Engineering, 2013, 5, 50-55
doi:10.4236/eng.2013.51b009 Published Online January 2013 (
Copyright © 2013 SciRes. ENG
Optimal Design of Photovoltaic–Battery Systems Using
Interval Type-2 Fuzzy Adaptive Genetic Algorithm
Ontoseno Penangsang, Muhammad Abdillah, Rony Seto Wibowo, Adi Soeprijanto
Department of Electrical Engineering, Institut Teknologi Sepuluh Nopember (ITS), Surabaya, Indonesia
Received 2013
Many countries have been triggered to provide a new energy policy which promotes renewable energy applications be-
cause of public awareness to reduce the global warming and rising in fuel prices. Renewable energy sources such as
solar energy are green and promising energy in the future for widespread use. Combining renewable energy sources
with battery makes electricity supply more economical and reliable to meet all possible load level. This paper proposed
a new hybrid method to optimize Photovoltaic (PV)-Battery systems. The proposed method was named Interval type-2
fuzzy adaptive genetic algorithm (IT2FAGA). Genetic algorithm (GA) is one of modern optimization techniques that
has been successfully applied in various areas of power systems. To enhance the ability of GA to prevent trapping in
local optima and increase convergence in a global optima, the crossover probability (pcross) and the mutation probability
(pmut), parameters in GA, are tuned using interval type-2 fuzzy logic (IT2FL). Objective function used in this paper was
the annual cost of sytem (ACS) consisting of the annual capital cost (ACC), annual replacement cost (ARC), annual
operation cost maintenance (AOM). The proposed method was also compared to fuzzy adaptive genetic algorithm
(FGA) and standard genetic algorithm (SGA). Simulation results indicated that the proposed method had a better
perfomance in minimizing the objective function than the other two methods.
Keywords: Photovoltaic (PV); Battery; GA; IT2FL; IT2FAGA
1. Introduction
The use of renewable energy resources has mapped in
many developed countries. One of the most promising
technologies among renewable energy resources is
Photovoltaic (PV). PV technology is growing rapidly in
developed countries and developing countries. An
optimal number of solar cell panels and battery storages
are very essential in the design of PV-Battery systems
applied in remote rural areas. The appropriate control
strategy is required in designing PV-battery systems.
Design of PV-battery system is a complicated task and it
needs a mathematical model involving a significant
number of variables. To solve such kind of problem, arti-
ficial intelligence (AI) technique is very powerful.
Nowadays, AI techniques are becoming a popular tech-
nique to solve complicated practical problems in various
fields [1]. One of the most commonly used of the AI
techniques is genetic algorithm [2]. In recent decades,
genetic algorithms (GA) are very popular algorithms to
solve optimization problems because of robustness in
finding the optimal solution [3]. The genetic algorithm is
faster in finding the best solution than other random
searching methods. However, the performance of stan-
dards GA significantly depends on the algorithm pa-
rameters. In addition, solution of GA sometimes gets
stuck in local optima. Therefore, to avoid this problem,
this study proposed hybrid algorithm called interval
type-2 fuzzy adaptive genetic algorithm (IT2AGA). In-
terval type-2 fuzzy logic (IT2FL) was used to adjust the
crossover probability (pcross) and the mutation probability
(pmut) in order to improve the performance of genetic
algorithm. IT2FL has been widely applied in many fields,
and the results are very good [4-7].
The proposed method in this study was used to opti-
mize PV-battery systems in minimizing the annual cost
of system (ACS). The paper is organized as follows:
Section II presents a brief review of the materials and
methods. The proposed method is described in Section
III. Part IV presents the implementation of proposed
method. Simulation and result are described in Chapter V.
The last section is the conclusion.
2. Materials and Methods
2.1. Photovoltaic (PV)
Equation (1) describes a simple model of PV panels.
Conditions of insolation and area of PV panel greatly
affect the power generated by PV panels [8].
Copyright © 2013 SciRes. ENG
() ()
  (1)
where η is energy conversion efficiency (%); Ap is area
of PV panel; NPV is the number of PV panel; E(t) is
insolation data (w/m2)
2.2. Battery
Equation (2) shows the power generated at the time t of
the PV panel.
