## 6 Grid Connected PV System Optimization Technique
### Numerical Methods  
As mention in Section 5.2, numerical is a detail simulation is done within a period for each time step, where the calculation may become too complicated if there are too many variables to investigate. In 2005, design optimization of GCPV system on top of Federal Office Building in Carbondale [108] was presented. Optimum array size and array size was determined by maximizing array output energy, and minimizing electricity sold to grid. To evaluate ratio of energy generated used by building, the effectiveness ratio was considered. Effectiveness factor was defined as ratio of energy used from generated energy to supply load over total PV array output. Array size was determined using graph of electricity sold. The limitation of the proposed method is the authors choose the optimum PV and inverter size manually, without fine explanation for optimization criteria and inverter to PV sizing ratio.  
In [2], numerical method was presented in 2013 to optimize PV system based on roof characteristics, either it is on flat or slightly tilted roof. The validation of developed simulation was done based on PVGIS, PVsyst and site measured data from several Swedish PV installations. Electricity generation profile was refined for all possible combinations constructed with different PV  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Year** & **Authors** & **Technique** & **Reliability Analysis** & **System Cost Analysis** & **Reference** \\ \hline
1984 & [PERSON], et al. & Analaytical & & & [102] \\
1984 & [PERSON], et al. & Analaytical & & & [103] \\
1984 & [PERSON], et al. & Analaytical & & & [104] \\
1986 & [PERSON], [PERSON], et al. & Analaytical & & & [105] \\
1987 & [PERSON] & Analaytical & & & [106] \\
1988 & [PERSON], et al. & Numerical & LOLP & LCC & [69] \\
1989 & [PERSON] & Numerical & & & [96] \\
1992 & [PERSON], et al. & Analaytical & LOLP & & [70] \\
1995 & [PERSON], et al. & Numerical & LOLP & & [72] \\
1995 & [PERSON], et al. & Numerical & LOLP & & [97] \\
1996 & [PERSON], et al. & Numerical & & LCOE & [97] \\
1997 & [PERSON], et al. & Intuitive & & & [92] \\
1998 & [PERSON], et al. & Numerical & LOLP & & [73] \\
2003 & [PERSON], et al. & Intuitive & & & [94] \\
2004 & [PERSON] & Numerical & & & [98] \\
2005 & [PERSON], et al. & Analaytical & LOLP & & [75] \\
2005 & [PERSON], et al. & Numerical & LOLP & & [74] \\
2005 & [PERSON] [PERSON], et al. & Numerical & LOLP & & [76] \\
2006 & [PERSON], et al. & Analaytical & & & [101] \\
2006 & [PERSON], et al. & Numerical & & & [99] \\
2007 & [PERSON], et al. & Numerical & LOLP & & [77] \\
2007 & [PERSON], et al. & Numerical & LOLP & & [26] \\
2008 & [PERSON], et al. & Numerical & Others & & [100] \\
2008 & [PERSON], et al. & Numerical & LOLP & LCC & [78] \\
2008 & [PERSON] [PERSON]. & Numerical & LPSP & LCC & [84] \\
2008 & [PERSON], et al. & Analaytical & LOLP & & [79] \\
2008 & [PERSON], et al. & Analaytical & LOLP & & [80] \\
2009 & [PERSON] & Numerical & LPSP & Others & [85] \\
2009 & [PERSON], et al. & Numerical & Others & & [33] \\
2009 & [PERSON], et al. & Numerical & LPSP & LCOE & [86] \\
2009 & [PERSON] & Intuitive & & LCC & [95] \\
2010 & [PERSON] & Numerical & LOLP & & [81] \\
2010 & [PERSON], et al. & Numerical & LPSP & Others & [87] \\
2012 & [PERSON], et al. & Analaytical & LOLP & & [82] \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of SAPV optimal sizing methods.  
types, panel tilt angle, ground covering ratio, and azimuth. After evaluation of economical and physical aspects, optimum distribution under different conditions was found, and several alternatives were developed. This research also investigates three case studies, with different kind of roof characteristics. However, this study did not involve inverter-to-PV array sizing. Besides, the technique is very complicated, and need systematic calculations.