Median and Radius-Driven Interval Uncertainty Modeling for Security-Constrained Economic Dispatch

The diverse uncertainties from renewable energy sources and loads make the security-constrained economic dispatch (SCED) problem more challenging. Inaccuracies in interval uncertainty models lead to overly conservative scheduling results. This paper proposes an interval modeling method from median and radius, using their respective uncertainties to characterize the randomness of an interval. Given multiple uncertain sources, a joint probability distribution is developed, followed by the construction of an uncertain interval and probability- driven Conditional Value at Risk (CVaR). A grid security indicator is proposed to represent the operating state of the power grid, with the line having the smallest security margin determining the overall security level. Furthermore, a multi-period SCED is developed, incorporating system security and reserve regulation through the uncertain interval and probability-driven CVaR method. Notably, the security margin is integrated into the SCED model as both an objective and a constraint. Security and reserve constraints are transformed into deterministic linear forms using the uncertain interval and probability-driven CVaR, reducing computational complexity while accurately reflecting the influence of various random sources on SCED. Case studies demonstrate the effectiveness and scalability of the proposed risk evaluation method and SCED model.