Performance of DVR Using Diffusion Norm Penalized LMS Fourth Adaption Algorithm With Optimized FOPID Gains

This paper deals with the integrated control scheme of adapt then combine (ATC) diffusion penalized least mean square fourth (DPLMSF) algorithm and optimized fractional order proportional integral derivative (FOPID). The estimation of the fundamental component (FC) from the non-ideal input voltage is extracted by the proposed ATC-DPLMSF algorithm, which employs a penalized L
$_{\mathrm{p}}$
norm in the cost function that minimizes the error utilizing the mean-fourth error of a diffusion strategy. This enhances the control scheme performance by reducing the error rate with increased convergence rate. The key contribution of the proposed approaches is adaptiveness of mixed step-size selection based on hybrid LMSF algorithm and reduced overshoot and undershoot oscillation in a dc link and ac link with optimized FOPID. These features enable accurate and fast estimation of fundamental component at abnormal grid condition. To address the error minimization, integral time square error (ITSE) is employed as a cost function by utilizing the features of the self-adaptive population (SAP)-Rao algorithm. The SAP-Rao has an inbuilt feature of self-adjusting the control parameters, which avoids local entrapment. The recommended control algorithm enhances performance of three single phases VSC-based DVR using the d-SPACE board.
Note to Practitioners
—In contrast to the traditional adaptive least mean square (LMS) algorithm, that employs exclusively mean square error (MSE) as a function of cost based on second order power error, this paper examines the efficacy of combined Least Mean Square/Fourth (LMS/LMF). This restricts the ability to separate the fundamental data from the noise and causes performance reduction in some dynamic situations. In order to solve this issue, a mixed norm-based step size adaptive algorithm is developed and used to estimate the basic components from the voltage of the contaminated grid. By utilising mixed LMS and LMF to enhance the error convergence quality of a filter, the proposed method’s convergence speed rate can be enhanced. Second, optimised fractional order proportional integral derivative (FOPID) acquires control voltage. Secondly, voltage regulation is performed by optimized fractional order proportional integral derivative (FOPID) gains, which can rapidly identify voltage anomalies and stabilize the voltage error with two additional “tuning gains” which provides more tuning freedom. This self-tuned FOPID controller can obtain a precise voltage regulation and with respect to industrial use the FOPID controllers has the immense benefit of improving the transitory response time over conventional PID/PI controllers in terms of fast settle time (T
$_{\mathrm{s}})$
, lesser peak time (T
$_{\mathrm{p}})$
, and less maximum overshoot (M
$_{\mathrm{p}}$
%). The performance can be assessed by using ITSE as an objective function. Experimental and simulations results, confirms the superior and dominance performance of the pproposed control scheme weighted diffusion LMS/F and fractional order PID controller which increases its implementation and interests of the industry.