1949-3029 (c) 2018 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TSTE.2019.2892670, IEEE Transactions on Sustainable Energy 1 Impedance Analysis of Virtual Synchronous Generator-Based Vector Controlled Converters for Weak AC Grid Integration Arash Asrari, Member, IEEE, Mehran Mustafa, Meisam Ansari, and Javad Khazaei, Member, IEEE. Abstract—Voltage source converter (VSC)-based high voltage direct current (HVDC) system is an emerging technology in high power applications. Previous research has shown that VSCs, with commonly used vector current control (VCC) technique, cannot transmit more than 0.4 p.u. of active power when connected to a very weak ac grid. This paper presents a virtual synchronous generator (VSG) control strategy integrated with VCC to al- low stable power transfer for very weak ac grid integration. Impedance analysis is used to analyze the designed controller in various scenarios. In addition, sensitivity analysis is performed to study the effect of virtual inertia gains on system stability. Time-domain simulation results using MATLAB/Simscape Power System toolbox show the effectiveness of the developed controller in very weak ac grid integration of VSC-HVDC systems. Index Terms—High voltage direct current (HVDC), short circuit ratio (SCR), virtual synchronous generator (VSG), voltage source converter (VSC). I. I NTRODUCTION I NTERCONNECTION of off-shore wind farms into weak ac grids via high voltage direct current (HVDC) transmis- sion systems has been a challenge in the recent years [1]. Voltage source converters (VSCs) are the most commonly used type of converters in HVDC applications. While VSCs provide noticeable advantages in HVDC systems, several studies have identified serious control problems when VSCs, equipped with the standard vector current control (VCC), are connected to a very weak ac grid. In [1]–[5], it was discovered that the converter fails to transfer 1 p.u. power when connected to very weak ac grids. This phenomenon has been studied using time-domain simulations and impedance models [6]–[9]. The main identified problem in previously discussed research is the low frequency resonance that can interact with the current controller, or the phase-locked loop (PLL) dynamics when the power converter is synchronized to weak ac grid [1], [10]– [12]. Several studies proposed new controllers for weak ac grid interconnection of VSCs [4], [13]–[16]. For example, a power synchronization control (PSC) method was introduced in [13], which used active power control loop, similar to operation of a synchronous machine, to synchronize the converter to the grid. The PSC is an effective approach in solving the stability challenges in very weak ac grids. However, since the converter current is not controlled, a back-up PLL is needed to be able to Arash Asrari, Mehran Mustafa, and Meisam Ansari are with the Department of Electrical & Computer Engineering at Southern Illinois University Carbon- dale, IL, USA and Javad Khazaei is with the School of Engineering & Tech- nology, Penn State Harrisburg, PA, USA (E-mail: arash.asrari@siu.edu). switch to the conventional VCC when a fault is experienced. Instead of completely removing PLL from the control system, an alternative solution was proposed in [15] using frequency- based synchronization control (FSC), which effectively added a frequency-based supplementary control loop in the inner control loop of VCC to damp the oscillations caused by PLL. An advanced VCC was introduced in [4] to enable transferring up to 1 p.u. in very weak ac grid conditions. Four feed-forward gains were designed for the outer control loop of the VCC and a gain-scheduling technique was used to tune the gains. In order to optimally identify the gains, H ∞ controllers were designed for each operating point of the converter associated with the individual SCRs. This methodology led to a higher complexity of the design. The idea of virtual synchronous generator (VSG) was first introduced in [17]. The motivation behind this concept is the huge influx of non-synchronous generation units in the overall ac power system, e.g., photovoltaic (PV) cells, wind turbines, etc. This causes a reduction in the total rotational inertia of the ac system [18], which can, subsequently, result in the instability of the entire power system due to the diminished frequency support. The non-synchronous systems equipped with VSG control can provide a virtual inertia to the system for short periods of time, which will enhance damping of frequency oscillations resulting from load fluctuations. The application of VSGs in power systems has been reported in the recent research [19]–[22]. For example, an improved VSG controller was proposed in [19] by linearizing and decoupling voltage deviation and damping factor in order to suppress output power oscillations. In [20], VSG was used to propose an adaptive active power and dc voltage droop control for multi- terminal HVDC (MTDC) systems. As another example, [21] provided a comparison of simple frequency droop control and VSG control using small-signal models. The VSG concept was successfully implemented in [23] for multi-terminal HVDC systems in order to propose a systematic control method that: 1) resolves the problem of low frequency oscillation and 2) enhances the power oscillation damping performance of the ac/dc system. In fact, VSGs provide numerous advantages to the power system stability in various applications. However, their application to weak ac grids has yet to be studied. The VSG-based approaches can be divided into the follow- ing two categories: 1) without current controllers [24] and 2) with current controllers [23]. The first category removes the PLL from the structure of the control, but suffers from fault ride through capability since the converter current is