Stochastic Economic Dispatch with Advanced Polynomial Chaos Expansion

The computational difficulties posed by stochastic economic dispatch are addressed in this article. In order to tackle the complex issue of stochastic economic dispatch, where uncertainty in renewable generation greatly affects decision-making, a novel advanced polynomial chaos expansion (APCE) is proposed in this article. The proposed methodology provides a flexible solution that effectively calculates important statistical metrics, such as mean, variance, probability density function, and cumulative distribution function, related to the stochastic economic dispatch solution. Additionally, the method succeeds without requiring the prior information of explicit probability distributions for the random inputs. In order to assess the effectiveness of this method, a thorough analysis has been performed using IEEE-14 bus system and wind generation and load data for simulation studies has been taken from the Bonneville Power Administration (BPA) Balancing Authority area. The outcomes of these simulation studies provide compelling evidence for the effectiveness and precision of our proposed methodology, highlighting its superiority with lowest mean absolute percentage error (MAPE) value of 6.89% over conventional Monte Carlo (MC)'s MAPE-26.09%, traditional polynomial chaos expansion (PCE)'s MAPE-13.45% and Sparse polynomial chaos expansion (SPCE)'s MAPE-11.29%. The proposed methodology eliminates the requirement for explicit probability distribution data, making it a flexible and practical option for real-world applications. This reaffirms the effectiveness of data-driven approaches in addressing intricate energy management issues.