International Conference on Electrical, Electronics, and Optimization Techniques (ICEEOT) - 2016
A Genetic Algorithm Optimized Fuzzy Logic
Controller for Shunt Active Power Filter
Moinuddin K Syed
Dr. BV Sanker Ram
Department of EEE,
Department of EEE,
SCIENT Institute of Technology,
JNTUH College of Engineering & Technology,
Hyderabad, TS, India. moinuddin_syed@hotmail.com
Hyderabad, TS, India
Abstract –Shunt Active Power Filter (SHAPF) have proven to
be indomitably the prominent among the constellation of
APFs to resolve power quality aberrations. Investigation for
an optimal controller in switching the DC capacitor in APF
had been incessant. To achieve the required level of total
harmonic distortion (THD), the conventional PI Controller
was improved with Fuzzy Logic Control (FLC). Fuzzy logic
can be termed as universilization of classical data. In fuzzy
logic, also called as diffuse logic, just two alternatives will not
be considered but truth values for propositions of complete
content. However, tuning the fuzzy membership functions
proved to be an obscure and extensive process. This paper
presents a Genetic Algorithm optimized Fuzzy Logic
Controller (GA-FLC) ameliorating the memberships of the
heuristic controller giving impetus to the creditable shunt
active power filter. This paper presents the importance of
fuzzy controller to reduce total harmonic distortions in the
system with shunt active filter. Total harmonic content in
source current was shown when the shunt active filter was
implemented with fuzzy controller. THD was limited with the
use of fuzzy controller than compared to PI controller.
extent as a substitute to a human expert in tuning the fuzzy
memberships [1-3].
Keywords – fuzzification, de-fuzzification, shunt APF.
I.
Introduction
Power quality aberrations and compliance to IEEE-519
standards limiting the Total Harmonic Distortion (THD)
had always been a vexation for electrical engineers.
Several control strategies and algorithms to transform the
coordinates have evolved to feed as the reference to the
conventional PI controller resulted in enormous
computational efforts. Though Fuzzy Logic Controllers
have brought relief proving to be robust and handling nonlinear problems to a good extent, shaping the memberships
involved the human expertise. Self reliant intelligent
controllers such as Artificial Neural Networks and
evolutionary Genetic Algorithms have proved to a great
978-1-4673-9939-5/16/$31.00 ©2016 IEEE
This paper presents a GA which has been applied to
optimize the fuzzy members fed to the conventional FLC
for the best known Synchronous Reference Frame (SRF)
control strategy of SHAPF to achieve much reduced
THDs. Fuzzification includes normalization by scale
transformation replicating the physical values to
normalized universe of discourse [4-8]. The normalization
of inputs is between -10 to 10 converting crisp data to
fuzzy sets random overlap among the membership
functions, so that, no more than two fuzzy membership
functions will have nonzero degree of membership.
Membership functions are chosen to be triangular for their
simplicity, minimizing memory space for computation,
symmetry and have zero value at centroid.
II. Conventional FLC
The Harmonic reduction is obtained by controlling the
error and the reference derivative fed as fuzzified inputs to
the rule base. Based on expertise, rule base is set; the
defuzzified output is given to the compensation capacitor
on hand in the Voltage Source Inverter (VSI). Fig. 1 shows
the conventional FLC.
Fig. 1 Fuzzy Logic Controller
TABLE 1: M ODEL OF F UZZY R ULES
Fuzzy memberships are shaped as shown in Fig. 2,
where both the input of reference current and the current
error derivative has seven membership functions NB
(Negative Big), NM (Negative Medium), NS (Negative
Small), Z (Zero), PS (Positive Small), PM (Positive
Medium) and PB (Positive Big) converting the
mathematical variables to linguistic variables.
ec
NB NM NS
e
Z
PS PM PB
NB NB NB NM NM NS NS
Z
NM NM NM NM NS NS
Z
PS
NS NM NM NS NS
PS PS
Z
Z
NM NS NS
Z
PS PS PM
PS
NS NS
Z
PS
PS PM PM
PS PM PM PB
PM NS
Z
PS
PB
PS
PS PM PM PB PB
Z
Fuzzy Rules: Fuzzy rules are based on perception rather
than an explicit model. The rules and shape of the
membership functions are developed through repeated
simulations and aptness. As the output membership
functions are expected to be non-linear the Mamdani
inference is best suitable and has been considered for
implementation. Mamdani model is beneficial to the
operator in framing the fuzzy rules, as it involves no
mathematical expression in the fuzzy rule base, and as the
weight is not significant, it is kept unity.
The dissemination of fuzzy IF-THEN rules with truncated
triangular membership functions is obtained implementing
the Mamdani min and prod operations.
Defuzzification: Centroid based defuzzifier is chosen for
better and smoother performance giving superior results.
Scaling method of defuzzification is implemented so as to
scale down the membership function and achieve
continuous transition of membership functions. The output
is the aggregate of the output fuzzy set. As the crisp output
is a physical in quantity the denormalization is kept unity.
The crisp output produces the change in reference current
which in turn controls the capacitor switching. The
defuzzification is done to convert the fuzzy variables to
crisp mathematical output. The dissemination of the output
with seven member functions similar to that of inputs but,
normalized between -3 to 3 can be seen in Fig. 2.
