# Performance Analysis of a Stand-Alone PV/WT/Biomass/Bat System in Alrashda Village in Egypt
## 2 Modeling of the Proposed System
### Biomass System  
Biomass comprises of the stored chemical energy from solar energy, so biomass can be used for heating by direct burning or transformed through many operations into liquid fuels and renewable gases [32; 33]. One of the major aspects in determining the type of technology used to generate biomass energy is the type of biomass to be used and the type of fuel to be produced from the conversion process [34].  
In this work, biomass gasification is the conversion process used which is a pyrolysis process in which the raw materials of biomass are heated in closed and pressurized vessels, the output gaseous fuel by this process is usually called the producer gas [35].  
In this study, sugarcane bagasse was used as a raw material for biomass to feed a small-scale downdraft gasifier, as the cane crop is one of the agricultural crops available in the New Valley city. The biomass generator was utilized as the primary generator to satisfy the electrical load requirement beside the PV and WT systems, the technical characteristics of the biomass system are illustrated in Table 3. The hourly generated power from the biomass system \(\text{BG}_{\text{P}}(\text{t})\) can be expressed according to the following mathematical formula [25; 27];  
\[\text{BG}_{\text{P}}(\text{t})=\text{ FS}_{\text{rat}}(\text{t})\times\text{HHV}_{\text{fs}}\times\eta_{\text{gas}}\times\omega \tag{4}\]  
where, \(\text{FS}_{\text{rat}}(\text{t})\) is the biomass raw material rate per hour (kg/h), \(\text{HHV}_{\text{fs}}\) indicates the higher heat value of the biomass raw material, \(\eta_{\text{gas}}\) denotes the efficiency of the gasifier reactor (75%), and \(\omega\) represents a factor for converting units from kJ to kWh (\(27.78\times 10^{-5}\)).  
The load ratio of the considered biomass generator is set to operate at no less than 30% (Gen\({}_{\text{min}}\) = 30%) of its rated capacity to avoid running at much lower demands, while its maximum load is 80% (Gen\({}_{\text{max}}\) = 80%) of its rated capacity. The generator output power (Gen\({}_{\text{out}}\)) can be described according to the following constraints [25; 27; 36];  
\[\text{Gen}_{\text{out}}=\left\{\begin{array}{cc}0&\text{ BG}_{\text{P}}<\text{Gen}_{\text{min}}\\ \text{ BG}_{\text{P}}&\text{Gen}_{\text{max}}>\text{Gen}_{\text{max}}\\ \text{ BG}_{\text{P}}&\text{Gen}_{\text{max}}<\text{BG}_{\text{P}}<\text{Gen}_{ \text{min}}\end{array}\right. \tag{5}\]  
Based on the previous mathematical expressions, \(\text{F}_{\text{con}}^{\text{BG}}(\text{t})\) is the average fuel consumption per hour, and \(\text{E}_{\text{Bio}}\) (kWh) is the annual energy output which can be computed as following;  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline Model type & & Fuhrlander FL 30 \\ WT\({}_{\text{rat}}^{\text{P}}\) & 30 & kW \\ wind turbine height & 50 & m \\ \(\text{n}_{\text{WT}}\) & 80 & \% \\ \(\text{V}_{\text{cut}}^{\text{in}}\) & 2.5 & m/s \\ \(\text{V}_{\text{rat}}\) & 12 & m/s \\ \(\text{V}_{\text{cut}}^{\text{off}}\) & 25 & m/s \\ lifetime of WT (\(\text{WT}_{\text{S}}\)) & 20 & year \\ wind turbine cost (\(\text{C}_{\text{WT}}\)) & 3200 & \$/\$/\$/kW \\ \hline \hline \end{tabular}
\end{table}
Table 2: The main parameters of the selected wind turbine model [30].  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** & **Unit** \\ \hline \(\eta_{\text{gas}}\) & 75 & \% \\ Generator rated & 50 & kW \\ Capital Cost [37] & 23,700 & \$/\$/\$/kW \\ Lifespan [37] & 15,000 & h \\ Replacement cost [37] & 15,000 & \$/\$/unit \\ Yearly O\&M cost [37] & 0.05 & \$/ h \\ \hline \hline \end{tabular}
\end{table}
Table 3: The main parameters characteristics of the biomass system.  
\[\mathrm{E_{Bio}}=\sum_{t=1}^{8760}\mathrm{N_{g}}\times\mathrm{Gen_{out}}\times t \tag{6}\]  
where, \(\mathrm{N_{g}}\) is the number of generators.