Competitive Advantages: Real-time dynamic estimation, Does not require taking generator offline, Accurate two-state four-parameter estimation, Reduces computing cost. Various examples are provided extended Kalman filtering estimators for generators. In one example, among others an extended Kalman filtering estimator includes a dynamics estimator configured to calculate an estimated variable such as an estimated dynamic state or an estimated parameter of a generator, a geometry estimator configured to estimate generator values, and a Kalman filter component configured to determine a correction to the estimated state variable.The inventors have designed a new method that makes parameter and state estimation of a synchronous generator simple. The application can perform real-time dynamic estimation for subsystems. This application can perform on-line estimation, hence does not require decommitting the generator and provides accurate operational-state readings. The model can estimate the state and parameter related to electromechanical dynamics. It gives reasonable estimation for two-state four-parameter estimation and has a limited capability to handle the two-state five-parameter estimation. Relay manufacturers can incorporate this model into their measurement devices for synchronophasor measurements.