Electrical systems and related operating methods are provided. One exemplary electrical system includes a sensing arrangement coupled to an electrical grid interface to measure an electrical characteristic of the electrical grid interface, a power conversion module having an output coupled to the electrical grid interface, and a control module coupled to the sensing arrangement and the power conversion module. The control module determines an estimated frequency of the electrical characteristic based on a measured value of the electrical characteristic from the sensing arrangement, adjusts a commanded reactive power for the power conversion module to increase a difference between the estimated frequency and a reference frequency, operates the power conversion module in accordance with the adjusted reactive power command, and thereafter initiates a remedial action when the difference between the estimated frequency and the reference frequency exceeds a threshold amount.