Flexible interconnection systems (FISs) improve distribution flexibility, yet they remain vulnerable to pronounced nonlinear instability and potentially severe DC-link voltage collapse during large disturbances such as constant power load (CPL) surges. Conventional linear control methods are often unable to prevent deep transient voltage dips under these conditions. To address this issue, this paper proposes a novel large-signal stability criterion based on mixed potential function (MPF) theory. Unlike conventional Lyapunov-based approaches, the proposed formulation explicitly incorporates the dynamics of the DC capacitor, thereby enabling the derivation of a closed-form stability boundary. On this basis, the proportional gains of the outer voltage loop are first optimized to guarantee an adequate static stability margin. Subsequently, a power differentiation feedforward control strategy is developed. Rather than passively counteracting transients, the proposed method dynamically adjusts the DC voltage reference according to the rate of change in power, thereby actively reshaping the transient trajectory. In this way, the simple PI control framework is preserved while avoiding the heavy computational burden associated with advanced methods such as model predictive control. Simulation results show that the proposed strategy increases the permissible CPL step power by 8.7%, from 92 kW to 100 kW. Moreover, under severe load surges and weak grid conditions, the method prevents voltage collapse and maintains the transient trajectory above the practical 600 V safe-operation threshold. This computationally efficient strategy significantly improves the robustness and continuity of operation of practical FISs.