Distributed Frequency Control for Multi-Area Power Systems Considering Transient Frequency Safety

High penetration of renewable energy sources intensifies frequency fluctuations in multi-area power systems, challenging both stability and operational safety. This paper proposes a novel distributed frequency control method that ensures transient frequency safety and enforces generation capacity constraints, while achieving steady-state frequency restoration and optimal economic operation. The method integrates a feedback optimization (FO)-based controller and a safety corrector. The FO-based controller generates reference setpoints by solving an optimization problem, driving the system to the steady state corresponding to the optimal solution of this problem. The safety corrector then modifies these references using control barrier functions to maintain frequencies within prescribed safe bounds during transients while respecting capacity constraints. The proposed method combines low computational burden with improved regulation performance and enhanced practical applicability. Theoretical analysis establishes optimality, asymptotic stability, and transient frequency safety for the closed-loop system. Simulation studies show that, compared with conventional FO-based schemes, the method consistently enforces frequency safety and capacity limits, achieves smaller frequency deviations and faster recovery, thereby demonstrating its practical effectiveness and advantages.