Mixed-norm Adaptive Algorithm Research Articles

Coordinated control of parallel operated renewable‐energy‐based DG systems

This study proposes a coordinated control algorithm for two parallel-operated distributed generation (DG) systems fed from different renewable energy sources. The control algorithm ensures accurate control of reference active power generation from the inverters in the DG systems. In addition to reference power generation, the control algorithm also offers compensation of harmonics and reactive currents of the local loads by utilising the remaining capacities of the inverters in the DG systems. For this purpose, the control algorithm estimates compensating factors for each inverter based on the distributed harmonic and reactive currents. The inverter with a higher surplus capacity contributes to higher compensation and vice versa. The harmonic and reactive currents of the load are extracted using least mean mixed-norm adaptive algorithm for effective compensation. Furthermore, the control algorithm automatically switches to low-voltage ride through (LVRT) on sensing the grid faults. During LVRT, the active power generation by the inverters in DG systems is reduced and reactive currents are injected to support the grid recovery. The proposed control scheme is thoroughly investigated using computer simulations and hardware-in-the-loop-based experiments to show its feasibility and effectiveness.

A Normalized Robust Mixed-Norm Adaptive Algorithm for System Identification

A normalized robust mixed-norm (NRMN) algorithm for system identification in the presence of impulsive noise is introduced. The standard robust mixed-norm (RMN) algorithm exhibits slow convergence, requires a stationary operating environment, and employs a constant step-size that needs to be determined a priori. To overcome these limitations, the proposed NRMN algorithm introduces a time-varying learning rate and, thus, no longer requires a stationary environment, a major drawback of the RMN algorithm. The proposed NRMN exhibits increased convergence rate and substantially reduces the steady-state coefficient error, as compared to the least mean square (LMS), normalized LMS (NLMS), least absolute deviation (LAD), and RMN algorithm.

Variable Weight Mixed-Norm Adaptive Algorithm

In this work, the convergence analysis of the variable weight mixed-norm least-mean squares (LMS)-least mean-fourth (LMF) adaptive algorithm is derived. The proposed algorithm minimizes an objective function defined as a weighted sum of the LMS and LMF cost functions, where the weighting factor is time varying and adapts itself to allow the algorithm to keep track of the variations in the environment. As a by-product of this novel approach, new necessary and sufficient conditions for the LMF algorithm have been derived. Furthermore, a more general expression for the excess steady-state error for the LMF algorithm has been derived.

Convergence and steady-state properties of the least-mean mixed-norm (LMMN) adaptive algorithm

Convergence and steady-state analyses of a least-mean mixed-norm adaptive algorithm are presented. This is formed as a convex mixture of the mean-square and the mean-fourth cost functions. The local exponential stability of the algorithm is shown by application of the deterministic averaging analysis and the total stability theorem. A theoretical misadjustment expression is then obtained by using the ordinary-differential-equation method. Simulation studies are presented to support the theoretical findings. The results demonstrate the advantage of mixing error norms in adaptive filtering when the measurement noise is composed of a linear combination of long-tail and short-tail noise distributions.