Comparison of Lead-Acid and Li-Ion Batteries Lifetime Prediction Models in Stand-Alone Photovoltaic Systems  
[PERSON]  
1 Departamento de Ingenieria Electrica, Universidad de Zaragoza, C/Maria de Luna, 3, 50018 Zaragoza, Spain; 1 jsartal@unizares (S.A.-S.); [EMAIL_ADDRESS] (J.L.B.-A. )1 Departamento de Ingenieria Electrica, Universidad de Zaragoza, C/Maria de Luna, 3, 50018 Zaragoza, Spain; 1 jsartal@unizares (J.A.B.-A. In standalone systems, different types of batteries can be used [2]. Lead-acid batteries (valve-regulated lead-acid type, VRLA) are the dominant technology for photovoltaic off-grid applications [3] due to their affordable costs for large installed capacities. However, lead-acid batteries are the overall weakness of the PV system and tend to be replaced by new technologies such as Li-ion batteries [4], which can be competitive in some cases [5] due to their higher cycle life, despite their higher cost. The total battery cost (including its replacement during the system lifetime) is the highest in the system's net present cost (NPC); thus, in the optimization process of standalone systems, the accurate estimation of battery life is one of the most critical issues. Significant errors in the battery lifetime prediction would lead to great errors in the estimation of the NPC. Lead-acid battery aging factors are charge and discharge rates, charge (_Ah_) throughput, the time between full charge, time at a low state of charge (SOC), and partial cycling. Several researchers have analyzed the lead-acid battery aging factors [6; 7]. Classical models widely used by researchers and software tools to estimate the battery life are the \"equivalent full cycles model\" and the \"rainflow cycle counting model\" [8]. The equivalent full cycles model counts the full charge (Ah throughput) cycled by the battery since the start of its lifetime, without considering SOC, temperature, current, or any other variable; when this value reaches the charge, the battery can cycle, considering the cycle life shown in the manufacturer datasheet obtained under standard tests, and the end of the battery life is reached. The rainflow cycle count model includes the effect of the depth of discharge (DOD). Nevertheless, real operating conditions (current rate, temperature, DOD, SOC, etc.) are different from the laboratory conditions of the cycles shown by the manufacturer datasheet, so a significant error in the lifetime prediction can be obtained. Most of the previously published studies of the simulation and/or optimization of systems with battery systems do not use advanced models to estimate battery lifetime. In many cases, the battery degradation is not considered or its lifetime is estimated in fixed values based on the experience of the researcher [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20]. In other cases, battery lifetime is estimated by using the equivalent full cycles model [21; 22; 23; 24; 25]. In the best cases, it may be estimated by using the rainflow cycle counting method [26; 27; 28; 29]. However, a battery's real lifetime can differ from the estimated lifetime by many years using the mentioned methods, depending on the operating conditions. As previously mentioned, a high error in the estimation of the battery life would imply a great error in the estimation of the total  
Figure 1: Direct current (DC) coupled standalone photovoltaic (PV) system. cost of the batteries in the NPC of the system; therefore, the real levelized cost of Energy (LCE) may be very different from the expectation. A much more accurate lead-acid aging model (and also more complex and with higher computational difficulty) is the one described by [PERSON] et al. [30], called \"weighted _Ah_ throughput model\" and used by iHOGA software [31]. The model is based on applying weighting factors for the battery's charge throughput to estimate the lost capacity (considering the different stress factors for cycling and corrosion). [PERSON] et al. 's model was used to estimate the battery life in PV systems [32; 33].