This preview shows pages 1–3. Sign up to view the full content.
543
14.
COST MINIMIZATION
Summary
Transformer design is primarily determined by minimizing
the overall cost, including the cost of materials, labor, and losses. This
minimization, however, must take into account constraints which may
be imposed on the transferred power, the impedance, the flux density,
the overall height of the tank, etc. Since the cost and constraints are
generally nonlinear functions of the design variables, a nonlinear
constrained optimization method is required. We examine several such
methods, developing in greater detail the one which appears to be best
suited to our needs. It is then applied to transformer design, considering
for simplicity only major cost components and constraints.
14.1
INTRODUCTION
A transformer must perform certain functions such as transforming power
from one voltage level to another without overheating or without
damaging itself when certain abnormal events occur, such as lightning
strikes or short circuits. Moreover, it must have a reasonable lifetime (>
20 years) if operated under rated conditions. Satisfying these basic
requirements still leaves a wide latitude in possible designs. A transformer
manufacturer will therefore find it in its best economic interest to choose,
within the limitations imposed by the constraints, that combination of
design parameters which results in the lowest cost unit. To the extent
that the costs and constraints can be expressed analytically in terms of
the design variables, the mathematical theory of optimization with
constraints can be applied to this problem,
Optimization is a fairly large branch of mathematics with major
specialized subdivisions such as linear programming, unconstrained
optimization, and linear or nonlinear equality or inequality
constrained optimization. Transformer design optimization falls into
the most general category of such methods, namely nonlinear equality
and inequality constrained optimization. In this area, there are no
algorithms or iteration schemes which guarantee that a global optimum
© 2002 by CRC Press
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document COST MINIMIZATION
544
(in our case a minimum) will be found. Most of the algorithms proposed
in the literature will converge to a local optimum with varying degrees
of efficiency although even this is not guaranteed if one starts the
iterations too far from a local optimum. Some insight is therefore
usually required to find a suitable starting point for the iterations. Often
past experience can serve as a guide.
There is however a branch of optimization theory called geometric
programming which does guarantee convergence to a global minimum,
provided the function to be minimized, called the objective or cost
function, and the constraints are expressible in a certain way [Duf67].
These restricted functional forms, called posynomials, will be discussed
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 10/19/2010 for the course ENGINEERIN ELEC121 taught by Professor Tang during the Spring '10 term at University of Liverpool.
 Spring '10
 TANG
 Strain

Click to edit the document details