# Optimal Sizing of Battery Energy Storage System for Implicit Flexibility in Multi-Energy Microgrids
## Abbreviations  
The following abbreviations are used in this manuscript: \begin{tabular}{l l} BESS & battery energy storage system \\ CAPEX & capital expenditure \\ CCHP & combined cooling, heating, and power \\ CF & capacity factor \\ CHP & combined heat and power \\ DAM & day-ahead market \\ DER & distributed energy resource \\ D-MES & district multi-energy system \\ DR & demand response \\ EMS & energy management system \\ EPR & energy to power ratio \\ EV & electric vehicle \\ HOMES & hierarchical optimization for multi-energy systems \\ ICE & internal combustion engine \\ IES & integrated energy system \\ GHG & greenhouse gas \\ LHV & lower heating value \\ LUT & look-up table \\ MEMG & multi-energy microgrid \\ MES & multi-energy system \\ MILP & mixed-integer linear programming \\ MPC & model predictive control \\ OPER & maximum profit electricity reduction \\ MV & medium voltage \\ NIE & negative injected electricity \\ NPV & net present value \\ O\&M & operation and maintenance \\ P2P & peer-to-peer \\ PDR & unto di r\(\acute{\text{o}}\)nsegna \\ POD & point of delivery \\ PV & photovoltaic \\ RES & renewable energy sources \\ RGS & relative grid sizes \\ SOC & state of charge \\ TES & thermal energy storage \\ ToU & time-of-use \\ V1G & vehicle-one-grid \\ \end{tabular} \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Chip** & \\ \hline \(\Delta t_{u}^{minTimeOn_{\text{chip}}}\) & 8 qrt & - \\ \hline \(\Delta t_{u}^{minTimeOff_{\text{chip}}}\) & 3 qrt & - \\ \hline \(\Theta_{u,i}^{\text{IB/inel}_{\text{chip}}}\) & [2247, 2696, 3146, 3595, 4045] kW\({}_{\text{fuel}}\) & - \\ \hline \(\Theta_{u,i}^{\text{IB/inel}_{\text{chip}}}\) & [2696, 3146, 3595, 4045, 4494] kW\({}_{\text{fuel}}\) & - \\ \hline \(\gamma_{u}^{\text{FUL}_{\text{chip}}}\) & 0.220 Smc/KWh\({}_{\text{el}}\) & DL 119/2018 [33] \\ \hline \(\Phi_{u,i}^{\text{EL}_{\text{chip}}}\) & [0.438, 0.457, 0.490, 0.426, 0.538] kW\({}_{\text{el}}\)/kW\({}_{\text{fuel}}\) & Experimental data \\ \hline \(\Phi_{u,i}^{\text{TH/CUP}}\) & [0.335, 0.349, 0.362, 0.449, 0.309] kW\({}_{\text{th}}\)/kW\({}_{\text{fuel}}\) & Experimental data \\ \hline \(\Omega_{u,i}^{\text{TLA}_{\text{chip}}}\) & [\(-44.8\), \(-97.0\), \(-201\), 30.1, \(-425\)] kW\({}_{\text{el}}\) & Experimental data \\ \hline \(\Omega_{u,i}^{\text{TH/CUP}}\) & [165, 128, 86.8, \(-225\), 342] kW\({}_{\text{th}}\) & Experimental data \\ \hline \(C_{u}^{\text{Ok/Mcipr}}\) & 5 \(\epsilon\)/qrt & - \\ \hline \(P_{u}^{\text{MAXel}_{\text{chip}}}\) & 2000 kW\({}_{\text{el}}\) & Technical sheet \\ \hline \(P_{u}^{\text{MINel}_{\text{chip}}}\) & 1000 kW\({}_{\text{el}}\) & Technical sheet \\ \hline \hline \end{tabular}
\end{table} 
Table 1: CHP techno-economic parameters employed in this study. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **BESS** \\ \hline \(\alpha^{\text{BESS}_{\text{Amax}}}\) & 25.5 kW/\({}^{\circ}\)C & Experimental data \\ \hline \(\beta^{\text{BESS}_{\text{Amax}}}\) & 38 kW & Experimental data \\ \hline \(\delta^{\text{BESS}_{\text{Amax}}}\) & 6.2 [-] & Experimental data \\ \hline \(\gamma^{\text{BESS}_{\text{Amax}}}\) & 265 kW & Experimental data \\ \hline \(\text{C}^{\text{O\&M}_{\text{BESS}}}\) & EUR 5/kWhinstalled & [35] \\ \hline \(\text{EPR}^{\text{BESS}}\) & [0.5, 1, 2, 3, 4] h & - \\ \hline \(\text{P}^{\text{BESS}_{\text{num}}}\) & [1, 2, 3, 4] MW & - \\ \hline \(\text{SOC}^{\text{BESS}_{\text{min}}}\) & 0\% & - \\ \hline \(\text{SOC}^{\text{BESS}_{\text{max}}}\) & 100\% & - \\ \hline \(\text{SOC}^{\text{BESS}}_{\text{t=0}}=\text{SOC}^{\text{BESS}}_{\text{t=T}}\) & 50\% & - \\ \hline \end{tabular}
\end{table} 
Table 14: Electricity tariffs used in this study based on the 2024 values published by AREA [36].