# Decentralized Robust Control of a Network of Inverter-Based Distributed Generation Systems
## 1 Introduction  
Nowadays, due to environmental issues and lack of sufficient resources, more renewable energy generation systems such as wind power and photovoltaic (PV) are being utilized in power generation systems [1, 2, 3]. Although such distributed energy resources (DERs) have significant contributions to increased energy resources and a cleaner environment, their extensive usage gives rise to new challenges in the regulation of power systems as a consequence of the intermittent behavior of DERs [4, 5]. Furthermore, conventional synchronous generators with large inertia are being replaced by DERs with small inertia (e.g., wind turbines) or even zero inertia (e.g., PV) [6], raising concerns about the stability of the power system. All of the above-mentioned issues can become worse when DERs are grouped together in low-voltage (LV) stand-alone nanogrids (NGs), where the distances among DERs become so short that the coupling interconnections among them strengthen significantly. The short distances among DERs correspond to larger R/X ratios, which can cause serious stability issues in the entire NG if the controllers are designed improperly. This issue was introduced by the authors of [7], where two inverters with LC output filters were connected together through an interconnection line modeled by series resistance and inductance. It was demonstrated that if the decentralized controllers were designed independently such that the coupling interconnection was not considered in the design process, the entire control system became unstable as the distance between the two inverters grew shorter. Motivated by the issue raised in [7] and based on the independent design of decentralized controllers, a new design scheme is proposed in this paper to address the problem of strongly coupled inverter-based NGs. Before delving into the details of the proposed control scheme, a literature review on the different control designs for the interconnected distributed generation systems in NGs is presented below. In [8], the authors proposed an improved robust control scheme for multi-feeder micro-network systems by taking into account the load feeder voltage regulation and power sharing as a quadratic optimization problem. The authors of [9] presented a control strategy to enhance the dynamic response of power systems by designing an automatic regulator for converter-based DERs. The controller included a proportional-integral controller plus a washout filter in parallel. The authors of [10] presented a decentralized one degree of freedom robust control scheme to control the voltage of an uncertain inverter-interfaced AC microgrid (MG) in stand-alone mode. In a similar work [11], the authors proposed a decentralized robust control scheme to regulate the voltage of an off-grid inverter-interfaced MG. A robust controller was computed by solving a convex optimization problem. In [12], a communicationless decentralized control scheme was proposed for a PV/battery-based distributed NG, based on an adaptive I-V droop control method. A self-sustained hierarchical decentralized control technique was presented in [13] for NGs in isolated areas. In [14], an adaptive control strategy was proposed to regulate clustered NGs. Each NG included a PV system, a battery energy storage system (BESS), local loads, and a gateway unit. In [15], a control methodology for smart loads in NGs was presented to mitigate the voltage and power fluctuations caused by load changes and variations in the power generation. An inertial control scheme was presented in [16] to balance power and enhance stability in a hybrid NG. In [17], the authors proposed a distributed direct power sliding-mode control scheme to replace the droop mechanism of each inverter in an islanded microgrid. A novel robust droop-based type-2 fuzzy logic controller was proposed in [18] to improve the stability of a cluster of NGs with constant power loads.