## 5 Standalone PV System Optimization Technique
### Analytical Methods  
In SAPV system sizing, the analytical method was used to obtain a close relation or correlation in a form of equation between capacities and reliabilities. From [34], usually there are three approaches applied, which are the probability-based approach, empirical coefficient determination, and application of novel methods, such as artificial neural networks (ANN). This technique allows designers to simplify their sizing methods into a representative equation, reduce calculation or computer process and the sizing procedure is more accurate. However, this method is not very popular because the constructed expression is not flexible. It is because the expression is very exclusive and restricted for specific sites. Moreover, it is hard to produce the relationship between capacities and reliabilities. The expression of system sizing also may have small errors compared to result from iterative sizing process. Before 1997, there were five studies used analytical method to find optimum sizing in SAPV system. Three studies recorded in 1984, one in 1987 and the last one was in 1992. In [102], an analytical method was presented to predict fraction of energy load covered by PV generation system. The researchers attained sizing's coefficients value from simulation based on long term Italian meteorological data. However, this model leads to an oversized system. Meanwhile, a similar analytical procedure was proposed in [103]. Analysis was done based on monthly average solar insolation at Italian sites as well. However, [PERSON]'s model produce too low sensibility to battery size, as analyzed in [70]. Loss of load probability model was derived by two-event probability density function for difference of PV generated and load demand in [104]. Battery storage size calculation for a given array size was developed. The authors constructed analytical expressions for the probability of system storage needed and auxiliary energy required to cover demands in that event. The method then extended in [105], by taken account the effect of day-to-day insolation values. In [106], a similar method was used, but the authors extended it using three states model. In this study, analytical approaches based on stochastic theory were examined and recommended. In 1992, a new analytical model was proposed based on meteorological data from three different locations in Spain [70]. An expression to relate array capacity, storage sized and LOLP was illustrated, with four different coefficient inputs, varies based on sites. Spain coefficient maps for two LOLP values were constructed to represent SAPV system sizing. After a long absence, in 2005, the authors proposed an ANN-based methodology to obtain LOLP curves for SAPV system in Spain by using the Multilayer Perceptron (MLP) approach. In 2003 [107], the author presented the three layer MLP structure consist two input only, which is ratio of accumulator capacity over average daily load consumption and LOLP. Then, the structure was improved with addition of yearly clearness index, as the third input. Last layer has one node, which is ratio of generator capacity over average load consumption. The LOLP curves obtained in these researches was compared with real curves and curves developed in Instituto de Energia Solar Madrid in [70]. By using different methods and consideration of clearness index, the proposed curves was more fit to the real curves, and improvement can be seen compared to previous ones. In 2006, a sizing procedure was proposed, where a curve was constructed using combination of several climatic cycles at low daily solar radiation [101]. The study used long term daily solar radiation from London, England. The procedure started with expressed array size equation and battery size'srange equation, in term of constant load. PV array sized based on assumption there were no variation of solar radiation, and load could be supplied by array sized. Meanwhile, battery sized to be able to supply load in low solar radiation time interval.