Least Mean Mixed Norm Square/Fourth Adaptive Algorithm With Optimized FOPID Gains for Voltage Power Quality Mitigation

The conventional adaptive least mean square (LMS) algorithm employs mean square error (mse) as a cost function based on second-order power error. This limits the extraction of fundamental signals from the noise and suffers from performance degradation in certain dynamic scenarios. The proposed approach addresses this problem with a mixed norm-based step size adaptive algorithm, which is devised from the second- and fourth-order error optimizations. The proposed mixed-norm constraint-based improved proportionate normalized LMS fourth (MNC-IPNLMS/F) control strategy extracts the fundamental weight quantity from the polluted grid voltage and generates the reference load voltage. This method exploits the enhancement of dynamic voltage restorer (DVR) performance in terms of convergence and stability. The dc- and ac-link voltages are regulated by a fractional-order proportional–integral–derivative (FOPID) controller. The coefficients of FOPID are self-tuned by several optimizations, namely, the JAYA algorithm, accelerated particle swarm optimization (APSO), and biogeography-based optimization (BBO). This reduces manual tuning and computational complexity. The major improvements of the proposed approach are less overshoot (6.6%), undershoot (3.3%), and fast settling time (0.14 s). The comparative study reveals that the FOPID control based on JAYA optimization (JO) outperforms the others. The efficacy of the MNC-IPNLMS/F is investigated through the performance results.