A continuous relaxation approach for optimizing under-frequency load shedding decisions

Under-Frequency Load Shedding (UFLS) is a critical protection mechanism that sheds load to prevent frequency collapse. With the proliferation of DER, the grid is becoming more bidirectional, making some locations less effective for the UFLS than others. This work proposes a nonlinear time-domain optimization framework that relaxes binary load-shedding actions into continuous variables and uses a Lasso-inspired regularization to enforce sparse, near-integer solutions. The method is tested on a 23-bus system under a 25% power imbalance scenario. Results show that the proposed approach effectively identifies load shedding locations to halt frequency decline with significantly reduced computation as compared to mixed-integer formulations, making it more suitable for real-time or large-scale applications.