Reduced-order estimation of power system harmonics using set theory

In this work, we consider state estimation of harmonic signals with time-varying magnitudes. The presence of such signals has been increasing in electric power systems due to the increased use of power electronics circuits possessing nonlinear voltage vs. current characteristics. In this work, harmonic signals are modelled using ellipsoidal set-theoretic methods and an optimal reduced-order estimator, which has one-half the dimension of the state vector, is introduced for predicting the unknown time-varying harmonic magnitudes. The optimality is in the sense of minimizing both the sum of the lengths of the principal axes and the volume of the ellipsoid for estimation error. This new estimator is compared with a full-order set-theoretic estimator in an example where each frequency component has a randomly changing magnitude.