The recent trend of encouragement to renewable integration has resulted in an inverter-dominated hybrid grid. The time-scale of such integrated grid activities and its response time varies in a wide range. In such a scenario, the first challenge is to have a model that can capture both the dynamics of fast as well as slow components, and the second is stability analysis without compromising its time-varying impact. To address these issues, the paper includes the Port-Controlled Hamiltonian (PCH) Inverter formulation related to a interdisciplinary model for voltage stability analysis of inverter-dominated distribution grids. The interactions between slow network, load dynamics, intermediate converter-control dynamics, and fast electromagnetic states can be captured in the model. The PCH formulation provides an energy-based representation of the inverter dynamics, enabling systematic analysis of transient voltage response and post-disturbance recovery in inverter-integrated power systems. MATLAB is used to validate the proposed methodology in weak-grid and load-varying scenarios. A new PCH-based controller has been designed to tune the inverter PWM signal so that voltage stability can be supported to maintain the grid voltage profile.