Sunlight is a spectrum of photons distributed over a range of energy. The electrons can be excited and move from the valence to the conduction band by photons whose energy is greater than the band gap energy, this being the energy required to jump the gap between the valence band and the conduction band. Here, they can exit the device and can then be used to generate electrical power in an external circuit. The photons which have an energy level that is less than the energy gap do not excite free electrons, this energy moves through the solar cell and is absorbed as heat in the back of the module. A metallic grid on the top side of the PV module forms one of the electrical contacts to the diode which allows light to fall onto the panel between the gridlines which is then absorbed into the material to be converted into electrical energy. An antireflective layer between the gridlines increases the transmission of light into the semiconductor material [1].

A Photovoltaic (PV) device is an element that converts sunlight into electricity. The basic PV device is the PV cell. A set of connected cells form a panel or module. Panels are generally composed of a series of cells in order to obtain a larger output voltage. Panels with large output currents are achieved by increasing the surface area of the cells or by connecting the cells in parallel. A photovoltaic array may be either a panel or a set of panels connected in series or parallel to form a large PV system.

Solar materials are chosen largely on how well their absorption characteristics match the solar spectrum. Another limiting factor is the cost of fabrication. Silicon is a common choice of material used to manufacture PV panels due to the materials absorption characteristics being a relatively good match to the solar spectrum; and silicon fabrication is well developed in the semiconductor electronics industry. Electronic grade semiconductors are extremely pure crystalline materials whose crystalline nature means that atoms are aligned in a regular periodic array. This periodicity, coupled with the atomic properties of the component elements is what gives semiconductors their useful electronic properties. However, under real operation conditions, it is apparent that the specifications provided by the manufacturers of commercial panels are not a true representation of how PV panels may behave when deployed in the field [2].

A PV cell is simply a semiconductor current rectifier, or diode with a photogenerated current source. The IV characteristics of this circuit is given in the Shockley solar cell equation [3]. (1)I=Iph−I0(qVekBT)where kB is the Boltzmann constant, T is the absolute temperature, q(>0) is the electron charge, and V is the voltage at the terminals of the cell. I0 is the diode saturation current. Iph is the photogenerated current, Iph is closely related to the photon flux incident on the cell, and its dependence on the wavelength of light is often discussed in terms of the quantum efficiency or spectral response [2].

The double-diode model (DDM), as illustrated in Fig. 1, describes the PN junction operation through the Shockley equation, and includes series and shunt resistances to incorporate the current-dependent and the voltage-dependent loss mechanisms. It has the important feature of modelling the carrier-recombination losses in the depletion region [4].

The non-linear equation giving the relationship between the current and the voltage at the PV source terminals is: (2)IPV=Iph−Is1[e(VPV+IPVRs)η1Vt−1]−Is2[e(VPV+IPVRs)η2Vt−1]−VPV+IPVRsRh

The photocurrent (Iph), the two diodes’ saturation currents (Is1) and (Is2), the two diodes’ ideality factors (η1) and (η2), and the two resistances (Rs) and (Rh) are all stated as unknowns and their values must be identified using measurements given by the module manufacturer or experiments made by the researcher, on the actual PV module being simulated. Vt=kTq is the thermal voltage of the PN junction in the PV cell. The value of the second saturation current Is2 is three to five times higher than the first [5].

On the other hand, the capacitance of the PV cell can be broken down into two different types, junction or barrier capacitance C_j which consists of mobile carriers in the depletion region and diffusion capacitance C_d which is attributed to the minority charge carriers in the bulk material. One is often referred to as low voltage capacitance (C_j) and the other a high voltage capacitance C_d. They are both dependant on the applied voltage, which allows combining the two into the strongly voltage dependent free carrier capacitance as discussed in [5]. PV cells using silicon-based technology tend to have the junction capacitance as the dominant capacitance at low voltages of (∼0−0.3V) which increases linearly, then free carrier capacitance ((∼0.3−0.7V) takes over and the total capacitance increases exponentially. For voltages above 0.7V a rapid decrease is shown in the total capacitance, this is attributed to the interface states. Experiments were carried out by various groups as in [6], which involved putting a ramp voltage across the PV cell under test in unlit conditions. The reasons for this is to have the charge carriers in the crystalline silicone (cSi) or amorphous silicon (aSi) cell at a steady state of equilibrium which saves the cell measurements from erroneous readings caused by factors such as the heating of the panel, where the physics of the junction is susceptible to change dramatically reducing the generation of power.

