# Dynamic Interactions between Parallel Grid-Forming Inverters in a Microgrid
## 1 Introduction  
The generation of electricity from eco-friendly sources is of significant interest worldwide, as there is an increasing integration of renewable energy into the power system [1]. A microgrid is a system that combines distributed renewable energy resources to function either independently as a stand-alone grid or as a single unit connected to the main grid [2, 3]. There are various types of microgrids, including AC, DC, or hybrid AC/DC configurations. An AC microgrid is a small-scale power system operating on alternating current (AC), which can function autonomously or in conjunction with an existing utility power grid. Both AC and DC microgrids provide distinct benefits and drawbacks, making it essential to consider the specific application and local conditions when selecting between them [4]. To ensure the safe and synchronized operation of microgrids, appropriate control is necessary. This involves managing the grid source, distributed energy resources, and distributed loads in an islanded microgrid, where grid-forming control is often employed for inverter-based resources (IBRs). Moreover, proper power-sharing between parallel inverters is essential. This is typically achieved through a real power/frequency (\(P\)-\(f\)) and reactive power/voltage (\(Q\)-\(V\)) droop control strategy, which governs the frequency and output voltage of the inverter by adjusting the output real and reactive power [5, 6]. The droop control strategy is inspired by the characteristics of synchronous generators. However, a high R/X ratio of low-voltage (LV) distribution lines can lead to power coupling issues. To address such concerns, numerous enhanced droop-based power control methods have been suggested [5]. One of the promising solutions is employing virtual output impedance, which has demonstrated excellent performance in managing these challenges [7]. The dynamic interaction between multiple devices has been seen in the past. For example, interaction between Flexible AC Transmission System (FACTS) controllers has been observed [8, 9, 10]. Examples of FACTS devices are the Static Var Compensator (SVC)and the Static Synchronous Compensator (STATCOM). In [9], a study case for SVC-SVC interaction is investigated. Based on the findings, both devices can adversely interact with each other depending on the grid conditions. In the case of high short-circuit ratio conditions, the effect of one SVC on the other SVC is not a concern. However, the effect is more pronounced if the short-circuit ratio is low. Another example of adverse interaction is between FACTS devices and High-Voltage DC (HVDC) systems [10]. The results in [10] indicate that no control interactions have been observed between SVC and HVDC if the grid is strong or the short-circuit ratio is high. In the case of a weak grid, however, the effect is strong. With the increasing number of voltage source converters (VSCs), dynamic interaction among VSCs may pose stability problems. Several real-world stability issues are listed in [11; 12; 13]. The dynamic interaction among VSCs can be organized as:  
* Interaction between similar VSCs, e.g., multi-parallel PV [11; 12; 14];
* Interaction between VSCs of a dissimilar kind, e.g., wind and STATCOM [13], Wind, and HVDC [15]. The multi-parallel inverters are coupled and influence each other due to grid impedance. In [16], the results indicated that when there are N paralleled inverters connected to the same PCC, each inverter will see the equivalent grid impedance amplified by N times the actual value. This indication illustrates why the VSCs do not behave as expected when they are connected in parallel, even when their specifications to operate individually are satisfied [17]. Another type of interaction is the converter-converter interaction when the converters are electrically close to each other. For this type of interaction, the stability issue occurs when the controls of the converters interact with each other.