31-08-2012, 02:50 PM
Design of Filters for Reducing Harmonic Distortion and Correcting Power Factor
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Abstract
This work presents a method capable of designing power
filters to reduce harmonic distortion and correct the power factor.
The proposed method minimizes the designed filters’ total
investment cost such that the harmonic distortion is within an
acceptable range. The optimization process considers the
discrete nature of the size of the element of the filter. This new
formulation is a combinatorial optimization problem with a
non-differentiable objective function. In addition a solution
methodology based on an optimization technique - simulated
annealing is proposed to determine the size of filters with
minimum cost. The proposed technique is compared with the
sequential unconstrained minimization technique in terms of
performance and investment cost, via the industrial distribution
system.
Introduction
Increasing concern over the harmonic
(voltage or current distortion) problem stems
from the growing numbers and power ratings of
the highly non-linear power electronic devices
used in controlling power apparatuses in
industrial distribution systems. Harmonic in
power systems shortens the equipment’s life
expectancy and can interfere with
communication lines and sensitive equipment.
The filter design has become essential for
industrial distribution systems. This work
examines the feasibility of designing a filter size
such that the total investment cost, (in which
unacceptable voltage profiles must be correct
and harmonic must be reduced within the
permissible maximal value e.g. IEEE Std. 519
[4]), is keep at a minimum.
Implement of SA to Design Filters
This section presents a solution algorithm for
designing harmonic filters to determine the size of
the filters with minimum cost.
An algorithm designed as the basis of SA
consists of four important elements: (1)
configuration space, (2) perturbation mechanism,
(3) an objective function and (4) a cooling
schedule.
Objective Function
The objective function used in the problem
of design filters is the cost function of filters.
The cost of C and L is generally not a smooth
function and not proportional to their sizes.
Therefor, the parameter KC and KL are
constructed by looking up tables in the computer
program.
Configuration Space
Configuration space is the set of allowed
system configurations. Design of configuration
space is critical to the iterations’ efficiency and
the final solution’s quality. Properly designing
configuration space requires good engineering
judgment.
Cooling Schedule
SA algorithm analogs to the cooling
down process of material crystallize. Low
speed cooling down generates a perfect
crystal; otherwise, it will fall to drawback.
The cooling schedule is crucial for both the
iterations’ overall efficiency and the final
solution’s quality. High temperature stage
initially employs a high speed cooling down
to enhance the annealing efficiency and at
low temperature stage employs a low cooling
schedule to upgrade the solution’s quality.
The cooling schema generally corresponds to
the rule: Tk+1 = α(Tk)*Tk where α(Tk) is
adjust to a higher value to avoid becoming
stuck at a local optimal configuration at low
temperature stage. Otherwise, the α(Tk) is
adjusted to value to increase the convergence
speed.