# Enhanced Quasi Type-1 PLL-Based Multi-Functional Control of Single-Phase Dynamic Voltage Restorer
###### Abstract
This can make the overall system computationally complex. It is to be noted here that the conventional SRF-PLL can be made robust to harmonics and DC offset by considering a slow loop-filter, i.e., by reducing the bandwidth. This has been considered in [17]. Although this is an interesting practical solution, this strategy is suitable for voltage compensation but not harmonics. Self-tuning filter (STF) is similar to SOGI; however, in the case of STF, the error feedback is independent of the grid frequency. In [18; 19], the authors have applied STF as the reference generator without considering frequency adaptation. As such, the reference generator in [18; 19] can be limiting when the grid frequency varies significantly. Quarter-delay is another popular method for generating orthogonal signal. This approach is considered in [20]. However, in off-nominal frequency condition, the required delay would be fractional which increases computational complexity. In [21], an adaptive notch filter (ANF) is used as the reference generator. However, the considered ANF did not use gain normalization. This can make the convergence time slow in the presence of voltage sag. Based on the literature review, it is clear that there is demand for a reference generator that is robust to harmonics and DC offset while at the same time is computationally simple to implement. For this purpose, in this study, a quasi type-1 PLL [22; 23; 24] is considered. This PLL has been selected for several reasons. Firstly, it can provide amplitude normalization without using any low-pass filter unlike conventional SRF-PLL, cf. [25]. Use of additional low-pass filter in the amplitude normalization block will introduce tuning complexity as there is one more gain to tune. Secondly, this PLL provides good harmonic robustness thanks to the use of a moving-average filter. Finally, it has only one gain to tune unlike SRF-PLL where the loop-filter has two tuning parameters. However, this PLL can work only for three-phase system. Thus, a single-phase version of this PLL is proposed in this study. For this purpose, first, a half-cycle delayed signal cancellation method is applied to reject the DC offset. Then, a frequency-fixed all-pass filter (APF) [26] is applied to generate the orthogonal signal. However, single-stage APFs will generate double frequency oscillations in off-nominal frequency conditions. As such, a two-stage APF is considered that can eliminate the double frequency error. The APF is selected in this study as it can generate orthogonal signals without using any tuning gain unlike other choices available in the literature such as SOGI [16; 27], ANF [21], etc. This is beneficial from the tuning simplicity point of view. Finally, the filtered grid voltage signal and its orthogonal component are used as the inputs to the quasi type-1 PLL. A small-signal model of the proposed PLL is developed and validated. Finally, tuning of the PLL gain is also presented. Compared to conventional PLL techniques summarized in [28], our approach is very simple to tune as it has only one tuning gain. All the techniques summarized in [28] have at least three parameters to tune if amplitude normalization is considered. Unlike most of the techniques in [28], our quadrature signal generator is frequency non-adaptive. As such, there is no frequency feedback which may be beneficial from the stability point of view. Once the reference signal is generated, the role of control system is to follow/track the reference. In the literature, synchronous frame approach in the form of proportional-integral (PI) controllers [29] are widely used. Although this controller can be easily designed and implemented, the dynamic response can be slow. In order to enhance dynamic performance, advanced controllers such as model predictive control (MPC) [7; 8], \(\mathcal{H}_{\infty}\)[30], and sliding mode control (SMC) [31; 32; 33] are proposed in the literature. MPC can be sensitive to model parameters mismatch. Computational complexity can be an issue for \(\mathcal{H}_{\infty}\) controllers.