25-09-2012, 12:55 PM
COMPREHENSIVE DISTRIBUTION POWER FLOW: MODELING, FORMULATION, SOLUTION ALGORITHMS AND ANALYSIS
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Introduction
The supply of electric power to homes, offices, schools, factories,
stores, and nearly every other place in the modern world is now taken for
granted. Electric power has become a fundamental part of the infrastructure
of contemporary society, with most of today’s daily activity based on
the assumption that the desired electric power is readily available. The
power systems which provide this electricity are some of the largest and
most complex systems in the world. They consist of three primary components:
the generation system, the transmission system, and the distribution
system. Each component is essential to the process of delivering power
from the site where it is produced to the customer who uses it.
Objectives and Contributions
The objective of this work was to develop a formulation and an efficient
solution algorithm for the distribution power flow problem which
takes into account the detailed and extensive modeling necessary for use in
the distribution automation environment of a real world power system.
A general framework was developed for each of the three classes of
existing algorithms, and a common set of network component models was
chosen. The general framework for each class helps in relating the proposed
algorithms to one another and also reveals variations of each class
that have not previously been explored. Within each class, new algorithms
were developed and, where necessary.
Basic Problem Framework
The distribution power flow problem is the problem of finding the
operating point of a distribution network at steady state under given conditions
of load and cogeneration. This involves, first of all, finding all of the
bus voltages. From these voltages, it is possible to directly compute currents,
power flows, system losses and other steady state quantities. This
chapter presents some of the fundamental concepts which are general in
nature and apply to all or at least several of the approaches discussed in
later chapters.
Mathematical Notation
Since this dissertation deals with three-phase unbalanced power flow,
vectors are typically used to represent voltages, currents, power flows, and
admittances. Many of the formulas presented in this work can be
expressed more clearly and compactly by using certain notational conventions.
The conventions shown in Table 2.1 for complex vectors x and y, for complex matrices A, X, and Y, and for functions f and g, will be used extensively
throughout this dissertation.
Bus and Lateral Indexing
In most typical power flow formulations, a set of equations and
unknowns is associated with each bus in the network, and these equations
and unknowns are organized by a particular bus ordering. Because of the
radial structure of the systems under consideration, the number of equations
and variables can be reduced so that each set of equations and
unknowns corresponds to an entire lateral instead of an individual bus.
Such a formulation therefore calls for an appropriate lateral indexing to
order these equations and variables.
Indexing Scheme
A radial system can be thought of as a main feeder with laterals.
These laterals may also have sub-laterals, which themselves may have
sub-laterals, etc. First, the level of lateral i is defined as the number of laterals
which need to be traversed to go from the end of lateral i to the
source. For example, the main feeder would be level 1, its sub-laterals
would be level 2, their sub-laterals level 3, etc.
Second, the laterals within level l are indexed according to the order
seen during a breadth-first traversal of the network. Each lateral can be
uniquely identified by an ordered pair where l is the lateral level and
m is the lateral index within level l.
Third, buses are indexed within each lateral, starting with the first
bus on the lateral, so that each bus is uniquely identified by an ordered triple
where n is the bus index. The ordered triple refers to
the nth bus on the mth level l lateral. The source is given an index of
. The number of levels in a network will be denoted by L, the number
of laterals on level l by , and the number of buses on lateral
by .