To ensure stable power system operation, grid-forming inverters (GFMs) are increasingly being deployed because they emulate the behavior of synchronous generators (SGs). While GFMs are introduced to replace conventional grid-following inverters (GFLs) by providing system inertia and contributing to fault current, they can paradoxically show unstable output characteristics under high short-circuit ratio (SCR) conditions. This paper presents a detailed mathematical plant model of a basic GFM structure and integrates it with a grid-connected GFM model that incorporates SCR variations to capture realistic grid dynamics. A single-input single-output (SISO) model of a GFM employing active power control (APC) is proposed to evaluate system stability under small grid disturbances. Additionally, a system frequency response (SFR) model is developed to analyze the dynamic behavior of SGs and GFMs during large-signal grid events. The proposed APC method is assessed through step-response and frequency-response analyses and benchmarked against existing strategies, including droop control and virtual synchronous machine (VSM) control. Simulation results obtained from MATLAB and PSS/E confirm the validity of the proposed approach. By actively tuning the controller in accordance with varying SCR conditions, stable GFM operation can be consistently achieved for both small and large grid events.