Quantifying Uncertainty Costs in Renewable Energy Systems Considering Probability Function Behavior and CVaR at Low-Probability Generation Extremes using Deterministic Equations

The increase and integration of renewable energy sources in electrical power systems implies an increase in uncertainty variables, both in costs and production, of economic dispatch (ED) and currently have a significant influence on wholesale electricity markets (MEM). Uncertainty costs refer to the quantification of additional expenses or economic losses associated with the variability inherent in the generation of renewable energy, such as wind, solar, or hydroelectric. Therefore, this article presents deterministic equations related to cost overestimation and underestimation, as well as CVaR, to model and evaluate the stochasticity of risks associated with the integration of renewable sources, allowing system operators and planners to make informed decisions. To mitigate or use said risks in energy systems with high penetration of elements, mainly smart networks. In this study, a mathematical analysis is carried out using the histogram spectrum formed by the power generated by the probability density function (PDF) for solar generation, although it is possible to consider other types of functions to determine energy generation. The objective of the proposed model is to provide another tool to the system operator for energy management and planning, which relieves a little of the weight of the computational load and at the same time presents more precision in the results by being able to work with a database. Historical data if these values are available. Commonly, for this type of analysis, values are estimated using probabilistic calculations by density functions when integrating these functions, or in other recent cases by estimating them by analytical methods of the same functions. A validation of the model is presented by comparing the result with the Monte Carlo simulation, developing the total cost of uncertainty only from "low probability generation extremes". Furthermore, the results are presented through analytical uncertainty cost functions (AUCF). This analysis includes the calculation of uncertainty costs for low and high-probability energy generation, determined by the Conditional Value at Risk (CVaR), using deterministic equations.