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The Three-Point Probability Density Function Approximation of the Stochastic Parameter Applicable for Technical and Economic Modeling of Renewable Sources

Abstract

Abstract— The research refers to the problem of the accuracy increase of simulation results for a wide class of physical objects with uncertain technical and economic parameters. Various deterministic and stochastic modeling techniques appear to be successfully used for economic and mathematical problems solution, particularly due to exploiting expedient for practical simulation probabilistic methods like Monte Carlo Simulation and Point Estimate methods. Both are extensively used to tackle uncertainties when modeling energy systems as well.
The standard functions to represent the stochastic (random) parameters of the model are analyzed with the use of three-point estimation technique for the distribution functions of their probable values. A synthetic asymmetric probability density function was constructed basing on the standard normal distribution, which is suitable for analytic representation of the predicted and/or statistical random sampling of the uncertain model parameters of energy system with renewables, and analytical expressions were obtained to compute the moments of proposed synthetic probability function.

Keywords— simulation accuracy in power engineering, uncertain parameter estimation, stochastic modeling, three-point approximation, integrated renewable technologies.

Authors

• Vasyl O Kostiuk (Igor Sikorsky Kyiv Polytechnic Institute )
• Mesbahi Abdessamad (National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”)
• Mykola Fedosenko ( Igor Sikorsky Kyiv Polytechnic Institute)