978-1-6654-5930-3/22/$31.00 ©2022 IEEE. Stochastic Eigen Analysis and Unified Control Mode for Grid-Forming and Grid-Following Inverter Based Resources Rajdip Debnath Dept. of EEE BIT Mesra Ranchi, India rajdip.mk@gmail.com Ajay Kumar Dept. of EEE BIT Mesra Ranchi, India ajaykumar.ee@bitmesra.ac.in Gauri Shanker Gupta Dept. of EEE BIT Mesra Ranchi, India gaurishankergupta@bitmesra.ac.in Innocent Kamwa Department of Electrical and Computer Engineering Laval University Quebec, Canada innocent.kamwa@gel.ulaval.ca Deepak Kumar Dept. of EEE BIT Mesra Ranchi, India deepakkumar@bitmesra.ac.in Abstract—A Grid-Forming Converter (GFMC) is a critical part for proper operation of an isolated microgrid (MG). Its aim is to generate voltage reference for rest of the inverter- based resources (IBRs) in the MG just like a traditional slack bus generator. To operate a GFMC in a d-q reference frame, single or dual loop proportional-integral (PI) controller is typically used. However, under system and grid parametric fluctuations, the above controller performs poorly. The voltage source converter (VSC) should operate for grid-tied (GT) as well as stand-alone (SA) mode to function as a grid following converter (GFLC) for power delivery to local loads where each mode has its own control loop. It should be seamless in providing an uninterruptible supply of power to the local load. Hence, for the addressable challenges, a non-linear model of both GFMC and GFLC that covers all system and grid parametric variables is devised along with stochastic eigen analysis. The suggested technique has an accurate model for the converter system which can cope with LC filter resonance and uncertainties more effectively where the need of any passive or active dampening methods is unessential. Simulations and tests were carried out to validate the suggested methodology. The simulation and experimental findings indicate that the suggested control strategy may be utilized to accomplish autonomous and smooth mode transitions even in the presence of norm-bound state uncertainty, as well as to offer resilience against grid impedance, system, and grid parameter fluctuations. Keywords— grid-forming converter, grid following converter, grid impedance variations, stochastic eigen analysis, inverter- based resources (IBRs) I. INTRODUCTION Previously, research on Grid-Tied (GT) converter controllers was concentrated on the basic operations of converters in a GFL mode, such as maximum power point tracking, harmonic correction and synchronization with the utility grid. As the number of renewable sources of energy (RSEs) in the utility grid grows, the electricity provided by them can no longer be disregarded for management of utility grid since their stochastic features might create grid instability [1]. Because of its appealing voltage source feature, the VSC, also known as the grid-forming (GFM) inverter, is currently growing interest [2, 3]. A converter must support the MG by working in both GT mode and SA mode for power delivery to local loads which is a method of creating a sustainable system [4, 5]. Its control objective varies for each mode as maintenance of VSC’s output power is necessary for the GT mode. However, in the SA mode, regulation of the output voltage is a prerequisite for the converter, and seamless transition is essential for stable operation [6, 7]. As a result, each mode has its control loop. VSC operation in weak grid conditions is unavoidable because of its high-Z (impedance) interconnections [8, 9]. It is proposed in [10] to minimize the PI gains of PLL to boost the output power delivered. On the other hand, the dynamic performance standards limit the value of PI gains. [11] proposes to add a new Z-conditional term in the PLL which helps in its virtual synchronization at a higher voltage level. Despite its advantages, this technique suffers from instability due to PLL non-linearities and is ineffective in ultra-weak grids. [12] proposes an impedance reshaping approach based on double-PLLs. However, the changes can only be applied to the outer control loops for determining the unstable states as the bandwidth of the inner CC is infinite [13, 14]. Voltage regulation of a GFMC can be improved by various traditional feedforward/feedback active damping techniques [15, 16]. The settings of the controllers used, on the other hand, are difficult to tune. In [17], an automated method to tune the PI gains for power converters is given, which is based on a linear model of the VSC, calculating the eigenvalue sensitivity matrices. However, for THD reduction and quick transient response, detailed modeling of the system is required, and the stability bandwidth is varying with switching frequency [18]. Furthermore, for both transfer function and state-space approaches, most traditional voltage controllers are primarily developed for islanded operation, and the effect of grid-z variations is seldom considered for grid-tied applications [19], [20]. When VSC is operated in grid-tied mode, the interaction stability of the GFMC is also critical [21]. As a result, the modeling employed in this study endeavor includes all the system’s nonlinearities and grid parametric fluctuations. As a result, the suggested approach can be used to analyze the grid and inverter impedance ratios to evaluate the effects of these system and grid parametric variations both in GFL and GFM mode. As a result, dynamic modeling of 3 –distribution networks with substantial renewable penetration is now possible. In this research, the proposed controller has many intrinsic qualities of providing resiliency against system and grid parametric fluctuations, fast transient response with negligible overshoot, and capacity to reject 2022 IEEE 10th Power India International Conference (PIICON) | 978-1-6654-5930-3/22/$31.00 ©2022 IEEE | DOI: 10.1109/PIICON56320.2022.10045198 Authorized licensed use limited to: IEEE Editors-in-Chief. Downloaded on February 26,2023 at 20:30:54 UTC from IEEE Xplore. Restrictions apply.