Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

MMSE-based analytical estimator for uncertain power system with limited number of measurements



Hamid Gharavi, Hasnae Bilil


The expected penetration of a large number of renewable distributed energy resources (DER’s) is driving next generation power systems toward uncertainties that can have a huge impact on the reliability and complexities of state estimation. Therefore, the stochastic power flow (SPF) and forecasting-aided state estimation of power systems integrating DER’s are becoming a major challenge for operation of the future grid. In this paper we propose a new state estimation method referred to as ‘mean squared estimator’ (MSE) to deal with the uncertain nature of the power system parameters. The estimator benefits from the prior study of SPF, which involves the probability density functions (PDF’s) of the system parameters. The main advantage of this estimator is based on its ability to instantaneously incorporate the dynamics of the power system. Moreover, the analytical formula of MSE expresses the mean value of the estimated parameters corrected by an additional term that takes into account the measurement of the parameters. It is shown that the proposed MSE can provide an accurate state estimation with a limited number of measurements with guaranteed convergence. MSE has been tested using IEEE 14, 30, 39 and 118 bus models for different measurement redundancies. The results have been compared to methods such as weighted least square (WLS), unscented Kalman filter (UKF) and compressive sensing-based UKF (CS-UKF). The numerical results show superior performances, especially under a limited number of measurements where WLS and UKF may lead to divergence
IEEE Transactions on Power Systems
Early Access


Dynamic state estimation, minimum mean squared error, Gaussian mixture model, analytic estimator, limited number of measurements


Gharavi, H. and Bilil, H. (2018), MMSE-based analytical estimator for uncertain power system with limited number of measurements, IEEE Transactions on Power Systems, [online], (Accessed May 20, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created February 2, 2018, Updated January 27, 2020