# Adaptive PI Control Strategy for Optimal Microgrid Autonomous Operation
## 1 Introduction  
### Problem Understudy  
To accommodate the spike in the load profile, decentralized renewable power networks are undergoing major reformation. These advancements have resulted in technical and scientific progress as well as environmental and economic advantages. Nevertheless, load demand is rising fast. This circumstance emphasizes the criticality of replacing centralized power plants with distributed generators (DGRs) placed over distribution networks [1]. This might be an effective countermeasure for reducing transmission losses and eliminating any need for extensive transmission networks. Some factors must be considered for the DGR units to supply the load continuously. As a result, the microgrid (MGD) concept arose as a set of DGRs and their associated loads in such a sub-network. The MGDs are tiny conventional grids that may be operated and managed electrically in either grid-connected or grid-disconnected (islanded) mode [2]. The system point of common coupling (PCC) voltages and frequencies are identified by the utility in the grid-connected mode. Nonetheless, their active and reactive powers must be managed. In contrast, the microgrid's voltage and frequency must be modified in the islanded mode [3]. As a result, it is necessary to manage the DGR unit's functioning in order to supply the load continuously. Different sophisticated control systems are used in islanded mode to ensure proper and reliable functioning. These control methods are classified into droop control (DPC), centralized, and multivariable and servomechanism (MAS) approaches. DPC provides peer-to-peer management and plug-and-play functionality by autonomously regulating the distinct DGR's outputs without requiring contact or communication among DGRs. A remote controller technique focused on active and reactive power DPC is suggested [4]. A fully decentralized method based on dual-frequency-droop control is proposed [5]. One of the profits of utilizing DPC is the capability to individualistically regulate scattered units without requiring contact between them. From the perspective of robustness and reliability, this technique beats previous power-sharing and MGD frequency-regulating methods. However, for lower voltage MGDs, line impedance significantly influences this control's efficiency, resulting in power conjugation [6]. The imaginary vectors conversion approach has been improved to avoid power conjugation [7]. However, it affects reliability. On the other hand, centralized control approaches need increased bandwidth linkages, and any break in those networks might cause a MGD collapse. A centralized control scheme for DC MGD built on independent communications was created and used [8]. Finally, a unique technique for creating multivariable robust servomechanism systems for several inputs and outputs and open-loop systems control is proposed [9]. Nevertheless, its immense complexity is a hindrance. Because of its high stability margins, the proportional-integral (PI) controller has become the most commonly used controller for non-linear systems. However, it has difficulty dealing with parameter variation sensitivity and network nonlinearities. Consequently, identifying the proper PI configuration in this scheme is a significant challenge. In recent years, extensive studies have been conducted to develop the ideal controller for MGD controls to maintain a reliable system. In this aspect, PI controllers use a d-q frame to adjust the voltage of the voltage source converter [10]. Furthermore, whenever the system is assumed linear, PI controllers are tuned by simple procedures such as the Ziegler-Nichols method [11]. In contrast, the PI controller produces a saturated result, reducing the system stability due to a more significant phase lag. A decentralized PI controller for regulating a hybrid power scheme is introduced in [12]. As a result, several metaheuristic algorithms that simulate biological or physical events can resolve objective functions.