## 4 Photovoltaic Systems Optimization Criteria
### System Cost Analysis  
There are several economic analyses used by past researchers in order to find the optimum configuration of proposed system. This criterion was applicable at both GCPV and SAPV system. Economic feasibility analyses that frequently used in past years are Net Present Cost (NPC), Levelized Cost of Energy (LCOE), and Life Cycle Cost (LCC). Economic analysis is worth doing to determine whether the project has or has not acceptable investment. Sometimes, economic analysis was used after reliability analysis, in order to propose a system with high reliability and lowest cost [86].  
NPC is the total present value of a time series and it was the development of discounter cash flow techniques. The net present worth is found by discounting all cash inflows and outflows, including cost of installation, replacement and maintenance, at an interest rate or internal rate of return (IRR) [90]. NPC can be described as,  
\[\text{NPC}(i)=\sum_{n=0}^{N}\frac{A_{n}}{\left(1+i\right)^{n}} \tag{31}\]  
where \(A_{n}\) is net flow cash at end of period \(n\), \(i\) is IRR, and \(n\) is project lifetime.  
LCOE ($/kWh) defined as the average cost per kWh of useful electrical energy produced by the system when a lifetime, investment cost, replacement, operation and maintenance, and capital cost is considered [91]. LCOE method was frequently applied in past year's economic feasibility research, since the approach is very useful in comparing different generating technologies with different operating characteristic [6; 86]. LCOE is calculated by dividing the produced electricity annualized cost on the total useful electrical energy generated. The mathematical model used to calculate LCOE is as follows,  
\[\text{LCOE}=\frac{\sum_{n=1}^{N}\frac{I_{n}+O_{n}}{\left(1+r\right)^{n}}}{ \sum_{n=1}^{N}\frac{P_{n}}{\left(1+r\right)^{n}}} \tag{32}\]  
where \(N\) is economical lifetime of the system, \(I_{n}\) is the investment cost in year \(n\), \(O_{n}\) is the maintenance and operational cost (O&M) in year \(n\), \(P_{n}\) is the electricity production in year \(n\), and \(r\) is the discount rate [2].  
The third system cost analysis is life cycle cost (LCC). LCC is an estimation for sum of installation cost, operating and maintenance of an item for a period of time, and expressed in today's value [92]. Equation (33) is used to calculate LCC of a PV system,  
\[\text{LCC}=C_{PV}+C_{bat}+C_{charger}+C_{inv}+C_{installation}+C_{batrep}+C_{ PWO\&M} \tag{33}\]  
where \(C_{PV}\) is PV array cost, \(C_{bat}\) is initial cost of batteries, \(C_{charger}\) is cost of charger, \(C_{inv}\) is inverter cost, \(C_{installation}\) is installation cost, \(C_{batrep}\) is battery replacement costs in present value, and \(C_{PWO\&M}\) is operation and maintenance cost in present worth. \(C_{PWO\&M}\)'s equation is:  
\[C_{PWO\&M}=\left(C_{\frac{OWM}{1}}\right)\left(\frac{1+i}{1+d}\right)\frac{ \left[1-\left(\frac{1+i}{1+d}\right)\right]}{\left[1-\left(\frac{1+i}{1+d} \right)^{N}\right]} \tag{34}\]  
Sometimes, some researchers also calculate annual basis expression of life cycle cost (ALCC), with this equation:  
\[\text{ALCC}=\text{LCC}\frac{\left[1-\left(\frac{1+i}{1+d}\right)\right]}{ \left[1-\left(\frac{1+i}{1+d}\right)^{N}\right]} \tag{35}\]