Hedge-Algebra-Based Phase-Locked Loop for Distorted Utility Conditions

Abstract

This paper presents the first application of the hedge-algebra theory in the field of grid synchronization. For this purpose, an optimized hedge-algebra controller (HAC) is developed and incorporated within the three-phase phase-locked loop (PLL) with moving average filters (MAFs) inside its feedback loop. Optimized fuzziness parameters and linguistic rule base of the HAC are obtained by a genetic algorithm using the integral of absolute error as the performance index during optimization. Calculated optimal parameter values of the HAC depend on the most frequently occurring disturbance in the electric grid. Two different PLL structures are proposed, depending on the types of disturbances occurring in the electric grid. The first structure is the conventional synchronous reference frame PLL with the nonadaptive MAF (i.e., MAF without order adjustment), but with the PI/PID controller in the phase loop replaced by the developed HAC. Such PLL structure is suitable for all analyzed disturbance types, expect for step-changes in the grid frequency. The second PLL structure introduces the adaptive MAF (i.e., MAF with order adjustment) and a new feedback signal in the output stage of the controller to achieve zero steady-state error in the case of step-changes in the grid frequency. The disturbance rejection capability of the two developed PLLs with the HAC (HAC-PLLs) is tested separately and compared experimentally with the PID- and fuzzy-controller-based PLLs.

Information and Mathematical Structures Contained in the Natural Language Word Domains and Their Applications

“…The results and analysis obtained above, and the results achieved in [15,16,17,18,19,20,21,22,23,25,26,27,28,29,30], most published in international journals ISI indexed, justify the meaning of discovering L-variables' word domain semantic structures and their quantification in problem-solving control.…”

“…The HA-methodology was applied first in the study [15], which proposes an HA-based method to design an optimized controller to solve an inverted pendulum control problem. It motivated many studies to develop HA-based controllers for controlling active vibration control of uncertain structures against earthquake [17,18,19,20,21,22,23], a self-excited induction generator [24], a grid synchronization [25], and the speed in a Stand-Alone WECS [26,27], and in solving control problems in the industry [28,29,30]. In the framework of this section, we summarize only some of these studies…”

“…, a n ) ∈ [0, 1] n . In general, there is a wide selection of such methods, including linear interpolation-exploration methods, e.g., bilinear interpolation-exploration-based methods [17,18,19,20,23,24], explicit linear formulas [21,22], or non-linear ones whose ideas are described as follows, when A falls in an n-cube, one can develop methods reasoning based on a weighted sum of the f Y -values at the n-cube's vertices [25,27]. Especially, these interpolation-exploration methods can preserve the monotonicity of their LRB.…”

“…These achieved theoretical results sufficiently form a necessary formalized basis for solving application problems in different fields. One can find its applications in cybernetics [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30], in classification and regression [31,32,33], decision making [38,39], multi-channel image processing [37], robotics [45,46,47,48,49], networking [43,44], fuzzy linguistic time series [40,41,42], linguistic data summaries [35,36], databases and object-oriented databases based on hedge algebraic semantic [58,59,60], and it is not the end.…”

A Non-Adaptive Single-Phase PLL Based on Discrete Half-Band Filtering to Suppress Severe Frequency Disturbances

“…For instance, Zarei and Karimadini [25] propose adding "initial phase-angle detectors" and adaptive MAFs, pursuing dynamic enhancements. Similarly, Vukadinović, et al [26] propose a PLL based on Hedge-Algebra-involving Fuzzy Logic-for which its tuning parameters are adjusted through an evolutionary algorithm, depending on the expected disturbance. In this case, resistance to the harmonic content is not even tested.…”