## 5 Standalone PV System Optimization Technique
### Numerical Methods
The proposed stochastic model is suitable to implement if original measured data is not available. For a given reliability index, energy balance using different pairs of PV array capacity and battery capacity was done to find the optimum combination. Reliability index was calculated using ratio of hours when load is satisfied over total simulation hours. The authors analysed fifteen different sites in Greece. [PERSON] proposed a new sizing approach using numerical method in [100], similar to her previous work in [101] by analytical method in 2008. This study constructed sizing curves for minimum PV generator capacity and battery storage, without losing the load. Minimum PV generation required was sized at least equal to load demand, by using the worst month daily radiation. Storage prerequisite for minimum generator size was calculated from minimum battery SOC for each year based on historical solar radiation data. However, this sizing method may cause oversizing, and the PV generated power may not fully used during high solar radiation energy period. Other than that, [PERSON] et al. presented optimum sizing method based on six years of meteorological data from five sites in Turkey [78]. Meanwhile, the authors obtained load profiles from five households in Turkey. The system performance simulated using hourly solar irradiation and ambient temperature data. The scheme was simulated iteratively, by increasing PV size gradually, while battery capacity is remained constant for five days storage capacity. Hourly energy generated flow in and out from battery and its state of charge was calculated. Then, the researchers constructed sizing curves after LOLP and LCC analysis, where they calculated LCC and cost payback time for three different LOLP values for each site in life cycle assessment. Technical and economic analysis for SAPV system in Malaysia were done in 2008 [84], by using annual daily radiation data. There are two design variables contemplated, which are tilt angle and battery's dead of discharge (DOD). For a given load demand, maximum DOD, and preset LPSP, the best consolidation of PV size and battery size was calculated iteratively for several tilt angle values. The optimum tilt angle was chosen based on the lowest unit cost value. Then, for preset LPSP and chosen tilt angle, the same analysis was repeated using several DOD values. The same author from [84] proposed new method for SAPV system sizing in 2009 [85]. This method implemented graphical approaches, where two graphs for a given LPSP was constructed, which are array size versus battery size, and partially differentiated of system cost function graph. The Tangent point of the graphs was the optimum size for PV array and battery. This method was much better compared to his previous work, since the most advantageous system was chosen based on graphical method, where the cost function was already minimized using partially derivation. [PERSON] et al. [33] presented chance constrained programming approach to solve uncertainty problem in solar radiation. For a specific energy source, demand, desired confidence level and system characteristic, a sizing curve for all possible combinations of photovoltaic array rating and storage capacity was plotted. Then, design space for feasible design was determined from the curve. Optimum configuration for a predefined reliability level was the combination with lowest cost of energy. As mention in [82], the limitation in this study is PV model prediction using deterministic approach was too simple, and cannot represent uncertainty in solar radiation [87]. Hence, it is better for future researchers to use time series meteorological data or another PV model prediction. Moreover, preset LOLP value used is considered high compared to other researches. [PERSON] et al. proffered an orderly optimal sizing method for PV array and battery system in Kerman, Iran, based on the site's hourly solar radiation data [86]. Panel's tilt angle is fixed as site latitude.