A Hybrid Index Matrix Framework for Python-Based Modeling, Simulation, and Local One-Step Sensitivity Diagnostics of Bidirectional DC–DC Converters

Bidirectional DC–DC converters are key interfaces in battery energy storage systems, electric vehicles, fuel cell vehicles, and DC microgrids, where transparent mathematical models are required for simulation, controller evaluation, and energy-flow analysis. This paper presents a hybrid index matrix framework for the Python-based modeling of a bidirectional buck–boost converter coupled to a first-order Thevenin battery model. In contrast to a classical state-space formulation, the index matrix is used as a label-aware model-assembly layer: component equations are aligned by explicit row and column identifiers and subsequently projected into ordered numerical matrices for solution. Charging, idle, and discharging equations are solved using a fixed-step backward-Euler procedure, and a PI current controller with duty-cycle saturation and anti-windup regulates the power-flow direction. A conventional switched ODE implementation is retained only as a software-level numerical-consistency check between two implementations of the same assumptions; it is not presented as experimental validation or as an independent physical benchmark. For the reported 60 s current profile, the model gives a current RMSE of 0.0863 A and a peak current of 4.3684 A, corresponding to 9.2094% overshoot at the idle-to-discharge transition. The power-integration balance is 1.6091 Wh input, 1.5868 Wh output, and 0.0223 Wh estimated loss under the adopted conduction-oriented loss model. The conditional one-step sensitivity matrices have a spectral radius of 1.00000 in all three modes; the unit eigenvalue is consistent with the slowly varying SOC state, while the remaining electrical eigenvalues lie inside the unit circle. These eigenvalue results are interpreted as local non-divergence diagnostics rather than proof of asymptotic closed-loop or switched-system stability. The framework provides a transparent and reproducible numerical workflow, while experimental validation, detailed switching-level loss modeling, step-size convergence, and formal closed-loop/switched-system stability analysis remain necessary future work.