・ I_ph is the current generated by the incident light.

・ I_D1 is the Shockley diode equation due to diffusion.

・ I_D2 is the Shockley diode equation due to charge recombination mechanisms.

・ I is the output Current of PV cell.

・ I₀₁, I₀₂ [A] are the reverse saturation current of the diodes D₁ and D₂ respectively.

・ q is the electron charge [1.60217646*10⁻¹⁹ C].

・ k is the Boltzmann constant [1.3806503*10⁻²³ J/K].

・ T [K] is the temperature of the p-n junction.

・ a₁ and a₂ are ideality factor of the diodes D₁ and D₂ respectively for two diode model.

・ a is ideality factor of diode for one diode model.

・ V_T is the thermal voltage of the module.

Proportion of output energy of the solar cell to input energy from the sun is described as efficiency. Simultaneously reflecting the capability of the solar cell itself, the efficiency relies upon the spectrum and intensity of the incident sunlight and the temperature of the solar cell [32] . Therefore, conditions, which are used to measure efficiency, must be regulated cautiously in order to correlate the performance of one apparatus to another. Form factor (FF) is delineated as the ratio of the maximum power output from the solar cell to the product of open circuit voltage (V_oc) and short circuit current (I_sc).

・ V_OC is open circuit voltage & I_SC is the short circuit current and

・ G_n is the irradiance, T_n is the temperature, all at standard test conditions.

・ K_V is the open circuit voltage temperature coefficient & K_I is the short circuit current temperature coefficient. η is efficiency.

The dominant phenomena that confine cell efficiency are [33] :

Ø Reflection from the cell’s exterior.

Ø Light that is not enough dynamic to isolate electrons from their atomic bonds.

Ø Light that has excess energy beyond that required to isolate electrons from bonds.

Ø Light-produced electrons and holes (empty bonds) that casually collide with each other and recombine before they can promote to cell performance.

Ø Light-produced electrons and holes that are brought together by exterior and material blemishes in the cell.

Ø Resistance to current movement.

Ø Self-shading ensuing from upper-surface electric contacts.

Ø Performance degradation at non optimal (high or low) conducting temperatures.

The efficiency of a PV appliance is contingent on the spectral distribution of the solar radiation. The Sun is a source of light and its radiation spectrum may be examined with the spectrum of a blackbody near 6000 K. Radiation of electro magnet in all wavelengths are absorbed and emitted by a black body [37] .

The study of the effect of the solar radiation on PV devices is difficult because the spectrum of the sunlight on the Earth’s outward is affected by components such as the variation of temperature on the solar disc and the impact of the ambient [38] .

As demonstrate in Figure 3(b) and Figure 4(b), an increase in solar irradiance causes the power curves to move upward. Along with this, Table 2 demonstrates that maximum power and efficiency are increased at a significant amount with increasing value of solar irradiance for both models of PV cell. When irradiance is 170 watt/m², efficiency of two diode models is 2.4% higher than one diode model. Consequently when irradiance is 250 watt/m², efficiency of two diode models is 3.4% higher than one diode model. Hence Table 2 clearly shows that two diode models provide better efficiency.

Increasing temperature increases the intrinsic carrier concentration. This urges the Fermi level adjacent to the intrinsic Fermi level (the middle of the band gap). Inequality between Fermi-levels of the p-type and n-type regions determines the built-in potential of a diode. As temperature increases, the Fermi level in each region shifts closer to the center of the gap, hence the built-in potential is decreased [39] [40] .

Diode’s built-in potential is relevant with the conducting voltage of a solar cell. As a solar cell gets hot, the voltage is reduced, and therefore the output power and efficiency both are reduced. Thus the performance of solar cells decreases at high temperatures. Figure 5(b) and Figure 6(b) clearly illustrate this fact for simulated mathematical models [41] .

Table 3 pageants that, at low temperature both model provide approximately same efficiency whereas at high temperature, double diode model provide better efficiency.

Power dissipation across internal resistances affects efficiency as well as maximum output power of solar cells. These parasitic resistances can be modelled as a parallel shunt resistance (R_p) and series resistance (R_S) [42] [43] . For an ideal cell, R_p would be infinite and would not provide an alternate path for current to flow, while R_S would be zero, resulting in no further voltage drop before the load.