() ()
PtP t (2)
when the total power output of PV panels is greater than
the load demand, battery charges, and the number of
battery charging at the time t can be expressed in Equa-
tion (3).
()(1) (()())
PtPt PtPt (3)
when the total power output of PV panels is less than the
load demand, the battery discharges, and the number of
battery discharging at the time t can be expressed in
Equation (4).
()(1) (()())
PtPt PtPt (4)
where PBAT(t) is battery capacity at time t, PBAT(t-1) is
battery capacity at an earlier time or t-1.
2.3. System Configuration
The system configuration model in this study was com-
posed of PV panel and battery connected to the load
demand through the inverter. The system configuration
model used in this study is described in Figure 1.
2.4. Operational Strategy
The concept of operational strategy for PV-battery sys-
tem is described as follows:
1. When load demand (PL(t)) is smaller than output
power generated by PV panels (PPV (t)), excess power is
used to charge the battery.
2. When excess power is higher than the inverter ca-
pacity, battery are filled equally to inverter capacity and
the surplus power is discarded.
Figure 1. System configuration.
3. When load demand (PL(t) is greater than PPV (t))
and PBAT(t) of battery are higher than PBATmin then lack of
power will be supplied by battery.
4. When lack of power is higher than inverter capacity,
battery is discharged equally to inverter capacity
2.5. Problem Formulation
2.5.1. Objective Function
Objective function used in this study for optimizing of
PV-battery system was the Annual Cost of System (ACS)
consist of the Annual Capital Cost (ACC), Annual Re-
placement Cost (ARC), and Annual Operation Cost
Maintenance (AOM) expressed in equation (5) [8].
ACS = ACC + AOM + ARC (5)
Annual Capital Cost (ACC) of each unit is represented
using Equation (6) [8].
(, )
CCCCRFi Y (6)
where Ccap is capital cost of each component (US$), Y is
duration project (year). CRF is capital recovery factor,
ratio to calculate the present value of a series of equal
annual cash flow.
Annual Maintenance Cost (AOM) of each unit as a
function of interest rates and duration project is ex-
pressed in Equation (7) [8].
(1) (1)Yproject
AOM 
where f is annual inflation rate (%)
Annual Replacement Cost (ARC) is the replacement
cost of each unit during time period of the project and it
is calculated using Equation (8) [8].
(, )
rep rep
ARCCSFFi Y (8)
where Crep is replacement cost per unit (battery) (US$).
Yrep is duration of each unit (year). SFF is sinking fund
factor, rasio to calculate the future value of a series of
equal annual cash flow.
2.5.2. Cons tr a i n
Power balance constraint for each period time t, total
power of PV-battery systems, must supply the load (PL)
demand with a certain reliability criterion. This relation-
ship can be represented by,
Constraints of the PV panels and batteries
NN (10)
Constraints of battery capacity
PPP (11)
Copyright © 2013 SciRes. ENG
3. Proposed Method
The discussion in this section is described briefly on ge-
netic algorithm, interval type-2 fuzzy logic and interval
type-2 fuzzy adaptive genetic algorithm:
3.1. Genetic Algorithm
Genetic algorithm is a part of the evolutionary algo-
rithms family, computational models inspired by nature.
Genetic algorithm is a powerful stochastic search algo-
rithm based on the mechanism of natural selection and
natural genetics. Flowchart of the GA is shown in Figure
Genetic algorithm is applied to optimize the parame-
ters of a very complex system which is difficult to be solved
by conventional methods. Genetic algorithm maintains a
set of candidate solutions called population and it re-
peatedly modifies them. In each generation, Genetic Al-
gorithm selects individuals from the current population
to be parents and uses them to produce children for the
next generation. Candidate solutions are represented as
strings called chromosomes. A fitness function is used to
reflect how well the value of each member of the popula-
tion is.
Genetic algorithm operates in cycles called genera-
tions, expressed as follows,
Figure 2. Flowchart of GA.
a. An initial population of individuals is randomly
b. Every member of population is evaluated using the
fitness function.
c. Based on the fitness value, some individuals will be
selected for the next generation. Selected individuals will
be combined through the process of crossover by ex-
changing genetic information between pairs of individu-
als contained in the current population. After that, each
individual in the population will be mutated with a given
probability, through random processes replacing one
gene with another to produce a new genetic structure.
