Recently, the augmented complex least mean square (ACLMS) algorithm has been shown to be an effective frequency estimator in unbalanced three-phase power systems. Its main idea is to reformulate the three-phase voltages using a widely linear complex-valued model by Clarke’s-transformation whose parameters are updated according to least squares. Since the derivation of the ACLMS is based on the \(\ell _2\) -norm, it cannot work properly in an impulsive noise environment, which is commonly encountered in smart grids. In this paper, a generalized version of ACLMS, referred to as improved ACLMS (IACLMS) is developed to provide robust and accurate parameter estimation in the presence of heavy-tailed noise, which replaces the \(\ell _2\) -norm by the \(\ell _p\) -norm with \(1<p\le 2\) . The IACLMS is solved using the steepest descent gradient, whose updates are influenced by the step size. Therefore, a new variable step size IACLMS (VSS-IACLMS) algorithm is devised to guarantee the convergence rate and accuracy. Computer simulations demonstrate that compared to the ACLMS algorithm, the proposed IACLMS and VSS-IACLMS algorithms exhibit stronger robustness and faster convergence speed. The VSS-IACLMS is superior to IACLMS as its mean square error performance can reach the Cramér-Rao lower bound.
