## 1 Introduction  
In the past decades, due to a foreseen exhaustion of conventional fossil-based energies and their climate impact, traditional centralized power generation using fossil fuels has been increasingly considered unsustainable in the long term. Consequently, many global efforts have been devoted to developing more renewable energy sources, such as wind and solar photovoltaics (PVs) [1]. Thus, the proportion of distributed power generation systems has increased quite fast, especially in Europe [2]. Moreover, due to the fact that the best locations to get wind and solar energy are often far from the main grid, the long-distance transmission-line impedance makes the grid weaker than before, which brings a significant challenge to effective power transmission [3]. Although a high voltage direct current (HVDC) system can replace the alternating current (AC) system for long-distance power transmission [4, 5], the grid-side converter of the HVDC system still faces the challenge of connecting to a weak grid in some cases [6, 7]. Therefore, it is necessary to study the maximum power transfer capability of grid-connected inverters. The strength of the grid is defined by the short circuit ratio (SCR), which is the ratio of the short circuit power at the point of common coupling (PCC) and the rated power of the inverter. When the SCR is below 6-10, the grid is weak. In the case that the SCR is above 20, the grid is strong [8]. According to the definition of the SCR, the increase of the rated inverter power or the transmission impedance will reduce the SCR and make the grid weaker. The PCC voltage varies easily when a large amount of active power is injected into a weak grid. Thus, the reactive power control has to be used to keep the PCC voltage around its rated value [9]. Since the total rated power of the inverter is constant, the more the output reactive power, the less the output active power, which will limit the power transfer capability of the grid-connected inverter. Therefore, the SCR is an important factor that influences the maximum power transfer capability of the grid-connected inverter. Most previous works have focused on improving the control strategies of inverters to increase the power transfer capability limited by control stability, such as improved grid-following control methods [10; 11; 12] and newly developed grid-forming control methods [13; 14; 15; 16]. A gain-scheduling controller with the H-infinity method is presented in [10] to extend the stability range of classical grid-following inverters. Similarly, a current error-based voltage angle and magnitude compensation method is proposed in [11] to improve system stability. Moreover, a power-synchronization-based grid-forming control method is proposed in [13], which has better stability performance than grid-following inverters. Differently, the natural maximum power transfer capability of grid-connected inverters mainly depends on the physical parameters of the system, which is constant for an existing system [17; 18]. Hence, it is a key property for engineering design and analysis. Recently, it was reported in [19] that not only the SCR but also the resistance-inductance ratio (R/X) of grid impedance affects the maximum power transfer capability of grid-connected inverters. However, [19] mainly discusses the inductive grid case, while the resistive grid case is not analyzed. In fact, both the inductive and resistive grids exist in real applications. Generally, high-voltage lines are inductive, while low-voltage lines are resistive [20; 21]. Therefore, the resistive grid case should also be analyzed. This paper attempts to fill this research gap and provides a full map of both cases. Since both current and voltage limitations are considered, this research is closer to reality. Furthermore, our early work in [22] mainly analyzes the impact of the SCR and the R/X ratio on the maximum power transfer capability in the constant PCC voltage case, where the impact of the PCC voltage is not considered.