AUTHORS: Julio Andre Bernal-Rubiano, Jorge Enrique Neira Garcia, Sergio Raul Rivera Rodriguez

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The economic dispatch of energy on power systems with high penetration of renewable generation is a mathematical problem of optimization. The solution techniques that have been used are programming techniques and heuristic approaches. In both cases, it is important to have a well-defined target function to be optimized. Nowadays, the power systems are more complex with the introduction of the renewable sources of energy with highly stochastic behavior. For this as follows it was pretended to obtain a model for the penalty costs in a photovoltaic generator. This paper shows a mathematical analysis with probabilistic methods contrasted with an analytic development for controllable renewable systems to be included in the target functions of economic dispatch problems. In order to validate the mathematical approach, Monte Carlo simulation was used to obtain the underestimation and overestimation penalty values of the scheduled power for the uncertainty cost of photo-voltaic (PV) generation in an instance of energy storage. Developed under a model with a uniform distribution of power, the document presents the validation for the uncertainty cost factor (UCF) comparing the Monte Carlo simulation with the analytic proposal where the low error in the results proved the advantages of using the analytic model due to its quadratic form and its coherence with the simulations that were performed.

KEYWORDS: Economic dispatch models, Mathematical modeling, Monte Carlo, Solar energy, Uncertainty cost

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