## 5 Standalone PV System Optimization Technique
### Numerical Methods  
Numerical approach is the most frequently used in optimal sizing techniques for SAPV. In this category, the design was simulated for each time step within a period. SAPV energy balance and battery's state is calculated and investigated. This technique is offer adequate and comprehensive analysis. It is very accurate, but the calculation is complex and need more time for calculation and simulation. Besides, since there are different kinds of approaches or manners applied in these techniques, the comparison between studies under this method is inconsistent. As shown in Table 1, there are 20 studies use numerical methods to determine optimal configuration in SAPV. However, before 1997, there were five studies on numerical method done. Optimization of tilt angle, PV size and battery storage using Greek Island's monthly average meteorological data size was presented in [69]. The optimum design was set to be the combination with lowest life cycle cost, in a predefined loss of energy probability. Number of battery bank replacements was determined using life cycle cost calculation. In [96], a simple technique for SAPV sizing was developed. This study used 23 years of hourly insolation data from 20 different sites in US to develop correlations between variability in insolation and average monthly horizontal insolation. Then, sizing nomograms that give array size as function of average horizontal insolation and storage capacity was generated as function of LOLP for long time interval. In [72], a computer aided program was developed to find optimum PV tilted angle, PV array size and battery storage. The authors predicted solar radiation model based on clear sky model. The difference between PV power generated and load demand was used to size battery capacity. Meanwhile, in [71], optimization of SAPV system was done by dividing the regions into four zone, based on sky clearness index characteristic. For a given LOLP, many combinations of battery capacity and PV array peak power were determined, and the system with lowest total cost is the best configuration. Afterwards, in 1996, optimal sizing method for SAPV was applied in Corsica [97]. Similar with [71], design with the lowest cost of energy is the optimum configuration to supply 1 kWh load. [PERSON] et al. proposed new sizing method based on combination of PV panel sizing, battery storage sizing, charge regulator and load requirement in 1998 [73]. A stochastic model of PV generation was representing random behaviour of solar insolation. Required load demand also has been well defined in hourly basis. In this research, the system with minimum cost and minimum loss of load probability is the most favourable configuration. However, since the researchers used experimental load modelling, the LOLP and LOLH analysis are not too reliable. Numerical code, named PHOTOV-III was presented to determine optimum configuration of SAPV system at Greece in 2004 [98]. The system objective is to operate in zero load rejections, with optimum tilt angle and minimum installation cost. In proposed system, hourly analysis using iterative technique to find all possible combinations of PV panel number and battery maximum size that able to perform zero load rejection operation. Then, based on analytical analysis, with minimum initial cost constraint, several alternatives were selected as possible optimum configuration. However, this method is not too convenience, since the possible configuration need to be selected manually. A different simulation model for SAPV system sizing in Delhi with interconnection arrays was approached in 2005 [76]. For a predefined load, the optimum combinations of PV array and batteries for zero LOLP were calculated. Moreover, the authors compared fixed and tilted aperture arrays with single tracking aperture arrays, and simple system cost analysis was carried out on both systems. In 2006 [99], a new sizing method was presented by using stochastic simulation for solar radiation.