Nonlinear Stability Analysis of the Conventional SRF-PLL and Enhanced SRF-EPLL

Abstract

Phase-locked loop (PLL) systems play a crucial role in grid synchronization. Since variations on the grid voltage parameters are in general uncertain, the dynamics of PLLs are by nature nonlinear. This fact imposes a relevant challenge to guarantee their stability. Unfortunately, as argued in this paper, there is a remarkable lack of global stability tests even for the most common approaches, such as the synchronous reference frame (SRF). In this case, there is only available a small-signal-linearized-modelbased approach to stability. The main issue of resorting to local conclusions is that synchronization is forced to operate under conservative conditions, where large-signal variations are forbidden. Needless to say, this has a detrimental impact on applications, since performance is limited by small disturbance assumptions. Motivated by this problem, in the present work, we provide global asymptotic stability tests for two fundamental PLL algorithms. Namely, the conventional SRF-PLL and the enhanced SRF-EPLL. To do so, we use a Lyapunov approach acting directly on nonlinear trajectories. Consequently, the provided stability proofs do not rely on any linearization technique, frequency-domain conversion, or small-signal model representation. The main contribution in this paper is a set of stability conditions that are valid in a global sense. Moreover, it is shown that these results have direct practical implications in the form of new robust PLL gain tuning guidelines.

Nonlinear Analysis of the Synchronous Reference Frame Phase-Locked Loop Under Unbalanced Grid Voltage

“…This does not change the system's orbits and, therefore, does not affect the comparison systems. The statement (15) then follows from (11).…”

“…defined by (11) are called, respectively, the left and right autonomous comparison systems for (10). Remark 6.…”

“…For large angles, SRF-PLL stability has been proven only under balanced conditions using the Lyapunov function method [11]. Extension of the nonlinear analysis to the unbalanced case is not easy for the reason that the nonlinear PLL equations affected by voltage unbalance are similar to those of a periodically forced nonlinear pendulum.…”

Voltage and frequency stabilization by fuzzy integrated droop control of a multi renewable source micro grid

“…The 3-ph inverter is either operated with SRF or droop control as per the grid available condition. The 3-ph inverter controller selection is done by islanding detection unit [4]- [6] which identifies the utility grid connection to the renewable micro-grid. The powers of the four renewable modules are utilized as per load demand and grid connection conditions.…”

An Optimized Enhanced Phase Locked Loop Controller for a Hybrid System

“…Reference [28] suggests a linear active disturbance rejection control-based nonlinear PLL which improves the filtering capacity and the dynamic response during synchronization. A stability analysis based on Lyapunov's approach was conducted in Reference [29] and it was concluded that SRF-EPLL is asymptotically stable when the gain values are positive. A new synchronization method called decoupling network αβ frame PLL design is suggested in Reference [30].…”