Converter-interfaced generation and large data center loads that connect to or disconnect from the bulk grid abruptly expose the power system to abnormal frequency excursions and to transmission congestion. At the device level, this dissertation develops a theory of approximate internal models for sinusoids of varying frequency, embedding a receding horizon approximation of the instantaneous frequency in the controller. The resulting current controller for single-phase grid-following inverters preserves tracking under frequency deviations well beyond the ranges contemplated by power quality standards. At the network level, optimal transmission switching is formulated within the linear-coupled AC power flow model using a node-breaker representation of the substations. Under an apparent power congestion metric, the resulting mixed-integer linear program departs from DC-based decisions and approaches the full AC reference. Together, these contributions support reliable grid operation under the stress imposed by large flexible loads.