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Engineering, 2013, 5, 50-55 doi:10.4236/eng.2013.51b009 Published Online January 2013 (http://www.SciRP.org/journal/eng) 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 Email: zenno_376@yahoo.com, abdillah@elect-eng.its.ac.id, ronyseto@yahoo.com, adisup@ee.its.ac.id Received 2013 ABSTRACT 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]. O. PENANGSANG ET AL. Copyright © 2013 SciRes. ENG 51 () () PVp PV P tANEt (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. () () GPV 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) (()()) BATBATG L 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) (()()) BATBATL G 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]. (, ) cap A CCCCRFi Y (6) where Ccap is capital cost of each component (US$), Y is duration project (year). CRF is capital recovery factor, ratio to calculate the present value of a series of equal annual cash flow. Annual Maintenance Cost (AOM) of each unit as a function of interest rates and duration project is ex- pressed in Equation (7) [8]. (1) (1)Yproject AOM f Yproject AOM (7) where f is annual inflation rate (%) Annual Replacement Cost (ARC) is the replacement cost of each unit during time period of the project and it is calculated using Equation (8) [8]. (, ) rep rep ARCCSFFi Y (8) where Crep is replacement cost per unit (battery) (US$). 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, P VBAT L PP P (9) Constraints of the PV panels and batteries ,0 PV BAT NN (10) Constraints of battery capacity min maxBATBAT BAT PPP (11) O. PENANGSANG ET AL. Copyright © 2013 SciRes. ENG 52 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 2. 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 generated. 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. O. PENANGSANG ET AL. Copyright © 2013 SciRes. ENG 53 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 rules. 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 method. 4. Implementation of Proposed Method In this section, the application of the proposed method for optimizing the PV-battery systems are expressed as follows 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- ness. 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. Best Fitness LOW MEDIUM HIGH Pcross HIGH MEDIUM LOW Pmut LOW MEDIUM HIGH O. PENANGSANG ET AL. Copyright © 2013 SciRes. ENG 54 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 IT2FL. 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]. Battery Maximum output power 1.000 W Capital cost US$ 400 Replacement cost US$ 400 Time periode of project 10 years Inverter 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. O. PENANGSANG ET AL. Copyright © 2013 SciRes. ENG 55 Figure 7. Convergence graphic of GA. Tabel 5. Simulation result of PV-battery system design. Method Number of Battery Number of PV Annual Cost System (US$) SGA 96 30 4483 Fuzzy GA 65 40 4429 IT2FAGA 89 30 4313 From Table 5 it can be seen that the optimization of PV-battery system using the proposed method can mini- mize the annual cost system (ACS) of US$ 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. REFERENCES [1] H. M. Fargli, F. H. 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