III. GA OPTIMIZING FLC
Fig. 2 Conventional Fuzzy Memberships
GA is parallel, global search techniques which take the
concept from evolution theory and natural genetics,
emulating biological evolution by means of genetic
operators such as reproduction, crossover and mutation.
GAs work with a set of artificial creatures (string) called
population. In every generation, GAs generates a set of
offspring’s from old population according to the defined
fitness function. By exchanging the information between
every individual, GA has kept the better schemata, which
yielded higher fitness, from generation to generation with
improved performance.
Fuzzy Logic Controller based on approximate
reasoning were widely applied to various situation where
the plants' models cannot be easily developed, but the
skilled operators satisfactorily control them merely follow
some experimental statements such as "IF something
happens THEN do some actions". By transferring human's
expertise into fuzzy IF-THEN rules, one can construct a
linguistic FLC to control complex or ill-defined systems.
However, in FLC design, it still has several well-known
difficulties: 1) The fuzzy control rules are experience
oriented and the suitable membership functions should be
obtained by time-consuming trial and error procedure; 2)
The characteristics of control system cannot be prespecified; 3) There is no criterion to get an optimal or at
least sub-optimal FLC. The genetic algorithms (GAs) were
adopted to search the parameter space of membership
functions for capacitor optimization and tried to fine out a
nearly optimal rule base which can drive the state to hit a
pre-defined capacitor voltage.
The parameters considered for genetic operation are –
Population Generation is 50, Population Size is 30, Length
of the Chromosome is 10, Crossover Rate is 0.60,
Mutation Rate is 0.001.
as 1.1535, kec as 20.9971 and the scaling factor ku as
11.8280; the output of the fuzzy controller is expressed as:
The fitness’s of solutions are improved through iterations
of generations. When the algorithm converges, a group of
solutions with better fitness’s is generated, and the optimal
solution is obtained.
Optimization of Capacitor Voltage
The actual output voltage vc is compared with the
reference voltage vc ref to produce an error signal and a
change of error signal defined as:
e(k ) = v cref − v c (k )
(1)
Δe(k ) = e(k ) − e(k − 1)
(2)
The cost function is chosen as
n
J =  e2 (k)
k =1
(3)
The fitness function F to maximize is defined as:
F=
1
n
2
 e (k )
k =1
(4)
It is defined for all strings within the search space, i.e., the
cost function takes an individual and returns a value. Then
the value is mapped into a fitness value so as to fit into the
genetic algorithm. The fitness value can be regarded as
how well a FLC can be optimized based on the string to
actually minimize the tracking error.
Generally speaking, an individual with a lower J should be
assigned a larger fitness value. The higher fitness value
implies that the corresponding string leads to a better
solution. GA selects a parent with higher fitness values to
generate better off-springs. Therefore, a better FLC could
be obtained by better fitness in GA’s. There are several
methods to perform the mapping from a cost value to a
fitness value. The windowing techniques using linear
mapping is considered and the equation is given by
Fig. 3 GA optimizing FLC for APF
The error and change in error constants of the Fuzzy
controller have been optimized by Genetic Algorithm to ke
F = AJ + B
(5)
where A must be negative however the fitness values
must be positive.
Based on the adjustments of parameters of the fuzzy
controller considered to be optimized by the Genetic
Algorithm and on reaching an optimized value and
repeating the GA operations for an agreeable number of
times and obtaining the same values of results the
optimization is finalized. The membership functions are
optimized by the GA and adjusted as per the optimized
triangular membership values spread over the stipulated
span of range considered initially. As the inputs considered
as error and change in error both have a membership
functions with triangles spread in between and for
smoother ends with zmf and smf fuzzy shaped polynomial
functions are used. They membership functions are
stretched based upon the optimization obtained by the
genetic algorithm.
The parameters are the parametric constants of error,
change in error and the scaling factor so as to obtain an
optimized rule table remarkable change in rules, further,
tuning the output variable in the process of achieving
optimization. The fuzzy and GA-optimized fuzzy
membership functions can be clearly seen in Fig. 5 and the
transition of rule happening when error is NM and error
change is NB.
As a result of which the response of controller
improves to a large extent, however, a nominal sacrifice of
the THD of the shunt active power filter under
consideration. This can be eradicated by incorporating new
GA’s so as to tune the parametric values of the THD. The
THD prorogated to the distort source from 8.03% in FLC
to a good 6.77% in GA-Fuzzy Controller depicted by the
current spectra in Fig. 5.
Fig. 4 GA Optimized Fuzzy Memberships
Fig. 5 Spectrum of THD in Conventional FLC and GA-Fuzzy Logic
Controller
V. CONCLUSION
The GA optimization has been achieved in modifying
the fuzzy memberships and the THD has been reduced to a
good extent. Investigations found that specific classical
algorithm suit to specific inputs fed through source mains
and distortions in the load. However as the fuzzy ensues a
longer period to respond, the response has been
accelerated by GA based optimization of the fuzzy
members of the conventional fuzzy logic controller.
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International Journal of Scientific & Technology Research
Volume 1, Issue 2, ISSN 2277-8616 pp. 52 – 54 ,March
2012