## 1 Introduction  
Renewable power plants are the long-term solution for oil importing countries. This is especially true for countries struggling to satisfy their energy needs, such as Jordan. It is well known that photovoltaic (PV) renewable energy systems (RESs) are clean, modular, and quiet resources of energy. Further, the World Climate Conference that was held in Paris in 2015 set the limit for the global average temperature rise to be 0.2 \({}^{\circ}\)C per decade, between the years 2000 and 2100. Furthermore, hybrid systems that couple PV with other RES topologies have been considered worldwide [1; 2; 3; 4; 5]. Moreover, PV arrays, combined with an energy storage technology, such as pumped hydro storage (PHS), provide a reliable source of electricity [6; 7; 8; 9; 10]. Therefore, an in-depth investigation should be done to precisely model the PV array's output power. This will realistically estimate the capacity or number of PV panels of the solar PV array. Thus, more realistic construction decisions can be made. These will also include environmental and reliability analysis. There are many models for the PV array to choose from when designing a system. These include the ideal single-diode (ISD), the single-diode (SD), and the two-diode (TD) models. The ISD is idealistic, as it ignores the series and leakage currents to ground losses. However, the SD model is described by five lumped parameters. These are light generated current, leakage or reverse saturation current, terminal voltage, series, and shunt resistances. However, SD is the most common model in RES-related studies, as it includes the aforementioned two losses [11]. However, the TD model introduces two more factors: The reverse saturation current of the second diode and the ideal second diode. In this case, a more complex model that has seven parameters is considered. This provides for a more detailed mathematical models to obtain more realistic I-V and P-V characteristic curves of a PV array [12; 13; 14]. The inclusion of the additional diode leads to a seven-parameter estimation problem. So, the complexity of this model is increased for estimating seven parameters instead of five as in the SD model [15]. However, the TD model is precise, leading to a true size for a hybrid renewable energy system (HRES) integration problem. It will give a more realistic computation for system performance, such as ecological and reliability indicators. A lot of work has been done in the literature to model the PV panel output characteristics. In [16], the authors investigated the performance of the TD model in estimating the maximum power point for different PV technologies, such as string ribbon silicon, monocrystalline silicon, and thin film materials. In [17], the authors presented a theoretical model, offering a good compromise between the accuracy and simplicity of the parameters of the SD model. The model was developed using MATLAB for determining the solar PV module parameters to get the I-V characteristic curves of a PV module, string, and array. In [18], the authors presented the mathematical SD model of a PV module. The study includes the performance analysis of a 250 W PV module and its behavior with different temperature and irradiance values. The effects of varying shunt and series resistances were also considered. In [19], the authors presented a detailed explanation of various characteristics of ISD, SD, and TD-equivalent circuits. The non-linear mathematical equations were solved using the Newton-Raphson iterative method. This was to produce the I-V and P-V characteristic curves. It was concluded that TD model gives more precise characteristics of PV solar modules when compared to SD model results. However, this is at the expense of the complexity and number of iterations, due to the two more unknown parameters of the TD model. Other studies investigated a power system that consists of both PV and PHS, using one of the three aforementioned PV models.