Abstract: Environmental awareness and the recent
environmental policies have forced many electric utilities to
restructure their operational practices to account for their emission
impacts. One way to accomplish this is by reformulating the
traditional economic dispatch problem such that emission effects are
included in the mathematical model. This paper presents a Particle
Swarm Optimization (PSO) algorithm to solve the Economic-
Emission Dispatch problem (EED) which gained recent attention due
to the deregulation of the power industry and strict environmental
regulations. The problem is formulated as a multi-objective one with
two competing functions, namely economic cost and emission
functions, subject to different constraints. The inequality constraints
considered are the generating unit capacity limits while the equality
constraint is generation-demand balance. A novel equality constraint
handling mechanism is proposed in this paper. PSO algorithm is
tested on a 30-bus standard test system. Results obtained show that
PSO algorithm has a great potential in handling multi-objective
optimization problems and is capable of capturing Pareto optimal
solution set under different loading conditions.
Abstract: An enhanced particle swarm optimization algorithm
(PSO) is presented in this work to solve the non-convex OPF
problem that has both discrete and continuous optimization variables.
The objective functions considered are the conventional quadratic
function and the augmented quadratic function. The latter model
presents non-differentiable and non-convex regions that challenge
most gradient-based optimization algorithms. The optimization
variables to be optimized are the generator real power outputs and
voltage magnitudes, discrete transformer tap settings, and discrete
reactive power injections due to capacitor banks. The set of equality
constraints taken into account are the power flow equations while the
inequality ones are the limits of the real and reactive power of the
generators, voltage magnitude at each bus, transformer tap settings,
and capacitor banks reactive power injections. The proposed
algorithm combines PSO with Newton-Raphson algorithm to
minimize the fuel cost function. The IEEE 30-bus system with six
generating units is used to test the proposed algorithm. Several cases
were investigated to test and validate the consistency of detecting
optimal or near optimal solution for each objective. Results are
compared to solutions obtained using sequential quadratic
programming and Genetic Algorithms.