# Estimating Degradation Costs for Non-Cyclic Usage of Lithium-Ion Batteries
## Nomenclature  
\begin{tabular}{l l} \(A\) & Heat transfer surface area of the cell in m\({}^{2}\) \\ \(C_{1}\) & Surface layer capacitance of cell in Farads \\ \(C_{BOL}\) & Capacity at the beginning of life in Ah \\ \(C_{loss,all}^{LFP}\) & Calendar capacity loss of LFP chemistry from the beginning of life normalized with \\ \(C_{loss,all}^{LFP}\) & \(C_{BOL}\) in \% \\ \(C_{loss,all}^{NMC}\) & Calendar capacity loss of NMC chemistry from the beginning of life normalized with \\ \(C_{loss,all}^{LFP}\) & \(C_{BOL}\) without dimensions in the range [0,1] \\ \(C_{loss,qvc}^{LFP}\) & Cyclic capacity loss of LFP chemistry from the beginning of life normalized with \\ \(C_{loss,qvc}^{NMC}\) & Cyclic capacity loss of NMC chemistry from the beginning of life normalized with \\ \(C_{loss,qvc}\) & \(C_{BOL}\) without dimensions in the range [0,1] \\ \(C_{p}\) & Specific heat capacity of the cell in J(kg K)\({}^{-1}\) \\ \(C\) & Cell remaining capacity at a given time in Ah \\ \(C^{\text{NMC}}\) & Cell remaining capacity for NMC chemistry at a given time normalized with \(CBOL\) \\ CF & Capacity Fade \\ \end{tabular}  
\begin{tabular}{l l} \(Cost_{bat}\) & Battery Replacement Cost in \(\mathfrak{C}\) \\ \(Cost_{deg}\) & Degradation Cost in \(\mathfrak{C}\) \\ \(CR\) & Charge/discharge current rate \\ \(\Delta CF\) & Capacity fade increment between two points in time of the cell life before and after a given use of the cell \\ \(\Delta Q\) & Elapsed Q of the actual use of the battery \\ \(\Delta t\) & Elapsed time of actual use of the battery \\ \(DoD\) & Depth of discharge or depth of cycle for NMC without dimensions in the range [0,1] \\ \(\mu_{CF}\) & Cell capacity factor at the end of life compared to the beginning of life, usually 0.8 \\  & Factor of the cell total resistance at the end of life compared to the beginning of life, usually 2 \\ \(h\) & Cell-ambient heat transfer coefficient in W K\({}^{-1}\) m\({}^{-2}\) \\ \(I\) & Cell current in Amperes \\ \(\epsilon\) & Aging life loss function without dimensions in the range [0,1] \\ \(\epsilon_{cal}\) & Calendar aging life loss function without dimensions in the range [0,1] \\ \(\epsilon_{cal}^{LFP}\) & The calendar aging life loss function of LFP chemistry without dimensions in the range [0,1] \\ \(\epsilon_{cal}^{NMC}\) & The calendar aging life loss function of NMC chemistry without dimensions in the range [0,1] \\ \(e_{cyc}\) & Cyclical aging life loss function without dimensions in the range [0,1] \\ \(\epsilon_{cyc}^{LFP}\) & The cyclical aging life loss function of LFP chemistry without dimensions in the range [0,1] \\ \(\epsilon_{cyc}^{NMC}\) & The cyclical aging life loss function of NMC chemistry without dimensions in the range [0,1] \\ \(m\) & Cell mass in kg \\ \(OCV\) & Open Circuit Voltage in Volts \\ PF & Power Fade \\ \(Q\) & Total Ah-throughput from the beginning of cell life in Ah \\ \(Q_{cyc}^{LFP}(CF)\) & Total Ah-throughput used by the cell until a given \(CF\) is reached with only cyclic degradation for LFP chemistry in Ah \\ \(Q_{cyc}^{NMC}(CF)\) & Total Ah-throughput used by the cell until a given \(CF\) is reached with only cyclic degradation for NMC chemistry in Ah \\ \(R_{0}\) & Ohmic resistance of cell in Ohms \\ \(R_{0,BOL}\) & Ohmic resistance of cell at the beginning of life in Ohms \\ \(R_{1}\) & Charge transfer resistance of cell in Ohms \\ \(R_{1,BOL}\) & Charge transfer resistance of cell at the beginning of life in Ohms \\ \(SoC\) & State of Charge for NMC without dimensions in the range [0,1] \\ \(SoC_{max}\) & Maximum \(SoC\) over the whole cycle for NMC without dimensions in the range [0,1] \\ \(SoC_{min}\) & Minimum \(SoC\) over the whole cycle for NMC without dimensions in the range [0,1] \\ \(T_{a}\) & Ambient temperature in K \\ \end{tabular}