State Space Least Mean Fourth Algorithm for Dynamic State Estimation in Power Systems

Abstract

Power system dynamic state estimation (DSE) has always been a critical problem in studying power systems. One of the essential parts of power systems are synchronous machines. In this work, we dealt with the problem of DSE of a synchronous machine by introducing a novel state space-based least mean fourth (SSLMF) algorithm. The rationale behind the proposed algorithm is the fact that a power system may encounter non-Gaussian disturbances/state errors and the least mean fourth algorithm is proven to be better in such environments. Moreover, we have also introduced a normalized version of the proposed algorithm, namely state space normalized least mean fourth (SSNLMF) algorithm to deal with the stability issue under Gaussian disturbances. Another motivation for developing the SSLMF algorithm is its simplicity as compared to other model-based nonlinear filtering algorithms such as Kalman filter, extended Kalman filter (EKF). Moreover, we also investigate the performance of the recently introduced state space least mean square (SSLMS). Performance of the SSLMF and the SSLMS is compared with existing EKF in both Gaussian and non-Gaussian noise environments. Extensive simulation results are presented which show superiority B Muhammad Moinuddin of the proposed algorithms, and hence, it verifies our rationale behind the work.

Least mean square fourth based microgrid state estimation algorithm using the internet of things technology

“…According to the steepest decent approach, the state updated rule is given by [ 2 , 3 , 24 ]: Here, is the predicted states, is the previous estimated states, μ is the scalar step size parameter, J ( k ) is the objective function to be minimized and Δ J ( k ) is the gradient decent. The cost function is defined by [ 2 , 3 ]: Here, e n ( k ) is the n-th error function, which is defined as follows: Here, and H n is the n-th row of the observation matrix.…”

“…According to the steepest decent approach, the state updated rule is given by [ 2 , 3 , 24 ]: Here, is the predicted states, is the previous estimated states, μ is the scalar step size parameter, J ( k ) is the objective function to be minimized and Δ J ( k ) is the gradient decent. The cost function is defined by [ 2 , 3 ]: Here, e n ( k ) is the n-th error function, which is defined as follows: Here, and H n is the n-th row of the observation matrix. The minimization of the cost function with respect to the predicted states lead to the following expression: From Eq (16) and Eq (19) , the update state estimation is expressed by [ 2 , 3 ]: Here, K is the user defined matrix, which depends on the specific application [ 2 , 3 ].…”

“…The cost function is defined by [ 2 , 3 ]: Here, e n ( k ) is the n-th error function, which is defined as follows: Here, and H n is the n-th row of the observation matrix. The minimization of the cost function with respect to the predicted states lead to the following expression: From Eq (16) and Eq (19) , the update state estimation is expressed by [ 2 , 3 ]: Here, K is the user defined matrix, which depends on the specific application [ 2 , 3 ]. In order to obtain the consistent estimation performance, the following normalization version is proposed: Here, ϵ is the small positive value to avoid division by zero [ 25 ].…”

“…Extensive investigations on power system state estimations have been carried out in the literature. To begin with, the least mean squares (LMS) based power system dynamic state estimation is explored in [ 2 , 3 ]. Unfortunately, it is very difficult to tune the step size parameter of this LMS scheme.…”

“…Unfortunately, it is very difficult to tune the step size parameter of this LMS scheme. The normalized LMS (NLMS) algorithm is proposed for state estimations [ 2 , 4 ]. This NLMS process normalises the input signal so that the step size parameter can guarantee the stability of this algorithm.…”