# Performance Tuning for Power Electronic Interfaces Under VSG Control
## 1 Introduction  
With the deficit of fossil fuels and environmental concerns, renewable power has been widely researched and utilized in recent decades [1; 2; 3]. Iceland and Norway obtain essentially all electricity from renewable sources, and other nations and regions are evolving towards 100% renewables [4]. However, renewable generation also brings great challenges. On the one hand, renewable generation is stochastic and fluctuant with meteorological conditions. The system power balance is persistently disturbed by renewable generation fluctuations. On the other hand, renewable generation (such as solar photovoltaic and wind power) is commonly integrated through power electronic interfaces (PEIs), which are with almost no inertia because of its fast and accurate switches [5]. By the increasing penetration of renewable generation, the frequency stability of the current power system deteriorates. The current power system has been through transitions in intrinsic properties, one of which is represented by the decreasing of the overall inertia. The inertia is an important indicator to evaluate the strength of the power systems because inertial response (IR) can slow down the rate of change of frequency (ROCOF) and buy time for the activation of primary frequency response (PFR) to reduce nadir/peak frequency (maximum frequency deviation) [6]. In order to tackle the loss of inertia in the inverter-based generation (IBG), the concept of the virtual synchronous generator (VSG) hasbeen proposed [7; 8; 9; 10; 11; 12; 13]. As the control strategies of the voltage-sourced inverters (VSIs) are commonly composed of a highly programmable supplementary controller and a double-loop controller in a cascade structure, by the implementation of the VSG algorithm, the PEI external characteristics can mimic those of synchronous generators (SGs) closely [9]. Therefore, the well-developed theory for the operation of the SG-based power system can still be exploited for the evolving power grids [7]. Two classical models, the'synchronverter' and Ise's, focus on the loss of inertia in conventional VSI droop control, and the emulation of the properties of the inertia and the speed-governor is implemented [9; 11; 13]. Experiment-based studies can be found in [14; 15] for stand-alone applications. In [12], the equivalence between the VSG and the frequency-droop algorithms are demonstrated. It is accurate for an individual unit, but when the VSG algorithm is implemented in the power systems, the damping coefficient of loads (which is typically 1-1.5) should be considered because it is much larger than that of the damper windings (such as 0.1) [16]. However, the above studies are all restrained in the stages of the short-term frequency response. The frequency control of the conventional power systems includes a hierarchical structure because the system operation requires the ability to respond to change in demand and supply in multiple temporal stages [17]. With higher penetration of renewable generation, the IBG units would eventually and inevitably take the responsibility of regulating the overall energy balance because of the consequent displacement of traditional SGs. Therefore, the flexibility of the power system operation requires the VSG algorithm to extend its application scope. As the parameters of PEIs are tunable rather than restrained by physical equipment, VSG algorithms can modify the inertia properties of the renewable units in real-time. General analysis for dynamic performance can also be found in [18; 19], in which the influence of inertia and droop properties are analyzed based on transfer functions. Continuous change and step change of virtual inertia parameters are designed to minimize frequency deviation and energy support [20; 21; 22]. The change of inertia is straightforward but arbitrary. In [10], the requirements for dynamic support are illustrated based on system operation, including the standards of the frequency nadir, the maximum ROCOF, and the duration of delivery.