A fuzzy state estimator based on uncertain measurements

A fuzzy linear state estimation model is employed, which is based on Tanaka’s fuzzy linear regression model, for modeling uncertainty in power system state estimation. The estimation process is based on uncertainty measurements as well as uncertainty parametric. The uncertain measurements and the parameters are expressed as fuzzy numbers with a triangular membership function that has middle and spread value reflected on the estimated states. The proposed fuzzy model is formulated as a linear optimization problem, where the objective is to minimize the sum of the spread of the states, subject to double inequality constraints on each measurement. Linear programming technique is employed to obtain the middle and the symmetric spread for every state variable. The estimated middle corresponds to the value of the estimated state, while the symmetric spreads represent the tightest uncertainty interval around that estimated states. For illustrative purposes, the proposed formulation has been applied to various test systems such as, 4-bus, 6-bus, IEEE 30-bus, IEEE 39-bus, IEEE 57-bus and IEEE 118-bus. Furthermore, an assessment of the time convergence of the proposed method has been carried out to demonstrate the applicability of the proposed estimator as an on-line tool for estimating the uncertainty bounds in power system state estimation.