## 6 Economic Analysis of the Off-Grid Microgrid  
The Life Cycle Cost (LCC) technique is widely used for economic analysis. The LCC has been estimated in this study by adding the Initial Capital Costs (ICC), Erection Costs (\(EREC\)), the Present Value of O&M Costs \((P_{V,O&M})\), the Present Value of Replacement Costs \((P_{V,REP})\) and the Present Value of Fuel Costs \((P_{V,FIEL})\) using all system components, which is expressed as follows [2]:  
\[LCC=ICC+EREC+P_{V,O&M}+P_{V,REP}+P_{V,FUEL} \tag{12}\]  
The initial capital cost (\(ICC\)) of the IRES components are calculated as follows [2]:  
\[ICC=\left[\begin{array}{c}\left(C_{BMG,cap}\right)+\left(N_{PV}\times C_{PV, cap}\right)+\\ \left(N_{BAT}\times C_{BAT,cap}\right)+\left(C_{BDC-CC,cap}\right)\end{array}\right] \tag{13}\]where, \(C_{BMC,cap}\), \(C_{PV,cap}\), \(C_{BAT,cap}\) and \(C_{BDC-CC,cap}\) are the initial capital costs of the biomass generator, PV panels, batteries and bi-directional converter with a charge controller respectively.  
The erection costs (\(EREC\)) of the IRES components are calculated as follows [2]:  
\[EREC=\left[\begin{array}{c}(N_{PV}\times C_{PV,rect})+\left((N_{BAT}\times C _{BAT,rect})\times\sum\limits_{b=1}^{N_{t}}\frac{(1+x)^{|N_{c}-1}}{(1+y)^{|N_{ c}}}\right)+\\ \left(C_{BDC-CC,rect}\times\sum\limits_{d=1}^{N_{t}}\frac{(1+x)^{|N_{c}-1}}{(1 +y)^{|N_{c}}}\right)+\left(C_{BMG,rect}\times\sum\limits_{g=1}^{N_{t}}\frac{( 1+x)^{|N_{c}-1}}{(1+y)^{|N_{c}}}\right)\end{array}\right] \tag{14}\]  
where, \(C_{PV,rect}\), \(C_{BAT,rect}\), \(C_{BDC-CC,rect}\) and \(C_{BMG,rect}\) are erection costs of the PV panels, batteries and bi-directional converter with a charge controller and biomass generator, respectively.  
The present value of annual O&M (\(P_{V,O\&M}\)) costs of the IRES components are calculated as follows [2]:  
\[P_{V,O\&M}=\left[\begin{array}{c}(N_{PV}\times C_{PV,o\&m})+(C_{BMG,o\&m})\\ (N_{BAT}\times C_{BAT,o\&m})+(C_{BDC-CC,o\&m})\end{array}\right]\times\sum \limits_{i=1}^{N}\frac{(1+x)^{i-1}}{(1+y)^{i}} \tag{15}\]  
where, \(C_{PV,o\&m}\), \(C_{BMG,o\&m}\), \(C_{BAT,o\&m}\) and \(C_{BDC-CC,o\&m}\) are O&M costs of the PV panels, biomass generator, batteries and bi-directional converter with a charge controller, respectively, and \(y\) is defined as follows [2]:  
\[y=\frac{I_{nom}-x}{1+x}. \tag{16}\]  
where, \(I_{nom}\) = nominal interest rate, \(y\) = discount rate, \(N\) = life span of the project and \(x\) = inflation rate of the project.  
The IRES components, such as a bi-directional converter with a charge controller, biomass generator are needed to replace because they have a shortened lifespan than the project lifetime. The present value of annual replacement cost (\(P_{V,REP}\)) of the microgrid is calculated as follows [2]:  
\[P_{V,REP}=\left[\begin{array}{c}\left(N_{BAT}\times C_{BAT,rep}\times\sum \limits_{b=1}^{N_{t}}\frac{(1+x)^{|N_{c}-1}}{(1+y)^{|N_{c}}}\right)+\left(C_{ BMG,rep}\times\sum\limits_{g=1}^{N_{t}}\frac{(1+x)^{|N_{c}-1}}{(1+y)^{|N_{c}}} \right)+\\ +\left(C_{BDC-CC,rep}\times\sum\limits_{d=1}^{N_{t}}\frac{(1+x)^{|N_{c}-1}}{ (1+y)^{|N_{c}}}\right)\end{array}\right] \tag{17}\]  
where, \(C_{BAT,rep}\), \(C_{BMG,rep}\) and \(C_{BDC-CC,rep}\) are the replacement costs of the batteries, biomass generator and bi-directional converter with a charge controller, respectively, and the \(N_{r}\) is defined as follows [2]:  
\[N_{r}=int\bigg{(}\frac{N-N_{c}}{N_{c}}\bigg{)} \tag{18}\]  
where, \(N_{r}\) = the number of replacements needed for the system components and \(N_{c}\) = life span of each system component.  
The present value of annual fuel cost (\(P_{V,FUEL}\)) of the microgrid is calculated as follows [2]:  
\[P_{V,FUEL}=\left[(C_{BM}\times Q_{BM})\right]\times\sum\limits_{i=1}^{N}\frac {(1+x)^{i-1}}{(1+y)^{i}} \tag{19}\]  
where, \(Q_{BM}\) and \(C_{BM}\) are the quantity and cost of the biomass.