Unit-7&8
Lecture 47
UNIT 7&8
Optimal Power System Expansion Planning
Optimization Techniques:
In everyday life, all of us are confronted with some decision makings. Normally,
we try to decide or the best. If someone is to buy a commodity, he or she tries to
buy the best quality, yet with the east cost. These types of decision makings are
categorized as optimization problems in which the aim is to find the optimum
solutions; where the optimum may be either the least or the most.
Most of the operational and planning problems consist of the following three major
steps
• Definition
• Modeling
• Solution algorithm
Decision variables are the independent variables; the decision maker has to
determine their optimum values and based on those, other variables (dependent)
can be determined. For instance, in an optimum generation scheduling problem,
the active power generations of power plants may be the decision variables. The
dependent variables can be the total fuel consumption, system losses, etc. which
can be calculated upon determining the decision variables. In a capacitor allocation
problem, the locations and the sizing of the capacitor banks are the decision
variables, whereas the dependent variables may be bus voltages, system losses, etc.
Mathematical Algorithms.
Dept. of EEE, NIT-Raichur
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Unit-7&8
Lecture 47
A mathematical optimization technique formulates the problem in a mathematical
representation; as given by (2.2) through (2.4). Provided the objective function
and/or the constraints are nonlinear, the resulting problem is designated as Non
Linear optimization Problem (NLP). A special case of NLP is quadratic
programming in which the objective function is a quadratic function of x. If both
the objective functions and the constraints are linear functions of x, the problem is
designated as a Linear Programming (LP) problem. Other categories may also be
identified based on the nature of the variables. For instance, if x is of integer type,
the problem is denoted by Integer Programming (IP). Mixed types such as
MILP(Mixed Integer Linear Programming) may also exist in which while the
variables may be both real and integer, the problem is also of LP type. For
mathematical based formulations, some algorithms have, so far, been developed;
based on them some commercial software have also been generated. In the
following subsections, we briefly review these algorithms. We should, however,
note that generally speaking, a mathematical algorithm may suffer from numerical
problems and may be quite complex in implementation. However, its convergence
may be guaranteed but finding the global optimum solution may only be
guaranteed for some types such as LP. There is no definite and fixed classification
of mathematical algorithms. Here, we are not going to discuss them in details.
Instead, we are going to introduce some topics which are of more interest in this
book and may be applicable to power system planning issues.1 Some topics, such
as game theory, which are of more interest for other power system issues (such as
market analysis of power systems), are not addressed here.
Dept. of EEE, NIT-Raichur
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