Application of polynomial chaos expansion in electrical systems considering uncertainties: an overview

Electrical engineering systems are commonly analyzed based on deterministic mathematical models with precisely defined input data. However, since such ideal situations are rarely encountered in practice, the need to address uncertainties is now clearly recognized, probabilistic methods are considered as possible solutions. Polynomial chaos expansion (PCE) is a new and powerful modeling approach for uncertain systems considering its fast computational capabilities compared with traditional methods, such as Monte Carlo. This paper gives a brief introduction on the basic concepts of PCE, as well as its expansion process. Different applications of PCE in the field of electrical engineering, such as PCE based observer, PCE based controller, sensor validation, protection schemes, as well as the distributed state estimation, have also been briefly investigated to show the capability of PCE in simulating uncertainties.