# Performance Tuning for Power Electronic Interfaces Under VSG Control
## 1 Introduction
However, it lacks the discussion on how to quantitatively tune the parameters to satisfy these standards. In [12], a step-by-step parameter design for virtual synchronous generators is conducted based on small-signal modeling, which focuses on independent decoupling and tuning of active and reactive power loops of a single grid-connected inverter. However, this approach is oriented for coping with unbalanced grid voltages, but not for quantitative performance indices. Also, the decoupling condition includes that the short-circuit ratio is no less than 10, which is typically not satisfied in power systems [23]. In [24], quantitative performance analysis is completed for the inertial response provided by the capacitor in the DC link. However, the capacitor can only provide frequency support as an energy buffer, and the response ability is restrained by the predesigned capacitance. Again, from the view of the operation flexibility, the quantitative performance analysis for the overall power systems should be considered for the generation mix (SGs and IBG units). Within a microgrid, based on the information technology and communication network, secondary frequency regulation (SFR) and tertiary frequency regulation (TFR) could also be implemented on VSIs [25; 26; 27; 28; 29]. In recent research, the VSG-based IBG can also participate in system frequency regulation when active power reserves (APRs) are implemented. Instead of the traditional maximum power point (MPP) tracking, the APR strategy controls the IBG units to operate at a sub-optimal point [30]. Therefore, generation availability is reserved to tackle the power imbalance caused by the uncertain nature of renewables [31]. Active power reserves by RG units can be realized by two types of control strategies: (1) the delta control, which deloads RG units by constant percentages or values, or both according to the meteorological conditions [32]; and (2) the balance control, which controls the RG output by upper limit when the surplus power acts as reserves [33]. The APR control strategy enables the IBG units with persistent generation availability to participate not only short-term frequency response stages (IR and PFR) but also long-term frequency regulation stages (SFR and TFR). Therefore, a complete hierarchical structure of multiple temporal frequency control stages could be emulated on the VSG-based IBG units. In order to enhance the VSG algorithm to sustain the flexibility level of power systems containing a mixed generation at all times, in this paper, a quantitative approach of performance tuning for VSG-PEIs participating in multiple temporal stages of frequency control is presented. The contributions of this work could be summarized as follows:  
(1) Besides the capabilities of IR and PFR, by referring to the knowledge of conventional generation and operation, an enhanced control strategy for the capabilities of SFR and TFR are designed to complement the VSG algorithm. Therefore, VSG-based PEIs could perform multiple temporal frequency control. (2) The analysis of frequency response dynamics, based on the simplification of the transfer function down to the second-order form, is conducted for both the stages of (1) IR and PFR, and (2) SFR. Six performance indices are proposed, and the frequency responses influenced by different parameters are analyzed. (3) It is noted that the performance indices are influenced by composite parameters, but the hierarchical stages of IR, PFR, and SFR operate in chronological order. Therefore, a parameter tuning algorithm is designed in which the parameters are also determined following a chronological sequence. (4) The proposed parameter tuning approach could either be used to analyze dynamic performance and tune parameters for either the bulk system performance after the power unbalance disturbances or the dominant generation units in a stand-alone scenario. The rest of the paper is organized as follows: Section 2 presents the complete emulation control strategies for PEIs with multiple temporal frequency control.