## 1 Introduction
The first one counts the charge (Ah throughput) cycled by the battery since the start of its lifetime; when this value reaches the charge, the battery can cycle (considering the cycle life shown in the manufacturer datasheet, obtained in standard tests), the end of the battery lifetime is reached. The second model includes the effect of the depth of discharge (DOD). Nevertheless, real operating conditions (current rate, temperature, DOD, SOC, etc.) are commonly different from the laboratory conditions of the cycles shown by the manufacturer datasheet, so a great error in lifetime prediction can be expected. In some of these cases, especially in full PV systems, the lifetime estimation can be two or three times greater than real lifetime [11]. A much more accurate lead-acid aging model (and also more complex and with higher computational effort) is described by [PERSON] et al. [12], called \"weighted _Ah_ throughput model\". It is used by iHOGA software [13]. This model includes Shepherd model [14] to calculate the battery voltage and Lander model [15] for the estimation of corrosion depending on voltage and temperature. The model is based on the application of weighting factors for the charge throughput of the battery to estimate the lost capacity (considering the different stress factors for cycling and corrosion). Regarding Li-ion batteries [16, 17, 18], they have higher cycle life, energy density and energy efficiency, and lower maintenance compared to lead-acid batteries. LiFePO\({}_{4}\) type is the most used in off-grid systems. The most significant aging external factors of Li-ion batteries are temperature, charge and discharge rate, and DOD [19]. In optimization of hybrid standalone systems, Li-ion cell level aging models [20] are commonly used, due to their simplicity. Electrochemical models are usually very complex, even the most simplified ones [19; 21; 22], thus they cannot be used in optimization due to excessive calculation times [23]. \"Calendar\" aging occurs when a battery is not being used while \"cycle\" aging occurs when the battery is under charge or discharge current [23]. Cycle aging is affected by the total charge (Ah) throughput from the start of battery lifetime, the current, the ambient temperature, and the SOC. Calendar aging main factors are temperature and SOC [20]. Arrhenius kinetic-based aging models [20] are the most used cycle aging models. For example, [PERSON] et al. [24] model was obtained by doing many accelerated cycling tests to commercial LiFePO\({}_{4}\) cells, obtaining a capacity fade model which takes into account the Ah throughput and temperature for different charge/discharge rates. Calendar aging has been modelled by different researchers [20]. For example, [PERSON] et al. [25] use an expression based on Arrhenius law, considering temperature, time, and SOC. In this work, researchers consider a condition to switch between calendar and cycle mode, assuming that cycle aging only occurs when the battery is in charge mode and the current is above a given threshold current. A recent study [26] proposed to use the model of [PERSON] et al. [12] for lead-acid batteries and, for Li-ion batteries, the model of [PERSON] et al. [24] combined with the calendar aging model of [PERSON] et al. [25]. Lifetime aside, there are other characteristics of Li-ion batteries that outperform lead-acid ones, such as lower maintenance costs, higher cycling efficiency, and greater allowed depth of discharge. Against these advantages there is the fact that currently, its acquisition price is higher. Therefore, the question is to determine in which cases it is profitable to pay its highest price. In the context of standalone energy systems, this has been addressed for specific cases in several studies, mainly located on geographical latitudes with very high solar resource. Limiting the review to recent studies, the best results are equally divided between Li-ion and lead-acid batteries, i.e., currently it is a match virtually tied.