Influence of phase-locked loop on input admittance of three-phase voltage-source converters

A regulated power converter can cause instability issues at its terminals with its input filter or the source. The Generalized Nyquist stability Criterion (GNC), when applied to the product of the source impedance and load admittance in the dq frame, can be used to analyze the stability of balanced three-phase ac systems. This paper presents the influence of the Phase-Locked Loop (PLL) on the input admittance of three-phase Voltage-Source Converters (VSC) for open loop, current-feedback and voltage feedback control conditions. Analytical results show that the PLL introduces a parallel admittance to the open loop admittance of the VSC, and that the current and voltage control loop have additional effects on it. Both simulation and experimental results are presented to verify this analysis. The possible instability due to different PLL design is also shown.

I. Introduction

Controlled power electronic converters are constant power loads that feature negative small-signal input impedance. The increase of constant power loads in a system can hence produce small-signal oscillations and even instability. For three-phase balanced ac systems, the Generalized Nyquist stability Criterion (GNC)[1] [2], which uses the source impedance and load admittance in the dq frame to predict stability at ac interface[3] [4] [5], is an effective method. When the source impedance is the same, changing of load admittance can potentially cause instability. This paper studies the impact of the Phase-Locked Loop (PLL) on the input admittance of three-phase Voltage-Source Converters (VSC). These converters are widely used as grid-tied inverters or active front end for motor drives. The impedance shaping of three-phase, grid-tied VSCs including PLL and current feedback control has been presented in [6], but the impedance was defined in the phase domain, and the paper is not focusing on PLL. Two dq domains, namely the converter and system domains were used in [7] to analyze the impact of the PLL on the input admittance of VSCs. This paper borrows this concept, expanding it to show that the PLL acts as bridge, through which, small-signal perturbations in the system voltage propagate to the duty ratio in both the system and converter domains as shown in Fig. 1, which has not been discussed in [7]. This effect further influences the VSC input admittance. Analytical results show that the PLL introduces a parallel admittance to the open loop admittance of the VSC, and when current and voltage feedback control are applied, they have additional effects on it. Experimental results are presented to verify the analysis. Changing of load converter input admittance could potentially cause instability issue as shown in [3]. This paper also shows an instable case caused by increasing PLL bandwidth with certain source. By applying GNC to the source impedance and load admittance, the instability can be predicted. Fig. 1. Influence of PLL on VSC input admittance