2.1.5. PV Model Review

Although the SDM, with its simple structure and fair accuracy, is presented at the very beginning of this section, it is not the earliest cell model. It is a development of the ideal PV cell model (IPCM). Compared to the IPCM, which has a straightforward structure consisting of only a current source and diode, the SDM simulates the flow resistance, electrode resistance, and surface contact resistance, explains the physical behavior, and is widely used in this problem [42]. To further improve the accuracy of the model's simulated conduct at low irradiance, a diode is added to the DDM to represent the loss of current in the depletion region. However, the added unknown parameters increase the difficulty of the solution. TDM has the potential to achieve higher accuracy than DDM after calculating the leakage current and grain boundaries with the addition of a diode. Again, the solution difficulty increases as the dimensionality of the problem increase.

In addition, there are many less commonly used improved diode models, such as the modified 3-diode model [43], the SDM with capacitance [44], the Generalized Multi-Dimension Diode Model [45], the Modified SDM (MSDM) [46], the Four Diode Model (FDM) [47], the Modified DDM (MDDM) [48] and the Modified TDM (MTDM) [49]. We note that metaheuristics have recently been used to solve the FDM and the modified SDM, DDM, and TDM models. Thus, it would be a trend for future research to consider these four models to find a cell model that matches the proposed method to achieve a balance between solution difficulty and accuracy.

For the modules, in addition to the SDM presented in Section 2.1.4, the use of DDM and TDM formations are also options considered by the researchers. Their accuracy and solution difficulty performance are similar to their performance in the cell model. The appropriate model-building module must be selected to fit the specific needs. In this paper, considering that counting all the above models would cause duplication of content, excessive length, and difficulty reading, only the computational results of the modules composed of SDM components are summarized. The increased accuracy, increased difficulty in solving, and increased computational resources due to the increase in diodes will be reflected in the computational results of the cell model.

In addition, several specific PV models exist to achieve accurate modeling of PV systems in specific situations. They are not commonly used for the time being, but are of great interest. The dynamic PV model is one of them. It considers underdamped currents, switching frequency harmonics, varying loads, and resonance of cables, and is more suitable for grid-connected operation [50,51]. Its equivalent circuit diagram is shown in Figure 2 [52].

**Figure 2.** Dynamic model's circuits.

The model's output current is shown as follows [53]:

$$\begin{pmatrix} I(s) = \frac{a\_{21}(s+b\_1) + b\_2(s-a\_{11})}{(s-a\_{11})(s-a\_{22}) - a\_{21}a\_{12}} \cdot \frac{V\_{\text{OC}}}{s} \\\ I\begin{pmatrix} a\_{11} & a\_{12} \\ a\_{21} & a\_{22} \end{pmatrix} = \begin{pmatrix} \frac{-1}{\overline{\mathcal{C}(R\_{\text{S}}+R\_{\text{C}})}} & \frac{-R\_{\text{S}}}{\overline{\mathcal{C}(R\_{\text{S}}+R\_{\text{C}})}} \\\ \frac{R\_{\text{S}}}{L(R\_{\text{S}}+R\_{\text{C}})} & \frac{-(R\_{\text{C}}R\_{\text{S}}+R\_{\text{C}}R\_{\text{S}}+R\_{\text{L}}R\_{\text{S}})}{L(R\_{\text{S}}+R\_{\text{C}})} \end{pmatrix}, \begin{pmatrix} b\_{1} \\ b\_{2} \end{pmatrix} = \begin{pmatrix} \frac{1}{\overline{\mathcal{C}(R\_{\text{S}}+R\_{\text{C}})}} \\\ \frac{R\_{\text{C}}}{L(R\_{\text{S}}+R\_{\text{C}})} \end{pmatrix} \tag{5}$$

where *s* is the time, *Rs* and the open circuit voltage *Voc* are usually known, the inductor *L*, the resistor *RC*, and the capacitor *C* are unknown. Therefore, *C*, *RC*, and *L* are the parameters to be extracted.
