Industrial electrification provides a motivation to explore new methods for electrical power management. This paper addresses the situation where the available power is not enough to meet the full demand of a large production site, which can happen because of an electrical contingency. An industrial power management system typically handles electrical power deficits by disconnecting equipment, also known as load shedding. However, disconnections may cause an industrial process to shut down giving a very significant negative economic impact. Using a gas export plant as an example, this paper shows that flexible operation of the plant can offer an alternative to disconnection by making optimal use of any remaining available power, thus avoiding load shedding and enabling an electricity-intensive process to ride through a contingency without an expensive shut-down. Instead of load shedding, the electrical drives will enforce an immediate partial reduction of the power supplied to electrical motors and other machinery on a timescale similar to that of a circuit breaker. An innovation of the research is a framework for pre-computing feasible operating points of the process that match the available power. Technology suitable for industrial implementation is identified in the article and practical considerations are addressed. The findings show promise for the development of new systems for managing electrical power in electricity-intensive sites.