Design and Tuning of the Super-Twisting-Based Synchronous Reference Frame Phase-Locked-Loop

The worldwide transition to climate-friendly energy systems entails the substitution of conventional energy generation based on synchronous generators by renewable energy sources based on power electronics. As a consequence, the overall inertia of the grid decreases, resulting in high volatility of the frequency and posing new challenges for the estimation of the latter quantity. To address this problematic, in the present paper a phase-locked-loop (PLL) based on the super-twisting algorithm is considered for the estimation of the phase angle and time-varying frequency of a symmetric three-phase signal. A rigorous proof of the algorithm’s exact convergence in the presence of a fast-varying frequency together with tuning rules for its gains are derived by means of Lyapunov theory. Additionally, an estimate of the region of attraction is provided. The effectiveness of the proposed tuning method is illustrated in numerical simulations, while comparing its performance against a standard synchronous reference frame PLL.