10-11-2012, 05:28 PM
Fuzzy multi-objective technique integrated with differential evolution method to optimise power factor and total harmonic distortion
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Abstract:
The main aim of active-filter-based power-quality improvement schemes is to reduce the total harmonic distortion
(THD) and improve power factor (PF). According to standards, selective harmonic distortion (SHD) should be controlled too.
Non-sinusoidal current owing to non-linear loads causes a non-sinusoidal voltage. Under such conditions, any attempt to
make the power factor unity by usual methods will cause a non-sinusoidal current, which increases the THD. Also, attempt
for harmonic-free current may not conclude unity power factor because of harmonics present in the voltage. Thus, there is a
tradeoff between reduction of THD and improvement in power factor. One of the solutions to this tradeoff is to optimise PF
while keeping THD and SHD into their specified limits. Differential evolution (DE) is introduced in this study and used for
this optimisation problem, and the results are compared with four types of particle swarm optimisation (PSO), including
conventional PSO, linearly decreasing inertia PSO, Type 1 PSO, constant inertia PSO and with the traditional optimisation
method. It is seen that DE algorithm converges to a better result much faster than the other algorithms. Furthermore, using
fuzzy strategy a multi-objective optimisation is proposed to optimise PF and THD simultaneously while keeping SHD in its
limit. It is observed that using these optimisation methods, PF and THD are more improved.
Introduction
In recent years, with the advanced use of semiconductor devices,
power electronics technologies have been developed widely for
different applications, such as uninterruptible power supply
(UPS) systems, lighting and adjustable speed drivers (ASD).
These equipments draw non-sinusoidal current and result in
harmonic distortion. Both active and passive non-linear
devices can cause harmonic distortion in power systems.
Nowadays, most harmonic distortion is caused by the input
stage of the active electronic power converters. Harmonic
distortion due to non-linear power electronic equipment has
significantly deteriorated the power quality (PQ) in power
systems. PQ has become an important factor in differentiating
between successful utilities in the power system specially
deregulated environment [1]. In order to mitigate undesirable
effects of harmonics on PQ, various techniques such as the
use of higher-pulse converters, the modification of electric
circuit configurations, the choice of transformer connections
and the application of harmonic filters have been proposed
[2, 3]. Active power filters were developed for harmonic
compensation and power factor correction. Harmonic analysis
is an efficient application to power systems and it is a
significant approach to evaluate the injected total harmonic
distortion (THD) of currents.
Basic concepts and the proposed strategy
The proposed strategy calculates a reference current, which is
used to produce the compensating current by the inverter.
Assume the supply voltage vs(t) contains a set of harmonic
components (n1) that produce load current is(t) of same
frequencies, and a further set of components (n2) that do
not result in corresponding load current components. Also,
let the load contains a set of current components (n3) due
to its non-linearity, having no corresponding frequency
components in the supply voltage.
Fuzzy optimisation technique
The multi-objective problem is generally solved by three types
of methods. One is pareto-based approach to obtain a set of
non-dominated solutions in the process of optimisation. The
second approach is the coefficient method and the last
approach is transforming the multiple objective function into
a single-objective model and treating it through singleobjective
strategies [32]. In the method developed by
Bellman and Zadeh [33], the single-objective problem is
achieved by maximising the minimum degree of satisfaction
among the membership functions.
The fuzzy decision is marked out due to the intersection of
fuzzy objectives and fuzzy constraints. The first operation is
the fuzzification process of the merged objective function
and the constraints. In this procedure, two types of function
m(x) are defined for each objective function and constraint,
as shown in Fig. 2. In these figures, minimum value for
each objective is obtained by single-objective optimisation
and the maximum value is specified by the initial value. In
other words, single-objective optimisation can provide the
minimum of each objective and in each optimisation, the
other objective will be much worse than its minimum.
Multi-objective technique is employed to optimise the
objectives simultaneously as much as possible. To do so, a
maximum value should be considered for each objective.
These values are determined using the initial value of the
initial vectors of DE. So, when DE generated its initial
vectors, the maximum value of these vectors for each
objective is considered as the maximum required for multiobjective
technique.
DE algorithm for optimisation problem
Like all EAsDEis a population-based optimiser that attacks the
starting point problem by evaluating the objective function at
multiple random initial points. A population composed of NP
individuals evolves over several generations to reach an
optimal solution. This section discusses the application of
DE for the proposed problem. The flowchart of DE
optimisation is illustrated in Fig. 3. It includes several steps
that are explained in this section.
Conclusion
In this paper, DE and four modified PSO methods were used in
order to improve PF and THD while limiting the total and
individual harmonic distortion. Owing to tradeoff between
reduction of THD and improvement in power factor, two
solutions to solve this tradeoff were proposed. The first
solution optimised PF while keeping THD and SHD into
their specified limits. In this paper DE and four types of PSO
were used for this optimisation problem and it was seen that
DE algorithm converges to better solution much faster than
the other algorithms. At the next stage fuzzy strategy was
embedded into the optimisation algorithm to optimise PF
and THD simultaneously while keeping SHD in its limit and
different priority of PF rather than THD and their opposite
effect on each other is discussed. The compensating current
of the shunt active filter with these methods were calculated.
Finally to show the applicability of the algorithm, simulation
was carried out on the same supply with [15] for two cases
(1 and 2) and observed by using DE algorithm for the
optimisation problem that best results were achieved and
both PF and THD get better.