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Summary: This paper is concerned with innovative approaches to renewable energy sources computation methodologies, which provide more refined results than the classical alternatives. Such refinements provide additional improvements especially for replacement of fossil energy usages that emit greenhouse gas (GHG) into the atmosphere leading to climate change impact. Current knowledge gap among each renewable energy source calculation is rather missing fundamentals of plausible, rational, and logical explanations for the interpretation of results. In the literature, there are rather complicated and mechanically applicable methodologies, which require input and output measurement data match with missing physical explanations. The view taken in this review paper is to concentrate on quite plausible, logical, rational, and effectively applicable innovative energy calculation methodologies with simplistic fundamentals. For this purpose, a set of renewable energy methodological approaches is revisited with their innovative structures concerning solar, wind, hydro, current, and geothermal energy resources. With the increase in the renewable energy utilizations to combat the undesirable impacts of global warming and climate change, there is a need for better models that will include physical environmental conditions and data properties in the probabilistic, statistical, stochastic, logical, and rational senses leading to refined and more reliable estimations with application examples in the text. Finally, new research directions are also recommended for more refined innovative energy system calculations. [ABSTRACT FROM AUTHOR]