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 phase error corresponding to a measured value of the electrical characteristic obtained from the sensing arrangement, determines a frequency correction power command based on a difference between the estimated frequency and a target frequency, and operates the power conversion module in accordance with the frequency correction power command. The frequency correction power command regulates the frequency of the electrical characteristic of the electrical grid interface to the target frequency, for example, by charging or discharging a battery.