Many equivalent circuits have been proposed in the literature in order to assess the behaviour of the PV cell. The most commonly used equivalent circuits are the single diode models. These models are assumed that there is no recombination loss in the depletion region. But, real solar cell, the recombination loss represents a substantial loss, especially at low voltages. In the high voltage, diode ideality factor is 1 and in the low voltage, diode ideality factor is 2. So, consideration of this loss can draw a more precise model known as the two-diode model.

Figure 2 shows the equivalent circuit for solar cell based on two diode model. Using Kirchhoff’s first law, the output current of the cell is given by Equation (1).

Figure 2: 
Equivalent circuit for solar cell based on two-diode model

I_ph is proportional to the sun irradiance and the cell temperature, and it can be given by Equation (2)

I_sc is the light-generated current at 25℃ and 1000W/m2 irradiation. T_ref is Nominal temperature at 25℃. G_n , the nominal irradiation, is 1000W/m2. I_sc , K_I and T_ref can be obtained from the PV cell data sheet.

I_D1 is the current dut to the diode action (corresponds to the diode D1), and I_D2 is the recombination process in the depletion region (corresponds to the diode D2). These are following Equation (3), (4) and (5).

To simplify this, some researchers assumed that α₁ =1 and α₂ =2. These values are approximation of the Schokley – Read - Hall recombination in the space charge layer of the photodiode.

Equation (6) can be expressed by diode saturation current of the temperature variations.

Figure 3 and Figure 4 show a block diagram and front panel of solar cell by LabVIEW respectively.

Figure 3: 
Block diagram of the solar cell by LabVIEW

Figure 4: 
Front panel of the solar cell by LabVIEW

In the typical PV generation system, the modules are configured in a series-parallel structure as shown Figure 5.

Figure 5: 
Equivalent circuit for solar array

In this case, the output current can be given by Equation (7).

N_s and N_p are the number of series and parallel connected in solar cells in a array, respectively.

In the marine environment, solar generation system is installed in different directions. Differences of installation angle between PV panels make a difference of the intensity of radiation irradiated on each PV panel, and it brings loss of generation quantity due to the partial shading effect. Figure 6 shows the series configuration of two PV modules that receive irradiance of G₁ and G₂ respectively.

Figure 6: 
Circuit diagram of partial shaded module in series

The output current and voltage in partial shaded module can be obtained by solving the following formula Equation (8), Equation (9)

Figure 7 and 8 show a block diagram and front panel of solar array by LabVIEW respectively.

Figure 7: 
Block diagram of the solar array in series

Figure 8: 
Front panel of the solar array in series (partial shading)

In order to simulate the reliable power characteristics of the solar power system, solar irradiation data measured for a long time is required. However, in order to measure these data, there is a difficulty in equipment management, compensation, cost, etc. If the measurement is difficult, the calculating models of the amount of solar irradiation is made. These models have been used for studies such as the tilt angle and azimuth angle of the solar panels. In this chapter, a daily model of the solar irradiation which can be applied to the model of the solar power system is provided.

2.4.5 The amount of light incident on the solar panel

When the elevation angle and azimuth angle of solar is determined, and the tilted angle and azimuth angle of solar panel is given, the amount of light irradiated on the solar panel can be represented by the following formula.

Figure 9: 
Angles about position according to panel installation

SPV=Sdirect{cosh⋅sinθ⋅cos(β-α)+sinh⋅cosβ}

(14)

At first, we selected PV panel and examine specification. Table 1 shows the specifications for the BP MSX 60.

Figure 12, 13 and 14 show the elevation angle, solar irradiation and intensity on modules, respectively. Negative value means that the sun is located below the horizon. It was simulated in the autumn equinox (September 23).

Figure 12: 
Elevation angle

Figure 13: 
Solar irradiation

Figure 14: 
Intensity on modules

The output characteristic will be results in three dimensional characteristic shown in Figure 13 and 14. In this figure, x axis is the time (September 23), y axis is the output voltage of the solar array, and z axis is the output power of the solar array, respectively.

In the results of case 1, the maximum power points are located in region 1 and 2. But, in the result of case 2, the maximum power points are located in region 1.

In the Figure 15 and 16, the graph of the maximum generated power are approximately similar to case 1 and case 2.

Figure 15: 
VP curve in 3D (Case1)

Figure 16: 
VP curve in 3D (Case2)

Figure 17 and 19 are maximum power and voltage at maximum power point in Case 1. Figure 18 and Figure 20 are maximum power and voltage at maximum power point in Case 2. It means that Case 2 (the opposite-side panel connected by series) is better than Case 1 (the close-side panel connected by series) from a control perspective.

Figure 17: 
P_max (Case 1)

Figure 18: 
P_max (Case 2)

Figure 19: 
V_mppt(Case 1)

Figure 20: 
V_mppt(Case 2)