IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 23, NO. 2, APRIL 2008 915
Multistage Model for Distribution Expansion
Planning With Distributed Generation—Part I:
Problem Formulation
Sérgio Haffner, Member, IEEE, Luís Fernando Alves Pereira, Luís Alberto Pereira, and
Lucio Sangio Barreto, Student Member, IEEE
Abstract—This paper presents a model for use in the problem
of multistage planning of energy distribution systems including
distributed generation. The expansion model allows alternatives
to be considered for increasing the capacity of existing substations,
for installing new ones, for using distributed generation, and for
the possible change to feeders in terms of addition and removing
feeders sections; combining, subdividing, and load transfer be-
tween feeders; and replacement of conductors. The objective
function to be minimized is the present value of total installation
costs (feeders and substations), of operating and maintaining
the network, and of distributed generation. The model takes
operational constraints on equipment capacities and voltage limits
together into account with logical constraints, aimed at reducing
the search space. This paper presents: 1) an extension to the linear
disjunctive formulation to represent the inclusion, exclusion, and
replacement of branches and 2) a generalization of constraints
related to the creation of new paths which can be applied in
more complex topologies. The resulting mixed integer linear
model allows the optimal solution to be found using mathematical
programming methods, such as the branch-and-bound algorithm.
The validity and efficiency of the model are demonstrated in Part
II of this paper.
Index Terms—Distributed generation, power distribution,
power distribution economics, power distribution planning.
NOMENCLATURE
A. Sets
,
Branches of the fixed network and
defined changes for each branch
.
,
Branches of the replacement
network and alternatives for each
branch
.
,
Branches of the addition network
and alternatives for each branch
.
,
Nodes of the existing and candidate
substation and alternatives for
expanding the capacity of the node
.
Manuscript received August 14, 2006; revised February 2, 2007. This work
supported by Companhia Estadual de Energia Elítrica (CEEE). Paper no.
TPWRD-00470-2006.
S. Haffner is with the Electrical Engineering Department of the State Uni-
versity of Santa Catarina (UDESC–CCT–DEE), Joinville, SC, CEP 89223-100,
Brazil (e-mail: haffner@ieee.org).
L. F. A. Pereira, L. A. Pereira, and L. S. Barreto are with the Electrical
Engineering Department of Pontifical Catholic University of Rio Grande do
Sul (PUCRS), Sala 150, CEP 90619-900, Brazil (e-mail: pereira@ee.pucrs.br;
lpereira@ee.pucrs.br; barreto@ieee.org).
Digital Object Identifier 10.1109/TPWRD.2008.917916
Load nodes.
Distributed generation nodes.
B. Binary variables
Alternative of the replacement
branch
at stage .
Alternative of the addition
branch
at stage .
Fixed costs for installation or
expansion of substation node
at
stage
.
Alternative for expansion of
substation node
at stage .
Investment vector at stage .
,
Alternative for utilization of the
branch
at stage :
means that the alternative is
available.
,
Alternatives and for
utilization of the replacement branch
at stage .
Alternative for utilization of the
addition branch
at stage .
C. Continuous
variables
,
Current of branch in the fixed
network at stage
.
, ,
Current of branch in the
replacement network at stage
and their maximum capacities
and .
,
Current of branch in the addition
network at stage
and its maximum
capacity
.
, ,
Current vectors for the fixed,
replacement, and addition branches
at stage
.
, ,
Generation at node at stage and
the substations’ maximum capacity.
Nodal-load shedding at stage .
Vector of nodal-load shedding at
stage
.
,
Distributed generation at node at
stage
and its maximum capacity.
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