Fuzzy Linear Regression Approach for Uncertainty Modeling in Power System State Estimation

`Abstract: -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. Both measurements uncertainty as well as parametric uncertainty is considered by fuzzy estimator. 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. Preliminary results from application of the proposed on regression and D.C problems are promising.