Evaluation of Quadrature Signal Generation Methods with Reduced Computational Resources for Grid Synchronization of Single-Phase Power Converters through Phase-Locked Loops

Abstract

Low-cost single-phase grid connected converters require synchronization with the grid voltage to obtain a better response and protection under diverse conditions, such as frequency perturbations and distortion. Phase-locked loops (PLLs) have been used in this scenario. This paper describes a set of quadrature signal generators for single-phase PLLs; compares the performances by means of simulation tests considering diverse operation conditions of the electrical grid; proposes strategies to reduce the computational burden, considering fixed-point digital implementations; and provides both descriptive and quantitative comparisons of the required mathematical operations and memory units for implementation of the analyzed single-phase PLLs.

A Single-Phase Globally Stable Frequency-Locked Loop Based on the Second-Order Harmonic Oscillator Model

“…The proposed SOHO-based FLL comprises a copy of system (5) with an additional damping term, which is referred to as the SOHO-based quadrature signal generator (SOHO-QSG). The SOHO-QSG, represented by subsystem (11) and (12), is an oscillator aimed to follow the response of the SOHO (5) by forcingv α to follow v α . The proposed SOHObased FLL is enhanced with an adaptive law (13) to reconstructω 0 , which is referred to as the fundamental frequency estimator (FFE).…”

“…This section shows that the estimatesv α ,v β andω converge towards their corresponding references v α , v β and ω 0 with guaranteed stability. The study is based on the transformation of subsystem (11) and (12), originally expressed in terms of virtual αβ-coordinateŝ v α andv β , to its representation in terms of the equivalent synchronous-reference frame coordinates, i.e., in terms of the corresponding dq-coordinates. For this, the Park transformation above described (10) and its inverse (8) are considered.…”

“…The design of the estimator for the nth harmonic component is based on the structure of the SOHO-based FLL, i.e., copies of the SOHOs of the generator model of the periodic signal. In particular, the first two Equations (11) and (12), representing the SOHO, are modified and tuned for the nth harmonic ofω 0 , i.e., it is proposed to estimate the nth harmonic component as follows:…”

“…Hence, these schemes were also referred to as the VCO-less representation of the PLL. Furthermore, in the FLL case, the fundamental frequency is directly estimated and the operation is based on such an estimate, while the operation in the PLL is based on the estimation of the phase angle [6,10,11]. Both types of schemes have been thoroughly explored; in some schemes, such a difference is not very clear, and thus, the name PLL and FLL has been used indistinctly.…”

SOGI-PLL Aprimorado por Algoritmo de Fourier de um Ciclo

“…Embora essa estrutura tenha uma demanda mínima de recursos aplicando uma constante ω 0 =ω, a mesma é muito sensível às oscilações de frequência do PLL devido ao detector de fase e ao filtro passa-baixa utilizados. [27]. Este PLL tira vantagem do bom desempenho do PLL de quadro de referência síncrono (SRF-PLL) que originalmente opera com as tensões trifásicas da rede.…”