**1. Introduction**

With increasing awareness of how quickly conventional energy sources like coal and petroleum products are depleting, renewable sources of energy are gaining relevance on a global scale today [1]. According to data from the U.S. Energy Information Administration's monthly energy review article as of June 2021, natural gas accounts for 58.8% of all energy usage, followed by electricity at 39.1% and petroleum at 9.6% and 7%. The situation in India indicates a greater reliance on coal and oil. As a result, conventional resources are quickly running out. Due to the availability of non-conventional energy sources in nature, they are prepared to offer services at permissible tweaks. As previously noted, solar energy is the most practical resource for creating electrical energy because it does not generate any greenhouse emissions or other hazards. However, due to the inability to deliver optimum power under load without interruption, it is necessary to implement the maximum power point tracking (MPPT) method. In addition to maximizing the power generated by the PV source, MPPT also helps the PV system last longer [2].

There are numerous ways to obtain the maximum power possible out of a photovoltaic source [3–7]. The ability to follow the actual maximum power point (MPP), speed of convergence, robustness, efficiency, cost, and hardware implementation is the criteria used to classify MPPTs. MPPTs are divided into three categories based on the aforementioned requirements:online, hybrid, and offline methods. Offline techniques are dependent on the solar cell model's parameters. It is also known as a "model-based" approach. Online approaches are known as "model free" methods, which denote that they are independent of the solar model's parameters. The two previously described strategies are combined to create the hybrid method [8]. The most popular online MPPT techniques are perturb and observe (P&O). Incremental conductance (IC) and hill climbing (HC) are two techniques that function effectively when ambient temperatures and solar irradiation do not fluctuate quickly [9–13], but offline approaches are effective when solar irradiation is changing rapidly. Popular techniques include ANN-based MPPT, PI, fuzzy logic controller (FLC), GA- and ACO-optimized MPPT, and others [14]. Hybrid MPPTs are used to retain the maximum amount of PV panel power production in order to circumvent the drawbacks of the aforementioned approaches [15–17]. A grid-connected system's power quality should also be evaluated in addition to power quantity monitoring. The interfacing of nonlinear loads, such as power electronics components, results in harmonic content, which lowers the quality of the power sent to the grid. In order to manage the power quality within a certain range, DVR and D STATCOM are introduced [18]. IEEE Std (1250-2011) [19], states that the maximum voltage deviation is 10% of the base value, the maximum frequency deviation is ±0.1 Hz, and the maximum voltage/current deviation is 5% of the base value. According to IEEE Std (519-2014) [20], THD shall not exceed 5%, while IEC [60831-1/2] standards specify that the power factor must be more than or equal to 0.9 [20]. When operating a PV system connected to the grid, good power quality must be satisfied while taking into account all of the aforementioned constraints. Due to the fractional order PID controller's quick convergence and response for both linear and nonlinear loads, the theory of factional calculus gained popularity [19,20]. The enhanced version of AFO+PID, known as adaptive fractional order PID controller, is applicable for both linear and non-linear loads and has a high degree of efficiency when operating in perturbed conditions. The system is interfaced with an adaptive FOPID controller to increase gain and robustness. The ideal system's dimension and energy cost must also be taken into consideration in order to ensure the successful functioning of a system, in addition to power quantity and quality study. By adjusting peak demand when carrying a fixed energy demand and vice versa, the grid-interfaced system is optimized to reduce energy costs (COEs), with a reduction in peak load conditions [21]. The implications of various storage capacities on the performance analysis of a hybrid micro-grid system are described in [22] along with a sensitivity analysis. In [23], the performance evaluation of HRES was provided, and it was proven that the pumped storage hydropower plant was the best option in terms of cost savings. By talking about the constraints, a novel, multi-objective HHO-AFOPID

control topology is provided to overcome the problems, and the evaluations of sensitive SPV parameters that are dependent on LCOE and TNPC are carried out.

The work's main contributions are noted below:


The organization of this article is as follows: Section 2: System Model Simulation; Section 3: Solar Photovoltaic (SPV) Control Implementation Adaptive Fractional Order PID Controller Design; Section 4: Results and Clarifications; Section 5: Sensitivity Analysis; Section 6: Conclusions and Future Directions.
