  For the first time quaternions have been used for real-time frequency
estimation, where the multi-dimensional nature of quaternions allows for the
full characterization of three-phase power systems. This is achieved through
the use of quaternions to provide a unified framework for incorporating voltage
measurements from all the phases of a three-phase system and then employing the
recently introduced HR-calculus to derive a state space estimator based on the
quaternion extended Kalman filter (QEKF). The components of the state space
vector are designed such that they can be deployed for adaptive estimation of
the system phasors. Finally, the proposed algorithm is validated through
simulations using both synthetic and real-world data, which indicate that the
developed quaternion frequency estimator can outperform its complex-valued
counterparts.

Systems and Control;Applications