Reliability Evaluation of Rooftop Solar Photovoltaics Using Coherent Threshold Systems
Rudi Uswarman
Department of Electrical and Computer Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
Ali Muhammad Rushdi *
Department of Electrical and Computer Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
The trend for use of rooftop solar photovoltaics (PV) is rising due to their promising economic potential as a source of clean renewable energy. In general, a source of renewable solar energy consists of solar PV, an automatic charge controller, a battery pack, and an inverter. The reliability of a rooftop solar PV system is evaluated herein as that of a coherent threshold system (CTS). First, we utilize the unit-gap method and the fair-power method to verify that a given Boolean function is a threshold one and to identify its threshold and component weights. Both methods utilize specific features of the Karnaugh map (K-map). The unit-gap method uses the map to list all necessary inequalities by inspection, and then reduce them significantly by omitting dominated ones. The fair-power method uses the Karnaugh map to compute Banzhaf indices by appropriate map folding followed by XORing of true cells and false cells. We evaluate the CTS reliability via a recursive algorithm based on the Boole-Shannon’s expansion in the switching domain, which is transformed via the real transform to the total probability law in the probability domain.
Keywords: Solar photovoltaics, coherent threshold system, fair-power method, Banzhaf index, recursive algorithm.