3.2. Interval Type 2 Fuzzy Logic (IT2FL)
The concept of interval type-2 fuzzy set was introduced
by Zadeh [9] as an extension of the usual concept of
fuzzy set, ie, type-1 fuzzy set. Explanation of interval
type 2 fuzzy logic (IT2FL) is as follows,
Similar to type-1 fuzzy logic, interval type-2 fuzzy logic
has fuzzifier, knowledge base, inference engine, and the
output processor. The output processor consists of type
reducer and defuzzifier. It generates a type-1 fuzzy set
output (from the type-reducer) or a crisp number (from
the defuzzifier). The basic structure of type-2 fuzzy logic
is shown in Figure 3 is as follows.
a. Fuzzifier: It converts the input (real value) into the
values of fuzzy membership functions.
b. Inference System: Fuzzy reasoning mechanisms are
applied by the interval type-2 FL to get the output fuzzy.
c. Defuzzifiier/ type reducer: Defuzzifier function is to
convert the fuzzy output into a precise value, while the
function of the type reducer is to transform the interval
type-2 FL set to type-1 fuzzy set.
d. Knowledge Base: In this section, it consists of a
fuzzy set rule called set of basic rules and membership
functions called the database.
Figure 3. The structure of interval type-2 fuzzy logic.
Copyright © 2013 SciRes. ENG
3.3. Adaptive Interval Type 2 Fuzzy Logic
Genetic Algorithm
In this study, two parameters of GA are the probability of
crossover (pcross) and mutation probability (pmut) to be
varied dynamically during the generation. IT2FL was
used to improve the performance of GA in order to be
optimal and efficient. Membership functions and the rule
base were the basic criteria that determine the perform-
ance IT2FL. Defining these parameters according to the
characteristics of the system has significant meanings to
achieve optimal performance should be considered in the
IT2FL design procedure. Membership functions for the
Best Fitness, crossover probability (pcross) and mutation
probability (pmut) consisted of fuzzy set LOW, MEDIUM
and HIGH. To determine the IT2FL rules, BestFitness
was used as input of IT2FL, while the IT2FL outputs
were the crossover probability (pcross) and the mutation
probability (pmut). For IT2FL rule, Mamdani type was
used to formulate the conditional statement of IT2FL
Figure 4 shows that the input and output variables of
Best Fitness, pcross and pmut are used as IT2FL fuzzifica-
tion. Two parameters of GA, pcross and pmut vary based on
the fitness function value according to the following
logic [10],
a. Best fitness value for each generation is expected to
change over several generations. Yet, if it doesn’t change
significantly over a few generations, it is necessary to
make changes on the probability of crossover (pcross) and
mutation probability (pmut).
b. The diversity of population is one of the factors that
affect in searching the optimum value. The variation of
the fitness value of the objective function of a population
is a measure of its diversity. Therefore, pmut and pcross can
be changed to get good results.
Figure 4. Input and output membership func tion of IT2F L.
c. For example, if Best Fitness is LOW, then (pcross is
HIGH) and (pmut is LOW). The rules of IT2FL is used to
tune pcross and pmut as shown in Table 1 . The defuzzifica-
tion method which used in IT2FL design is centroid
4. Implementation of Proposed Method
In this section, the application of the proposed method
for optimizing the PV-battery systems are expressed as
1. Input data which included annual meteorological
data, parameters of PV panels, inverters, batteries and
load demand.
2. Initialize the population: Initial a number of chro-
mosomes consisted of two genes x
id = [xi1, xi2, ..., xid] =
[NPV , NBAT] randomly. NPV is the number of PV panel
dan NBAT is number of battery. Initialize the solution of
the problems generated using mathematical formulation
as follows,
xi = rand(upper-range lower-range) + lower-range
where xi is the-ith individual candidate solution of the
genetic algorithm, rand is a random number with uni-
form distribution in [0,1], while the upper range and the
lower range are the upper range and the lower range of
PV panel and battery value.