Additionally, various recent research approaches have investigated the different parameters that could affect the performance of the solar cells and their qualities. Papers [7,8] have explored the output power factor (PF) and total harmonic distortion (THD) of the solar panels at different irradiance conditions. Other research [9,10] has provided experimental evaluation of the solar panels as a Photovoltaic/Thermal System, where the panel acts as a source of electric and heat energies. Nevertheless, all these papers have evaluated the solar panels by only assessing their output electrical measurements including, their output voltage, current and power without deepening into their internal static and dynamic parameters.

On the other hand, other research papers have evaluated some of these internal parameters in the individual solar cells using different approaches of machine learning techniques. Paper [11] used only the one-diode model to represent the solar cell and has simply combined the two capacitance types together into one bulk parameter.

Other papers employed machine learning approaches to estimate these internal parameters in individual cells such as teaching-learning-based optimisation algorithms undertaken in [12], particle swarm optimization algorithm in [13], and Laplacian Nelder-Mead spherical evolution in [14]. However, they all investigated only the static parameters of the individual solar cells without insights on their dynamic parameters including the diffusion and junction capacitances and how to distinctively estimate them.

In view of that, the novelty of this paper is emphasised as it provides a comprehensive experimental framework to evaluate the whole static and dynamic parameters of a full PV panel of 36 series-connected PV cells. Such a full framework has not been presented before in the literature for PV panels. The paper measures the static parameters of the PV panel including the overall equivalent two diodes’ saturation currents, the two diodes’ ideality factors, and the series and shunt resistances. The paper then evaluates the dynamic parameters including the overall resultant junction and diffusion capacitances of the panel. These static and dynamic parameters govern the performance of the PV panel and assess its characteristics and qualities at different operational conditions. Accordingly, the main contributions of this paper can be demonstrated as follows: 1.

This paper presents for the first time a new comprehensive experimental evaluation for the static and dynamic parameters of a whole solar panel of multiple connected cells not of a single cell as has been provided in the state-of-the-art literature in this research scope.

The remainder of the paper is organized as follows. Section 2 demonstrates the experimental procedures for evaluating the static parameters of the PV panel at dark conditions. Then the dynamic parameters are measured in Section 3 using two unique experimental setups one for each capacitance type. Eventually, conclusions and discussions of the developed results are highlighted in Section 4.

To conduct the dark experimental measurements of the PV panel, a dark environment is created so that no influence from external light sources, including ambient day light, can affect the measurements being taken. The panel is then externally supplied with electrical sources meaning that no light source is required to stimulate the panel. Fig. 2 illustrates the construction of the box to enclose the panel to undertake the required tests. The schematic of the circuit used for the experiments is demonstrated in Fig. 3. The specifications sheet of the 10 W commercial PV panel under study stated a maximum supply current of 0.6 A, so a safe limit was set at 0.5 A along with a maximum voltage limit of 40 V to ensure that the panel would not be damaged. The external resistance (R) is chosen to be 47 Ω. The experiment was started at 0 volts and was increased in 0.1-V steps and the corresponding current measured in microamps so that no information was lost. The resulting measurements were then used to generate the plot developed in Fig. 4. The developed plot is divided into the higher-values portion to extract the R_s and first diode I_s1 and η₁. While the lower-values portion is then used to extract the R_h and second diode I_s2 and η₂.

