Modeling and simulation have emerged as an indispensable approach to create numerical experiment platforms and study engineering systems.However,the increasingly complicated systems that engineers face today dramatically challenge state-of-the-art modeling and simulation approaches.Such compli-cated systems,which are composed of not only continuous states but also discrete events,and which con-tain complex dynamics across multiple timescales,are defined as generalized hybrid systems(GHSs)in this paper.As a representative GHS,megawatt power electronics(MPE)systems have been largely inte-grated into the modern power grid,but MPE simulation remains a bottleneck due to its unacceptable time cost and poor convergence.To address this challenge,this paper proposes the numerical convex lens approach to achieve state-discretized modeling and simulation of GHSs.This approach transforms conventional time-discretized passive simulations designed for pure-continuous systems into state-discretized selective simulations designed for GHSs.When this approach was applied to a largescale MPE-based renewable energy system,a 1000-fold increase in simulation speed was achieved,in comparison with existing software.Furthermore,the proposed approach uniquely enables the switching transient simulation of a largescale megawatt system with high accuracy,compared with experimental results,and with no convergence concerns.The numerical convex lens approach leads to the highly effi-cient simulation of intricate GHSs across multiple timescales,and thus significantly extends engineers\'capability to study systems with numerical experiments.