Load Redistribution (LR) attacks operate by adversarial manipulations of load measurements in electrical power grids. Machine Learning (ML) based detectors have been effective to detect LR attacks where the attacked load vectors are outliers of the distribution of normal load vectors. On the other hand a recent family of attacks, known as dummy LR attacks, are capable of bypassing the ML-based detectors by choosing attack load vectors that are not outliers. This paper presents an approach for defense against such stealthy third-generation dummy LR attacks by identifying and monitoring critical loads. A case study on the IEEE 30 bus system demonstrates the effectiveness of the proposed approach for defense against dummy LR attacks. A larger case study on actual load and line power flow measurements of the Delhi Power Grid demonstrates that the proposed approach can be extended to real-world grids.