaction between the planner and
the program is not only possible but
necessary:
a. New, updated information should
be fed into the program regularly.
The program cannot be expected
to give satisfactory results over
many planning periods unless it
"knows" everything the planning
engineers know.
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b. A variety of generation and load
schedules should be considered
for the network under study.
c. Various ratings of network com-
ponents should be considered:
for example, emergency ratings,
normal summer, normal winter,
etc. Ratings on other components
such as breakers or line traps
may also limit the flow in a
branch.
d. The reliability criterion incorpo-
rated in the program is a single
contingency criterion. The user
might want to examine other
contingency cases. Generator
outages and multiple line contin-
gencies can also be simulated.
e. The program cannot introduce
either new nodes or new rights-
of-way into the system. The
planner can represent potential
but initially unusedrights-of-way
as lines of high impedance, and
potential but initially unused
nodes as nodes connected to the
network by potential rights-of-
way.
f. If abnormal plans result, the
planner should consider alterna-
tives such as lines of higher
voltage, changes in transformer
taps, or additional lines for
voltage support.
7. Several avenues for future research
are apparent:
a. Further work on the load-flow
algorithm should include trans-
former tap changing under load.
b. Combining network reduction
and network planning into one
program would overcome the
need for multiple editing programs
and relax restrictions on the
system size.
c. The program should be modified
to include other techniques for
network reduction.
d. Research is needed to implement
sparse matrix techniques in the
planning programs.
e. Continued efforts are needed to
quantify the broad range of
environmental and social costs of
transmission networks.
Farrokh Albuyeh and James J. Skiles are with the University of Wisconsin,
Madison, Wt 53706.
Gary E. Glass is the EPA Project Officer (see below).
The complete report, entitled "A Simple Transmission Network Planning
Method: Wisconsin Power Plant Impact Study," (Order No. PB 84-199 553;
Cost: $ 16.00. subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Environmental Research Laboratory
U.S. Environmental Protection Agency
6201 Congdon Blvd.
Duluth.MN 55804
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United States
Environmental Protection
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Center for Environmental Research
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Official Business
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