**3. Results and Discussion**

The simulation results for the configurations with traditional bypass diodes and power electronic-based DPP architectures are shown in Figures 8–11. The systems are evaluated at 1000 <sup>W</sup>/m2, 800 <sup>W</sup>/m2, 600 <sup>W</sup>/m2, 500 <sup>W</sup>/m2, 400 <sup>W</sup>/m2, and 200 <sup>W</sup>/m<sup>2</sup> by using a power sim (PSIM).

**Figure 8.** Output for series-parallel (SP) connection under various shading conditions with: (**a**) diode connection and (**b**) DPP connection.

**Figure 9.** Output for total-cross-tied (TCT) connection under various shading conditions with: (**a**) diode connection and (**b**) DPP connection (zero output).

The unshaded modules in Figure 7 experience an irradiance of 1000 <sup>W</sup>/m2. It is seen in Figures 8 and 10 that PV strings with DPP architectures have higher output power for the SP and CCT configurations than the systems with traditional bypass diodes. However, when DPP converters are adopted, there is almost zero or below 1 W of output power for all the shading scenarios with the TCT and BL configurations, as shown in Figures 9b and 11b. As the SL-based DPP architecture requires at least two series-connected PV modules for the converter to work properly, as shown in Figure 3. However, in TCT and BL architectures, their interconnections with other parallel PV strings affect the working principle of the used SL-based DPP topology.

In SP configuration, the output power for bypass diode and DPP under all shading patterns is shown in Figure 8a,b. The output power is 778 W, 826 W, 847 W, 872 W, and 933 W with bypass diode for one module, short wide, long narrow, central, and diagonal shading patterns, respectively, as shown in Figure 8a. In SP, output power with proposed SL-based DPP architecture is 905 W, 918 W, 924 W, 930 W, and 942 W at 200 <sup>W</sup>/m2, 400 <sup>W</sup>/m2, 500 <sup>W</sup>/m2, 600 <sup>W</sup>/m2, and 800 <sup>W</sup>/m2, respectively during one module, short wide, long narrow, central, and diagonal shading, respectively (see Figure 8b). For bypass diode technique, the power output in SP using short wide and central shading is almost similar as four PV modules are shaded under both schemes, two from each PV strings. Whereas, in the diagonal shading, each module is shaded from each parallel-connected PV string. Therefore, it has a more severe effect on output power, especially for diode bypass architecture, which can be seen from Figure 8a. DPP with SP interconnection, which is shown in Figure 8b has almost the same output power under given irradiances.

The power output received from CCT interconnection is shown in Figure 10. Similar to SP, in CCT one module shading has maximum power for all shading patterns, i.e., 821 W, 857 W, 870 W, 900 W, and 945 W at 200 <sup>W</sup>/m2, 400 <sup>W</sup>/m2, 500 <sup>W</sup>/m2, 600 <sup>W</sup>/m2, and 800 <sup>W</sup>/m2, respectively with bypass diode architecture. Similarly, 905 W, 918 W, 925 W, 930 W, and 942 for SL-based DPP architecture at 200 <sup>W</sup>/m2, 400 <sup>W</sup>/m2, 500 <sup>W</sup>/m2, 600 <sup>W</sup>/m2, and 800 <sup>W</sup>/m2, respectively under one module shading scheme.

**Figure 10.** Output for central-cross-tied (CCT) connection under various shading conditions with: (**a**) diode connection and (**b**) DPP connection.

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**Figure 11.** Output for bridge-linked (BL) connection under various shading conditions with: (**a**) diode connection and (**b**) DPP connection (zero output).

For short wide, long narrow, central, and diagonal shading the output power is given in Figure 10a,b with bypass diode and DPP, respectively. Figures 9 and 11 show the output power from TCT and BL interconnections for the traditional diode. In TCT and BL connections, DPP architecture is not applicable as discussed before. Therefore, the output power is almost 0 W, as shown in Figures 9b and 11b. Power losses are also calculated from Figures 8 and 10 during one module, short wide, long narrow, central, and diagonal shading for SP and CCT traditional bypass diodes and DPP converters. These losses are calculated only for the SP and CCT interconnections because TCT and BL interconnection schemes are not applicable on the SL-based DPP converter. For instance, power losses during one module shading for the worst case—i.e., 200 <sup>W</sup>/m<sup>2</sup> are 15.34%, 10.66% for SP and CCT, respectively by using the bypass diode. It is only 1.52% for the DPP architecture by using SP and CCT interconnections during one module shading. The power losses decrease with an increase in irradiance. For short wide and long narrow shading at 200 <sup>W</sup>/m2, the power losses for traditional bypass diode are 24.19% and 19.12% during short wide and 40.42% and 40.73% during long narrow shading for SP and CCT, respectively. Similarly, at 200 <sup>W</sup>/m2, DPP architecture has 3.66% and 3.40% power losses during short wide shading for SP and CCT, respectively. Power loss for DPP during long wide shading is 37.51% and 40.58% for SP and CCT at 200 <sup>W</sup>/m2. For the rest of the irradiances, the power loss decreases as the irradiance increases both for diode and DPP.

The power losses for SP and CCT string interconnections during central and diagonal shading for diode at 200 <sup>W</sup>/m<sup>2</sup> is 24.19% both for SP and CCT while 4.11% by using DPP. During diagonal shading, it has similar power losses for SP and CCT interconnections, which is 60.85% for bypass diode and 4.05% for DPP at 200 <sup>W</sup>/m2. Similarly, these power losses decrease with an increase of irradiance in a diagonal shading pattern also. Overall, PV strings with SP and CCT interconnections with DPP architecture have more output power than a traditional diode. For short wide, central, and diagonal shading, PV strings with DPP architecture are producing almost the same output power because four PV modules are shaded for all of them. DPP architecture is not applicable to TCT and BL interconnections. In all, DPP extracts more power from the 4 × 4 PV array system than traditional bypass diode for all interconnection schemes where it is applicable. However, SL-based DPP topology has higher cost with a complex circuitry in comparison to traditional bypass diode topology.