As shunt resistance declines, current passed through it increases for a given level of junction voltage. Consequence is that the voltage-controlled portion of the I-V curve begins to sag far from the origin, producing a remarkable devaluation in the terminal current I and a minor reduction in V_OC. Hence output power is reduced. Very inferior amount of R_p will attain a significant deflation in V_OC. Much as in the case of a large value of series resistance, a poorly shunted solar cell will take on operating attributes analogous to those of a resistor [44] .

PV cell efficiency as well as maximum power is increased with increasing value of shunt resistance. Figure 7 and Figure 8 expose this fact. Scrutinizing Table 4, it is examined that, PV cell efficiency will become almost constant after a certain value of shunt résistance. And this constant point occurs earlier (considering value of shunt resistance) for one diode model comparing with double diode model.

For the same amount of current, the voltage drop between the junction voltage and the terminal voltage becomes greater as series resistance increases [44] . As a result, current-controlled segment of the I-V curve initiates to sag toward the origin, causing a remarkable decrease in the terminal voltage and a minor contraction in I_SC, the short-circuit current. Tremendous values of R_S will also generate a significant reduction in I_SC; in these regimes, series resistance governs and the behavior of the solar cell resembles that of a resistor [44] .

Inspecting Figure 9 and Figure 10, it is detected that maximum Power as well as cell efficiency reduced with increasing value of series resistance for both models. Therefore, Table 5 presents that, double diode model furnish better performance for changing values of series resistance.

Multiple numbers of solar cells are connected to form panels. Therefore panels can be connected in series string

to increase the voltage level and in parallel to increase the current level or in a consolidation of the two. The accurate configuration depends on the current and voltage load prerequisites. Efficiency of the array can be maximized by coordinating interconnected panels in respect of their outputs [45] .

Imbalance in the short-circuit current of series connected solar cells can, contingent upon the conducting point of the module and the degree of conflict, have a severe repercussion on the PV module.

Series connections increase output power because voltage output is increased whereas output current remains almost constant. Figure 11 and Figure 12 clearly justify this fact. Efficiency of solar panel is increased with increasing number of series connected cells. For different values of series connected cell, double diode model serve with higher efficiency than single diode model. This evaluation is clearly exhibited in Table 6.

Parallel mismatch is not an issue for small modules, because in these cases cells are connected in series. Large arrays are generated by combining modules in parallel. So conflict mostly contributes at a module level rather than at a cell level.

Expanded number of parallel connected cells causes the output current to increase and the horizontal part of the I-V curve moves upward. Along with this, Figure 13(b) and Figure 14(b) show that maximum power moves upward with respective changing parameter. Also Figure 13(a) and Figure 14(a) clearly show that efficiency increased proportionally with increasing number of parallel connected cells. Similar with other parameters, two diode models contribute improved performance than either model. With percentage values of efficiency for both models shown in Table 7 confirms authenticity of this finding.

Ideality factor of a diode is an assessment of how intimately the diode pursues the conceptual diode equation. It is also evaluate the junction feature and the type of recombination in a solar cell [46] .

A constant value for the ideality factor is assumed for single diode equation. Practically, ideality factor is a function of voltage across the device. At high voltage, when surfaces and the bulk provinces command the recombination in the device, the ideality factor (a₁) is approximately one. However the ideality factor (a₂) approaches two when recombination in the junction dominates at lower voltages. The junction recombination is designed by including a second diode in parallel with the first and locating the ideality factor typically to two [47] .

A superior value of diode ideality factor degrades the FF and efficiency for a single diode model. However it usually signals high recombination and gives low open-circuit voltages [48] . Figure 15 justifies this theoretical assumption properly.

Diode ideality factors a₁ and a₂ respectively represent the diffusion and recombination current components for a double diode model. In accordance with Shockley’s diffusion theory, the diffusion current, a1 must be unity [49] . Nevertheless, the value of a₂ is malleable. Figure 16 describes that, P_max and efficiency are almost constant after a₂ reaches the value of (1.2). Hence this will be the appropriate ideality actor for diode (D₂) to have maximum cell efficiency. Table 8 validates theoretical recognitions for both models regarding diode ideality factor.