Use of multiple regression analysis to develop equations for predicting Li-Al/iron sulphide cell performance

A multiple regression analysis was conducted to develop predictive equations for the specific energy and specific power of Li-Al/iron sulphide cells over a wide range of cell designs and operating variables. The intent was to make these equations as general as possible such that one set of equations would predict the performance of Li-Al/FeS or Li-Al/FeS₂ cells with bicell (one positive electrode and two facing negative electrodes) or multiplate cell configurations. Data from 33 cells were used in the analysis of specific energy, and 26 cells were used to develop the specific power equation. The calculated specific energy and specific power showed good agreement with the measured values for these cells. In general, the deviation between the calculated and measured values was within ±10%. A check of the predictive capability of these equations also showed good agreement. The specific energy and specific power calculated for 14 cells not used in the regression analysis deviated by ±10% from the measured values. These equations were used to identify the most likely cell designs to meet selected electric-vehicle battery performance goals. These designs were included in an experimental programme for further performance evaluation.Nomenclature A _e limiting electrode area (cm²) - AHREFF coulombic efficiency (%) - b _i constants in multiple regression equation - CCO cell charge cut-off voltage (V) - CF charge factor (1.0 for fully charged cell, 0.5 for cell 50% discharged, 0.05 for cell discharged to a cut-off of 0.9–l.0 V) - DCO cell discharge cut-off voltage (V) - FCCF fully charged correction factor (1.0 for fully charged cell, 0.05 for any state of discharge) - FSLMUL product of FSUBL and MUL (defined below) - FSUBL calculated utilization factor of the limiting electrode (%) - i _c charge current density (A cm^–2) - i _D discharge current density (A cm^–2) - MUL theoretical specific energy factor (W h kg^–1) - NSPTHC negative-to-positive capacity ratio - OCV cell open-circuit voltage (V) - OFFEUT factor related to LiCl composition in electrolyte (%) - PF power factor (W kg^–1) - POSPIN reciprocal of the number of positive electrode plates - PPXCYC product of the number of positive electrode plates in the cell and the number of deep discharge cycles - R ² correlation coefficient - ¯R _c average cell resistance () - SP calculated cell specific power (W kg^–1) - SPECYC calculated cell specific energy (W h kg^–1) - SPEBAS calculated cell specific energy early in life (W h kg^–1) - TEMPR temperature ratio - TSUBCR thickness ratio of counter electrode and electrode separator - VFSNEG volume fraction salt in the negative electrode - VFSPOS volume fraction salt in the positive electrode - VOLT1R discharge voltage factor - VOLT2R charge voltage factor - W cell weight (kg) - X _i independent variables in regression equation - dependent variable in regression equation