3. Annual simulation was conducted to achieve the
optimal configuration based on the proposed system.
4. Evaluation of the objective function: The evaluation
processes in searching the total values of PV panels and
battery were as follows:
a. The calculation of the fitness function value using
Equation (5), based on the NPV and NBAT value obtained
for each individual.
b. For each generation, the best fitness value can al-
ways be obtained. Generation process continues until
meet the desired criteria stop and obtained the best fit-
5. Selection process: Individuals selected in the next
generation of the best individuals in the previous genera-
tion and compared for generations progress. The next
generation is known to the child (offspring) is formed
from the union of two individuals who acted as the cur-
rent generation using crossover operators.
6. Crossing over: Crossover is the main genetic op-
erator. Crossover allows the genes from different parents
to be combined in children by exchanging materials be-
tween two parents. Cross over function randomly selects
Table 1. IT2FL rules.
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a gene at the same coordinate from one of two parents
and assign it to the child.
Mutation: Mutation was used to introduce some artifi-
cial diversification in population to avoid premature
convergence to local optima. Uniform mutation method
is used in this study.
5. Simulation and Analysis
Remote areas of the Rote Island were used for the case
study in this study to design the PV-battery system
simulation. Daily load demand characteristic in Rote
Island is shown in Figure 6. This simulation used data
per hour for one day and repeated for one year or 8760
hours. The time period of this project was 20 years. The
value of inflation and interest rate established in this
study were 8.17% and 8.25% based on the real condi-
tions economics in Indonesia. The specification of PV
panel, battery and inverter used in this study can be seen
in Table 2 and 3. The parameters of GA used in this
study are shown in Table 4. The crossover probability
and the mutation probability were made adaptive using
Figure 5. Flowchart of proposed method.
Figure 6. Load demand characteristic in Rote Island.
Table 2. Specification of PV panel [11].
Maximum output power 120 W
Efficiency 90%
Area of single PV panel 1.07 m2
Capital cost US$ 230
Time periode of project 20 years
Table 3. Specification of battery and inverter [11].
Maximum output power 1.000 W
Capital cost US$ 400
Replacement cost US$ 400
Time periode of project 10 years
Inverter capacity 2000 W
Capital cost US$ 900
Time periode of project 20 years
Table 4. The parameter of GA.
Number of population 30
Number of generation 40
The convergence speed of the proposed method was
tested. Figure 7 shows the number of generation needed
in order to converge to the best solution founded by re-
spective algorithms required for the proposed method.
The test results show that the proposed method convergence
characteristic was better compared to others in terms of
the required number of generations. Simulation result of
PV-battery system which optimized using the proposed
method and compared to two other methods can be seen
in Table 5.
Copyright © 2013 SciRes. ENG
Figure 7. Convergence graphic of GA.
Tabel 5. Simulation result of PV-battery system design.
Method Number of
of PV
Annual Cost System
SGA 96 30 4483
Fuzzy GA 65 40 4429
IT2FAGA 89 30 4313
From Table 5 it can be seen that the optimization of
PV-battery system using the proposed method can mini-
mize the annual cost system (ACS) of US$ 4,313 lower
than two other methods
6. Conclusion
A new method for optimizing PV-Battery system based
on interval type-2 fuzzy adaptive genetic algorithm
(IT2FAGA) was proposed in this paper. The annual cost
of system (ACS) is used as an objective function of the
optimal PV-battery systems problem design. Test results
indicate that the proposed method algorithm is efficiently
found the optimal PV-battery system design, compared
to Fuzzy GA and standard GA.
7. Acknowledgements
The authors acknowledge LPPM-ITS for giving financial
support to this research via Laboratory Research Grant
Scheme. The second author is very grateful to the Gov-
ernment of Indonesia, especially Directorate General of
Higher Education (DIRJEN-DIKTI) for Excellency Schol-
arship awarded during his study in Graduate Program,
Department of Electrical Engineering, Institut Technol-
ogy Sepuluh Nopember (ITS), Surabaya, Indonesia. Last
but not least, the authors are also very thankful to the
Laboratory of Power System Simulation for all the - fa-
cilities provided during this research.
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