###### Abstract  
The modern power system is progressing from a synchronous machine-based system towards an inverter-dominated system, with large-scale penetration of renewable energy sources (RESs) like wind and photovoltaics. RES units today represent a major share of the generation, and the traditional approach of integrating them as grid following units can lead to frequency instability. Many researchers have pointed towards using inverters with virtual inertia control algorithms so that they appear as synchronous generators to the grid, maintaining and enhancing system stability. This paper presents a literature review of the current state-of-the-art of virtual inertia implementation techniques, and explores potential research directions and challenges. The major virtual inertia topologies are compared and classified. Through literature review and simulations of some selected topologies it has been shown that similar inertial response can be achieved by relating the parameters of these topologies through time constants and inertia constants, although the exact frequency dynamics may vary slightly. The suitability of a topology depends on system control architecture and desired level of detail in replication of the dynamics of synchronous generators. A discussion on the challenges and research directions points out several research needs, especially for systems level integration of virtual inertia systems. frequency stability; microgrid control; renewable energy; virtual inertia +
Footnote †: journal: Applied Physics Letters  
_Applied Physics Letters_  
Recent reports and studies have shown frequency stability to be a matter of significant concern due to lack of inertial response from RESs. The independent system operator, Electricity Reliability Council of Texas (ERCOT) has reported a continuous decline in the inertial response of its system and recommends additional inertial response [7,8]. Figure 2 illustrates the change in frequency in the ERCOT interconnection for two time periods for the same amount of generation loss. The change in frequency per generation loss is increasing yearly, and this trend is highly correlated with increased RES penetration over the same time-period. Similarly, the European Network of Transmission System Operators for Electricity (ENTSO-E) has reported increased frequency violations in the Nordic grid correlated with increased RES penetration [9]. As a consequence, inertial response from wind turbines is now mandatory in many countries [10,11] and the trend is extending towards PV plants as well. Accordingly, there is a strong practical relevance to research on virtual inertia systems which was of an academic nature in the past. In order to maintain the power generation and load balance, various control actions are implemented in a power system over multiple time-frames as illustrated in Figure 3. The governor response is the primary control action which takes place within the first few seconds (typically 10-30 s) of a frequency event and aims at reducing the frequency deviation. The automatic generation control is the secondary control action which takes place within minutes (typically 10-30 min) and restores the system frequency back to the nominal value. The tertiary control action is the reserve deployment when actions are taken to get the resources in place to handle present or future disturbances in the system. Whenever there is an imbalance between the generation and consumption in a power system, the generators cannot respond instantaneously to balance the system. The kinetic energy stored in the rotors is responsible for counteracting this imbalance through inertial response until the primary  
Figure 1: Evolution towards an inverter dominated power system. Figure 2: Increase in frequency changes in Electricity Reliability Council of Texas (ERCOT) connection due to generation loss [7]. frequency control has been activated. As conventional generators are displaced by RESs, the inertial response also decreases.