# Modelling, Analysis and Performance of a Low Inertia AC-DC Microgrid
###### Abstract  
In a world where the energy crisis is becoming overwhelming, demand for integrating renewable energy sources is increasing and forming microgrids is becoming an essential solution. The new microgrid systems, which depend mainly on renewable energy sources instead of conventional synchronous generators, come with a low inertia concern. This paper proposes a virtual inertia controller based on a high-pass filter (HPF) to support the frequency of the AC microgrid while maintaining the DC voltage of the DC microgrid within the nominal ranges in cases of contingencies. The proposed system encounters an AC-DC microgrid with a renewable energy source on the DC microgrid alongside constant power load and resistive loads, while on the AC microgrid side, a synchronous generator is used to present the low inertia of the grid with dynamic loads and static loads. The state-space linearized model of the system is developed and verified using Matlab Simulink. The dynamic response of the proposed controller is compared to the low-pass filter (LPF)-based controller. Moreover, the effect of changing the system's parameters on eigenvalues is investigated. microgrids; induction motor; stability; dynamic loads; low inertia; frequency support; virtual inertia +
Footnote †: journal: _Applied_  
connecting the reference voltage of the DC bus to the system frequency. A new technology called Distributed Virtual inertia (DVI) was implemented in [7]; this technology aims to increase the inertia of the future power grids where many grid-connected converters would be utilized to interface the renewable energy sources. In this study, the capacitors used on the DC side of each converter are utilized as energy storage to produce virtual inertia during contingencies. This approach will reduce the cost of new installations by utilizing the installed converters. In contrast, virtual synchronous generators (VSGs) or virtual synchronous machines (VSMs) are different because they produce virtual inertia by using a control loop to mimic the behaviour of synchronous generators [10]. Recent studies of the applications and future trends of virtual synchronous generators along with fundamentals, different topologies and a detailed structure of the VSG can be found in [11, 12]. Strategies for controlling the grid-connected inverter to function as a synchronous generator are introduced in [13]. Although the synthetic virtual inertia value may be altered by adjusting the control settings, a high power rating of the power converter and extra energy storage units are required. However, the possibility of inconsistency in the input and output power of the converters under VSG control is a concern. Because power converters cannot handle power imbalances like synchronous generators by absorbing or delivering the required kinetic energy, an energy storage device such as batteries is always necessary to provide power control in VSG. However, it was assumed that the VSG has no limitations over the power that can be given or absorbed, which needs more experimental studies to be proven. The energy storage systems must be adequately designed in accordance with the VSG to produce the desired inertial response, which will result in system complexity [14]. The value of DC link capacitances would limit the virtual inertia of the VSGs if no energy storage systems were used. Battery Energy Storage Systems (BESSs) can be used to support the frequency while the grid frequency fluctuates. The battery will often oscillate between charging and discharging status, resulting in a decreased lifespan and system efficiency. This becomes the most significant disadvantage of utilizing BESSs alone [15]. However, new studies proposed new technologies that offer accurate monitoring of the state of health of lithium-ion batteries, allowing energy storage systems to play an essential role in the inertial support [16].