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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]

Summary: The produced energy from varied sources in modern power systems is to be optimally planned for planning and operating of power system under the determined limit conditions. Recently, the rising overall people population of the world, the increasing of people requirements, improvements of technology, and ecosystem and global climate changes have caused with the increasing of electric energy demand. One of the most important solution methods to meet this energy demand is considered as utilization of renewable energy sources (RESs) in power systems. The structure of power systems has become with the usage of RESs more complex. The optimal power flow (OPF) from planning and operation problems has converted to difficult problem with RESs integrated into modern power systems. This paper presents the OPF problem of power systems with a high penetration of controllable renewable sources. These kinds of sources are able to inject a determined power since they have a back‐up unit (storage). Uncertain solar irradiance and wind speed are simulated via log‐normal and Rayleigh probability distributions, respectively. The proposed OPF problem with controllable renewable sources is solved by the differential evolutionary particle swarm optimization (DEEPSO) algorithm. Simulations conducted on various test systems illustrate the effectiveness and efficiency of DEEPSO as compared with other algorithms including moth swarm algorithm, backtracking search algorithm, and differential search algorithm. In addition, the Wilcoxon signed‐rank test is applied to show the supremacy, effectiveness, and robustness of DEEPSO algorithm. [ABSTRACT FROM AUTHOR]