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AUTHOR(S): Julian Garcia-Guarin, Sergio Raúl Rivera Rodríguez
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ABSTRACT The energy dispatch presents high variability due to the high increase due to the stochasticity of renewable resources. The deviations from unforeseen events increase the marginal cost of power generation, thus improving cost estimation It turns out to be essential. The estimation of uncertainty costs by the energy use wind presents an impact significant due to its stochasticity. This study aims to validate the uncertainty cost function for wind energy systems using Monte Carlo simulations, numerical integration, and analytical methods, where the power output is related to wind speed by (P = k∙ V3). Wind speed is modeled using the Weibull distribution, and uncertainty costs are computed for overestimation and underestimation scenarios. Numerical integration, and closed-form analytical expressions are formulated based on the lower incomplete gamma function. Monte Carlo simulations are used to generate wind speed scenarios, while numerical integration and analytical formulations are employed to derive expected costs. The mean uncertainty cost obtained from Monte Carlo simulations matches the results from numerical integration and analytical methods, validating the proposed approach. The study demonstrates the reliability of the uncertainty cost function for wind energy systems, providing a robust framework for managing uncertainty in renewable energy integration. This framework allows system operators to accurately quantify uncertainty costs, thereby improving dispatch decisions. Relative errors between methods ranged from 0.008% to 0.042%. Other methods evaluated include Kalman filtering and neural network wind forecasting, which significantly reduced costs for two low-power scheduled dispatch cases: 1 MW and 10 MW, to 50.694% and 62.285%. |
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KEYWORDS Uncertainty Cost Functions, Cubic Wind Speed-Power Relationships, Controllable Energy Systems, Monte Carlo, Wind Energy, Stochastic Modeling |
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Cite this paper Julian Garcia-Guarin, Sergio Raúl Rivera Rodríguez. (2025) Uncertainty Cost Functions in Cubic Wind Speed-Power Relationships for Controllable Energy Systems: Monte Carlo, Numerical, and Analytical Validation Approaches. International Journal of Control Systems and Robotics, 10, 13-21 |
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