Journal of Power Sources, Vol.110, No.2, 445-470, 2002
Calendar- and cycle-life studies of advanced technology development program generation 1 lithium-ion batteries
This paper presents the test results and life modeling of special calendar- and cycle-life tests conducted on 18650-size generation I (Gen 1) lithium-ion battery cells (nominal capacity of 0.9 Ah; 3.0-4.1 V rating) developed to establish a baseline chemistry and performance for the Department of Energy sponsored advanced technology development (ATD) program. Electrical performance testing was conducted at the Argonne National Laboratory (ANL), Sandia National Laboratory (SNL) and the Idaho National Engineering and Environmental Laboratory (INEEL). As part of the electrical performance testing, a new calendar-life test protocol was used. The test consisted of a once per day discharge and charge pulse designed to have minimal impact on the cell yet establish its performance over a period of time such that the calendar-life of the cell could be determined. The calendar-life test matrix included two states-of-charge (SOCs) (i.e. 60 and 80%) and four test temperatures (40, 50, 60 and 70 degreesC). Discharge and regen resistances were calculated from the test data. Results indicate that both the discharge and regen resistances increased non-linearly as a function of the test time. The magnitude of the resistances depended on the temperature and SOC at which the test was conducted. Both resistances had a non-linear increase with respect to time at test temperature. The discharge resistances are greater than the regen resistances at all of the test temperatures of 40, 50, 60 and 70 degreesC. For both the discharge and regen resistances, generally the higher the test temperature, the lower the resistance. The measured resistances were then used to develop an empirical model that was used to predict the calendar-life of the cells. This model accounted for the time, temperature and SOC of the batteries during the calendar-life test. The functional form of the model is given by: R(t, T, SOC) = A(T, SOC)F(t) + B(T, SOC), where I is the time at test temperature, T the test temperature and SOC the SOC of the cell at the start of the test. A(T, SOC) and B(T, SOC) are assumed to be functions of the temperature and SOC; F is assumed to only be a function of the time at test temperature. Using curve-fitting techniques for a number of time-dependent functions, it was found that both the discharge and regen resistances were best correlated with F(t) having a square-root of test time dependence. These results led to the relationship for the discharge and regen resistances: R(t, T, SOC) = A(T, SoC)t(1/2) + B(T, SOC). The square-root of time dependence can be accounted for by either a one-dimensional diffusion type of mechanism, presumably of the lithium-ions or by a parabolic growth mechanism for the growth of a thin-film solid electrolyte interface (SEI) layer on the anode and/or cathode. The temperature dependence of the resistance was then investigated using various model fits to the functions A(T, SOC) and B(T, SOC). The results of this exercise lead to a functional form for the temperature dependence of the fitting functions having an Arrhenius-like form: A (T, SOC) = a(SOC) {exp[b(SOC)/T]) and B(T, SOC) = c(SOC) {exp[d(SOC)/T]}, where a and c are constants, and b and d are related to activation energy (E-b and E-d) by using the gas constant (R) such that b = E-b/R and d = E-d/R. The functional form, therefore, for the discharge and regen resistances, including the SOC, is then: R(t, T, SOC) = a(SOC){exp[b(SOC)/T]}t(1/2) + c(SOC){exp[d(SOC)/T]}. The a, b, c and d parameters are explicitly shown as being functions of the SOC. However, due to the lack of testing at SOC values other than 60 and 80% SOC, the exact form of the SOC dependence could not be determined from the experimental data. The values of a, b, c and d were determined, thus permitting the function R(t, T, SOC) to be used to correlate the discharge and regen data and to predict what the resistances would be at different test times and temperatures. This paper also presents, discusses and models the results of a special cycle-life test conducted for a period of time at specified temperatures of 40, 50, 60 and 70 degreesC. This test, consisting of specified discharge and charge protocols, was designed to establish the cycle-life performance of the cells over a time interval such that their cycle-life could be determined. The cycle-life test was conducted at 60% SOC, with SOC swings of Delta3, Delta6 and Delta9%. During the cycle-life test, the discharge and regen resistances were determined after every 100 test cycles. The results of the cycle-life testing indicate that both the discharge and regen resistances increased non-linearly as a function of the test time at each Delta% SOC test. The magnitude of the resistances and the rate at which they changed depended on the temperature and Delta% SOC at which the test was conducted. Both resistances had a non-linear increase with respect to time at test temperature, i.e. as the number of test cycles increased the discharge and regen resistances increased also. For a given Delta% SOC test, the discharge resistances are greater than the regen resistances at all of the test temperatures of 40, 50, 60 and 70 degreesC. For both the dis At each of the four test temperatures, the magnitude of the discharge and regen resistances was generally in the following order: Delta3% SOC > Delta9% SOC > Delta6% SOC, but the ordering was dependent on test time. A model was also developed to account for the time, temperature, SOC and Delta% SOC of the batteries during the cycle-life test. The functional form of the model is given by R(t, T, SOC, Delta% SOC) = A(T, SOC, Delta% SOC)F(t) + B(T, SOC, Delta% SOC) where t is the time at test temperature, T the test temperature. SOC the SOC of the cell at the start and end of the test and Delta% SOC the SOC swing during the test. A(T, SOC, Delta% SOC) and B(T, SOC, Delta% SOC) are assumed to be functions of the test temperature, SOC and Delta% SOC swing. F(t) is assumed to only be a function of the test time at test temperature. Using curve-fitting techniques for a number of time-dependent functions, it was found that both the discharge and regen resistances were best correlated by a square-root of test time dependence. These results led to the relationship for the discharge and regen resistances having the form R(t, T, SOC, Delta% SOC) = A(T, SOC, Delta% SOC)t(1/2) + B(T, SOC, Delta% SOC). This model is essentially the same as used to analyze the calendar-life test data. The temperature dependence of the resistance was then investigated using various model fits to the functions A(T) and B(T). The results of this exercise lead to a functional form for the functions having again an Arrhenius-like form: A (T) = a[exp(b/T)] and B(T) = c[exp(d/T)] where a and c are constants, and b and d are related to activation energies. The functional form, therefore, for the discharge and regen resistances including the SOC and Delta% SOC is R(t, T, SOC, A% SOC) = a(SOC, Delta% SOC) {exp[b(SOC, Delta% SoC)/T]}t(1/2) + c(SOC, Delta% SOC){exp[d(SOC, Delta% SOC)/T]). The a, b, c and d parameters are explicitly shown as being functions of the SOC and the Delta% SOC. However, due to the lack of testing at SOC values other than 60% SOC, the exact form of the SOC dependence could not be determined from the experimental data. In addition, no model was found that consistently correlated the observed resistance changes with the Delta% SOC of the tests. Eliminating the SOC and Delta% SOC from the resistance function, the function R(t, T) was then used to correlate the discharge and regen resistances data. This model also allows the prediction of what the resistances would be at different test times at a particular Delta% SOC test condition and temperature. Published by Elsevier Science B.V.
Keywords:lithium-ion batteries;battery calendar-life;battery cycle-life;battery modeling;arrhenius kinetics