# Optimal power flow using a genetic algorithm and linear algebra [electronic resource] /

Abstract (Summary)

Optimal Power Flow Using a
Genetic Algorithm and Linear Algebra
Reid S. Maust
Artificial intelligence is used to help a hypothetical electric utility meet is electric
load economically. The optimal power flow problem (OPF) problem is an optimization
problem, in which the utility strives to minimize its costs while satisfying all of its
constraints. A genetic algorithm (GA)—a specific type of artificial intelligence—is
employed to perform this optimization. To speed convergence, some theory from linear
algebra is incorporated into the algorithm.
A GA provides several advantages over more traditional OPF algorithms. For
instance, a GA does not constrain the shape of the generators’ cost curves and is flexible
enough to incorporate control devices such as tap-changing transformers and static VAR
compensators.
In the literature, GA-based methods typically use the GA to find the real power and
voltage magnitude at each generation bus. To enforce the inequality constraints on
voltage magnitudes and angles, these algorithms must compute these quantities for all
buses. This requires the solution of the load-flow equations, a set of nonlinear equations
that provide real and reactive power in terms of voltage magnitude and angle. Solving
for the voltage quantities is computationally intensive when performed repeatedly
through the iterations of a method. In contrast, the GA-OPF method presented here
reduces the number of load-flow solutions by having the GA find the voltage magnitude
and angle at each bus. The real and reactive power are then found by direct substitution
into the load-flow equations. To narrow the search for the optimal solution, a vector
space is derived that contains all solutions meeting the inequality constraints. This
speeds convergence of the algorithm by eliminating a large number of illegal solutions.
The effectiveness of this method is demonstrated on three test systems—the Steinberg
and Smith example, the IEEE 30-bus test system, and the IEEE 118-bus test system. For
the first two examples, the GA-OPF algorithm finds an answer that agrees with published
results. For the 118-bus system, the GA-OPF demonstrates its ability to enforce emission
constraints and its potential to be used with larger systems. Thus, the GA-OPF algorithm
is shown to be a valid tool to perform this optimization.
Bibliographical Information:

Advisor:

School:West Virginia University

School Location:USA - West Virginia

Source Type:Master's Thesis

Keywords:electric power systems genetic algorithms

ISBN:

Date of Publication: