# Improved Performance of Li-ion Polymer Batteries Through Improved Pulse Charging Algorithm
## 2 Determination of Optimal Pulse Charging Parameters
### Impact of Pulse Charging Parameters  
The pulse charging parameters investigated to determine their impact on battery performance were frequency, duty cycle, and the ambient temperature at which the battery was charged. The Li-ion polymer battery used in these experiments had a chemical composition of a lithium cobalt oxide cathode, graphite anode, lithium hexafluorophosphate electrolyte, and a microporous film blend of polyethylene and polypropylene for the separator. A limited number of experiments was used to determine which parameters and parameter values resulted in an improved performance of a Li-ion polymer battery and which combination ensured a faster charging and increased battery charge and energy efficiencies. Each OA has both input and output parameters. The input parameters were selected to be duty cycle, frequency, and ambient temperature at which the battery was charged. The duty cycle and temperature were set at three levels each with the duty cycle at 20%, 50%, and 80% and ambient temperature at 0 \({}^{\circ}\)C, 23 \({}^{\circ}\)C, and 45 \({}^{\circ}\)C, respectively. The frequency at which the pulse charger was operated was set at six levels, i.e., 0.1 kHz, 1 kHz, 6 kHz, 12 kHz, 50 kHz, and 100 kHz. These parameters are summarized in Figure 4. In this work [18], an important frequency point was included in the selected levels, i.e., 12 kHz the frequency at which the minimum impedance of the battery under test occurred. The impact of this frequency on the performance metrics of the LiPo was investigated. The outputs of the OA were established to be charging time, battery charge, and energy efficiencies. Based on the number of inputs and the selected levels, the OA row size was determined to be 36 [36] and experiments were conducted according to the OA combinations and results recorded. The results were analyzed using a number of statistical methods such as analysis of means and analysis of variance. Each factor and their level were examined and their impact on the performance metrics of the battery determined. When investigating the impact of ambient temperature, it was noticed that at 45 \({}^{\circ}\)C, there was a shorter charge time compared to charging at 0 \({}^{\circ}\)C. Poor battery charge and energy efficiencies were also observed at 0 \({}^{\circ}\)C. This can be attributed to the limited mobility of Li ions at 0 \({}^{\circ}\)C. Comparable efficiencies were observed at 23 \({}^{\circ}\)C and 45 \({}^{\circ}\)C. However, sustained charging at 45 \({}^{\circ}\)C could lead to accelerated degradation of the cycle life of the battery. Charging at 50% duty cycle produced the largest battery charge and energy efficiencies, with 20% duty cycle having about 25% less efficiency and 80% duty cycle having an average of 5% less. Investigating the different frequencies under test, frequencies outside the 12 kHz range, i.e., 0.1 kHz, 1 kHz, 6 kHz, 50 kHz,  
Figure 4: Pulse charging input parameters for the Taguchi orthogonal arrays (OA) design of experiment (DoE). and 100 kHz, produced poor battery charge and energy efficiencies, while frequencies less than 6 kHz and greater than 50 kHz produced longer charge times. Energy losses were minimized in the range of frequencies where the battery impedance was minimum, specifically at 12 kHz, thereby resulting in improved performance. The input parameters that had the most impact on the performance metrics of the LiPo battery and at which particular levels they occurred were investigated. Frequency and duty cycle were determined to have the largest impact on the performance of the battery and specifically, at 12 kHz, i.e., the frequency at which the battery impedance was minimum, and 50% duty cycle, which gives enough time for the Li\({}^{+}\) ions to intercalate in the electrodes. A confirmation experiment was run using these parameters at room temperature and compared with the benchmark constant current-constant voltage charging algorithm.