Fig. 4 shows a resemblance to the plot of [15] but this being for a single PV cell, where the regions of higher and lower I-V values are also identified to evaluate the static parameters associated to each region. On the other hand, to take into account the 36 series-connected PV cells in the panel under study, the equivalent circuit diagram for the connected cells has to be deduced at each region to facilitate the calculation of the required parameters per cell in this research. Fig. 5 demonstrates the equivalent circuit diagram of the PV panel at dark conditions, where the 36 cells are connecting in series across their external contacts. Consequently, at lower I-V values, both diodes in each cell would be turning off allowing the current to flow only through their R_s and R_h resistances as illustrated in Fig. 6. Conversely, at higher I-V values, both diodes of each cell would be acting as a short wire across their R_h. Fig. 7 shows such a circuit arrangement.

Accordingly, with the aid of the circuit diagrams of Figs. 5–7 and the captured measurements, the required static parameters are calculated using regression approaches for the developed curve of Fig. 4. Both the higher and the lower I-V regions of the curve were separated, and ranges of measurements have been selected that were deemed to most likely allow a successful ‘fit’ to the curves. For the higher part I-V characteristic, the curve can be fitted using the relation in (3) by neglecting the influence from the lower range. (3)IPV=Is1(exp⁡(η1(VPV−IPVRs))−1)

After that, Eq. (4) is then used to calculate the lower part characteristics as follows: (4)I2=Is2[exp[η2(VPV−IPVRs)]]=IPV−I1

Finally, a value for Rh can be calculated using the following formula in (5), (5)Rh=[(dIdV)V→0−η1Is1−η2Is2]−1

MATLAB generalised linear model [16] is utilized in this research to extract the required static parameters per cell of the PV panel under study, and the final resultants are provided in Table 1

A PV cell can be modelled during dynamically variable input conditions as shown in Fig. 8, where the capacitance features taking place are the junction (C_j) and the diffusion capacitance (C_d) which are due to the carrier change in the space charge “junction” region and in the neutral regions, respectively. When the PV cell is reverse-biased, there are much fewer minority carriers in the neutral regions, so C_d diminishes, and C_j dominates. For forward-biased conditions, the contribution from the rearrangement of the minority carrier density is highly raised leading C_d to dominate C_j under such conditions. The variation of both constituents of the PV cell capacitances with an external voltage is illustrated in Fig. 9 [17].

The static and dynamic electrical parameters of a solar panel of 36 series-connected cells have been evaluated in this research by employing three different distinctive experimental setups in a dark environment. With respect to the static parameters, this paper has calculated the PV panel resultant diodes’ saturation currents, their diodes’ ideality factors, their series, and shunt resistances, where the results are summarised in Table 1. After that, the dynamic parameters are evaluated starting with C_j using the experimental setup of Fig. 11, where they are estimated at different switching conditions and demonstrated in Figs. 17–19. Eventually, C_d is evaluated using the unique OCVD setup of Fig. 21 and its value per cell is plotted vs. the applied voltage in Fig. 26, where its average is calculated to be 7.33 pF for the PV panel under study.

The evaluation of the static and dynamic electrical parameters of solar panels is crucial for accurate performance assessment, system design and optimisation, and ensuring long-term reliability and safety. Static parameters define the solar panel’s performance under stable and static conditions, which is essential for informed purchasing decisions on system sizing and component compatibility, as well as quality control and efficiency assessment. On the other hand, dynamic parameters describe how a solar panel behaves under real-world, constantly changing conditions to be used for their performance forecasting, optimisation of their maximum power point tracking algorithm, and also evaluating their degradation analysis.

The fundamental contributions of this research, to evaluate the parameters of a complete solar panel, become evident when comparing to the recent state-of-the-art literature, which explored a single solar cell. The interconnected nature of a PV module, which comprises of multiple cells, metallic interconnects, and other parasitic elements, all these factors create an extremely complex electrical environment when compared to a single solar cell. The distributed effects and the material defects of these electrical parameters were deemed to be outside of the primary scope of this investigation but clearly highlighted a need for careful examination and interpretation of the experimental data, as the panel’s response is surely influenced by these factors. Future works are aimed to be carried out in this area.