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 complicated systems, which are composed of not only continuous states but also discrete events, and which contain 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 integrated 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 efficient simulation of intricate GHSs across multiple timescales, and thus significantly extends engineers' capability to study systems with numerical experiments.