Augmented Complex Least Lncosh Algorithm for Adaptive Frequency Estimation

In this brief, an augmented complex least mean lncosh (ACLlncosh) algorithm is proposed to estimate the frequency of the three-phase unbalanced power system in impulsive noise environment. By introducing the Clarke’s
$\mathrm {\alpha {\beta }}$
transformation and widely linear (WL) model into the Llncosh cost function, and using CR Calculus, the ACLlncosh algorithm is derived. Moreover, a variable parameter method is proposed to improve the performance of ACLlncosh. The mean and mean-square stability of the proposed ACLlncosh algorithm are analyzed, and the corresponding stable step size ranges are also given. Computer simulations under some typical power system operating situations verify the superiority of the proposed ACLlncosh algorithm than the complex least mean lncosh (CLlncosh) and augmented complex least mean square (ACLMS) algorithms in power system frequency estimation.