# Decentralized Robust Control of a Network of Inverter-Based Distributed Generation Systems
## 1 Introduction
In [19], the authors presented a data-driven decentralized reinforcement learning control structure to regulate the voltage of a distribution network with multiple MGs. In [20], the authors presented a multivariable adaptive robust control scheme for grid-forming stand-alone inverter-based MGs. In [21], a decentralized droop control scheme that utilizes the state of the battery charge to harmonize the power exchange was presented for an islanded LV NG. A nonlinear I-V droop control scheme based on the dynamic consensus algorithm was presented in [22] to balance the state of the charge of energy storage systems in NGs. The problem of high R/X in LV microgrids was studied in [23], where the effects of tie-line and droop controllers on the system were investigated. In [24], a decentralized model predictive voltage control scheme was proposed to compensate active and reactive power from PV inverters and electrical vehicles. Hybrid decentralized and distributed control schemes were presented in [25] to regulate the voltage in a distributed network of inverters. In [26], a distributed optimal control strategy was proposed for frequency regulation and economic dispatch of a power network. In [27], a distributed adaptive proportional-integral-derivative voltage controller was proposed and shown to be was robust against unknown uncertainties coming from external disturbances and parameter variations. In [28], the authors presented a technique to calculate the droop coefficient for voltage-current droop to consider the proportional power sharing among distributed generators. Table 1 demonstrates the characteristics of previous studies and the reported performance compared to the results of this paper. Although the aforementioned studies have acceptable performance in regulating the voltage and frequency of the network of inverters, they have not completely investigated the effect of variations in the strength of coupling interconnections among the inverters due to distance changes. As the distance among inverters shortens, the dynamic couplings among them strengthen, which puts the entire NG at risk of instability, as demonstrated in [7]. This problem is not critical in the case of grid-connected systems, where the power system is dominantly stabilized by synchronous  
generators. However, it is of high significance in stand-alone NGs, where all the DERs are within short distances from each other, leading to increased risk of instability. Of the references in Table 1, [10; 17] considered shorter distances (larger R/X) in their studies as well as parameter uncertainties. However, in [10] the authors did not take into account the effect of the overload disturbance and nonlinear load on the control performance; in [17], the authors did consider the nonlinear load analysis, but presented no overload analysis. Because isolated NGs have been growing rapidly in the past few years [29], it is highly critical that decentralized robust controllers be resilient against the coupling strength among the DERs, overload conditions, nonlinear loads, and system parameter variations. In this study, a novel technique for designing decentralized robust controllers is presented for a small network of inverters such as in the case of a stand-alone NG. The design of decentralized controllers is carried out sequentially such that the impact of strong coupling interconnections is considered in the design process. This significantly improves the robustness of the entire NG against variations in coupling strength and in the other parameters of the system. It should be noted that the coupling interconnections appear as shared dynamics among DERs which need to be addressed during the control design process. Thus, the main contributions of this work are as follows:  
* Proposing a procedure for systematic clustering of a network of inverter-based distributed generation systems (IBDGs) into subnetworks such that there are strong interconnection dynamics among the IBDGs of a subnetwork and weak interconnections across the subnetworks.