In this study, we discuss the concept of complemented soft groups or S-groups in detail. We provide definition an S-group and a investigate properties these groups. also prove theorem that characterizes relationship between normal subgroup group. Overall, research aims to contribute development theory S-groups.

In order to obtain more power from photovoltaic (PV) modules under mismatching operating conditions, the submodule-based MPPT technique is an important solution. this technique, since power-voltage (P-V) curve of a submodule cannot be multi-peaked, maximum point (MPP) tracking (MPPT) easily achieved through DC-DC converter connected each submodule. Since P-V in multi-peaked form, can obtained w...

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