# Renewable Energy-Based Energy-Efficient Off-Grid Base Stations for Heterogeneous Network
## 2 System Architecture and Mathematical Modeling
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Symbol** & **Meaning** & **Symbol** & **Meaning** \\ \hline \(\delta_{p}\) & Load dependency power gradient & \(\eta_{BM}\) & Efficiency of the biomass generator \\ \(\eta_{EE}\) & Energy efficiency & \(\eta_{ODEX}\) & Number of paging intervals in total eDRX period \\ \(\eta_{PV}\) & Panel efficiency & \(\sigma_{eucl}\) & Loss component of cooling system \\ \(\sigma_{DC}\) & Loss component of DC-DC regulator & \(\sigma_{MS}\) & Loss component of main supply \\ \(\tau_{D}\) & Data transfer timer & \(\tau_{DEX}\) & DRX timer \\ \(\tau_{PDX}^{\prime}\) & End of DRX timer & \(\tau_{ODEX}\) & eDRX timer \\ \(\tau_{ODEX}^{\prime}\) & End of eDRX timer & \(\tau_{i}\) & Radio Resource Control (RRC) inactivity timer \\ \(\tau_{i}^{\prime}\) & End of inactivity timer & \(\tau_{L}\) & eDRX long cycle timer \\ \(\tau_{PSM}\) & PSM timer & \(\tau_{PSM}^{\prime}\) & End of PSM timer \\ \(\tau_{S}\) & eDRX short cycle timer & \(\tau_{t}\) & \(\frac{\tau_{t}-\tau_{S}}{\tau_{DXS}}\) \\ \(X\) & Poisson packet in queue & \(\chi_{iL/DL}\) & UL/DL poisson packet in queue \\ \(X_{iLt}\) & UL poisson packet in queue & \(B_{att}\) & Battery autonomy \\ \(B_{c}\) & Capacity of the battery bank & \(B_{\text{DoDD}}\) & Depth of discharge of the battery bank \\ \(B_{SCONin}\) & Lower threshold limit of battery discharge & \(C_{f}\) & Capacity factor \\ \(CV_{BM}\) & Calorific value of the biomass & \(\hat{D}\) & Backup days \\ \(E_{BS}\) & Annual BS load consumption & \(E_{BC}\) & Renewable energy generated from BG \\ \(E_{BC}\) & Generated electricity from BG & \(E_{burst}\) & Energy afforded by the battery bank \\ \(E_{\text{h}turnax}\) & Maximum capacity of the energy storage devices & \(E_{huttrain}\) & Minimum capacity of the energy storage devices \\ \(E_{CS}\) & Yearly capacity storage & \(E_{D}\) & Total demand of electricity \\ \(E_{ED}\) & Yearly energy deficiency & \(E_{excess}\) & Excess electricity for critical time use (at least 10\% of \(E_{bat}\)) \\ \(E_{gen}\) & Total generated electricity & \(E_{l}\) & Sum of converter, battery bank and energy transfer losses \\ \(E_{gen}\) & Energy generated from solar PV array (kWh) & \(E_{Slater}\) & Shared energy (Permissible up to 90\% of Ebat) \\ \(I\) & Current through the conductor & \(K_{b}\) & Battery capacity co-efficient factor \\ \(L_{BS}\) & Average daily BS load in kWh & \(L_{int}\) & Lifetime of the battery bank \\ \(N\) & Total number of BSs & \(N_{bat}\) & Number of batteries in the battery bank \\ \(P_{BC}\) & Annual generated power & \(P_{BS}\) & BS power consumption \\ \(P_{b}\) & Power consumption at idle state & \(P_{PA}\) & Power amplifier power consumption (kWh/yr) \\ \(P_{RF}\) & RF power consumption & \(P_{slater}\) & Power consumption at sleep mode \\ \(P_{TX}\) & Maximum transmission power (W) & \(P_{BB}\) & Baseband power consumption \\ \(Q_{mon}\) & Nominal capacity of a single battery (Ah) & \(R_{batt}\) & Battery float life (year) \\ \(R_{total}\) & Total achievable throughput & \(R(I)\) & Resistance of the l km conductor length \\ \(R_{pv}\) & Rated Capacity for solar PV panel (KW) & \(T_{a}\) & Annual battery throughput (kWh/year) \\ \(T_{batt}\) & Lifetime throughput of a single battery (kWh) & \(T_{BM}\) & Average biomass availability (t/year) \\ \(t_{op}\) & BG running hours & \(II\) & Number of user equipments \\ \(V_{man}\) & Nominal voltage of a single battery (V) & \(V\) & DC bus-bar voltage (Volt) \\ \(CC\) & Capital cost & \(Comp\) & Lifetime of the component \\ \(CRF\) & Capital recovery factor & \(FC\) & Fuel cost \\ \(NPC\) & Net present cost & \(OMC\) & Operation and maintenance cost \\ \(PSH\) & Peak solar hour & \(RC\) & Replacement cost \\ \(Rem\) & Remaining lifetime & \(SINR\) & Signal-to-interference plus-noise-ratio \\ \(SV\) & Salvage value & \(TAC\) & Total annualized cost \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A list of the symbols and notations. from the perspective of both energy generation and consumption sides.