A phase tracking system for three phase utility interface inverters

Abstract

The analysis and design of the phase-locked loop (PLL) system is presented for the phase tracking system of the three phase utility interface inverters. The dynamic behavior of the closed loop PLL system is investigated in both continuous and discrete-time domains, and the optimization method is considered for the second order PLL system. In particular, the performance of the three phase PLL system is analyzed in the distorted utility conditions such as the phase unbalancing, harmonics, and offset caused by the nonlinear load conditions and measurement errors. The tracking errors under these distorted utility conditions are also derived. The phase tracking system is implemented in a digital manner using a digital signal processor (DSP) to verify the analytic results. The design considerations for the phase tracking system are deduced from the analytic and experimental results.Index Terms-Phase-locked loop, utility interface.

Second-order autoregressive model-based Kalman filter for the estimation of a slow fading channel described by the Clarke model: Optimal tuning and interpretation

“…(vi) (2πf AR(2) T ) 2 σu σw it will be seen afterwards, at the end of this section (through (29), also (34)), that this means that the Kalman filter is sufficiently fast compared to the fading process.…”

“…Recently, an alternative model, the random walk (RW) model, with a minimum asymptotic variance (MAV) criterion, has been employed for KF channel estimation [33,34]. The RW model is also a Gauss-Markov model (when p = 1, or an integrated version if p > 1) but unlike the AR(p) model, the RW(p) model is not stationary: it has a variance that grows to infinity with the number of iterations, and it is why it is most often used for the (modulo-2π) phase estimation problem.…”

“…These parameters are indeed the most used to tune second order filters, in the case of continuous-time systems [43,34]. The following notation will be used in the following sections: ω AR(2) = 2πf AR (2) and ω n,AR(2) = 2πf n,AR (2) .…”

Analysis of the Converter Synchronizing Method for the Contribution of Battery Energy Storage Systems to Inertia Emulation

“…The PLL parameters were selected according to the natural frequency ω n and damping ξ of the resulting second-order closed-loop transfer function. The PLL bandwidth was selected based on a compromise between the synchronization speed and filtering characteristics, as proposed in Chung [40], while the damping coefficient ensured a compromise between the synchronization speed and damping. The current controllers' PI gains depended on the MG characteristics in accordance with the zero-pole cancellation method proposed in Amirnaser and Reza [4].…”

Implementação de controladores para conversores trifásicos, sem transformações de coordenadas: análise geométrica através de vetores espaciais.

“…São usualmente denominados de SRF-PLL (Synchronous Reference Frame -PLL), como em (Kaura,1997) e (Chung, 2000). Entre as diversas denominações citam-se: dq-PLL, por (Lee, et al, 1999), , , (Kim, et al, 2008); Software PLL (SPLL) por (Zhan, et al, 2001), (Zhu, et al, 2004), (Awad, et al, 2005), (Bueno, et al, 2005), (Muyulema, et al, 2007); Auto adjustable SRF-PLL (ASRF-PLL) por (Milanes-…”