Dynamic Stability Analysis and Control of Grid-Connected Hybrid DC Microgrids Incorporating Solar PV, Diesel Generator, and Battery Energy Storage Using a Nonlinear Backstepping Approach

This paper presents a dynamic stability analysis and control strategy for a grid-connected hybrid DC microgrid incorporating a solar photovoltaic (PV) system, diesel generator with a rectifier, and battery energy storage system (BESS). A nonlinear backstepping controller (NBC) is developed to regulate power flow, minimize generation-consumption mismatch, and maintain a stable DC bus voltage. The proposed controller is designed recursively using Lyapunov stability theory, ensuring robust and stable operation under varying load and generation conditions. The control design leverages control Lyapunov functions (CLFs) to guarantee stability, with the negative semi definiteness of the CLF derivatives confirming the effectiveness of the proposed approach. The performance of the NBC is evaluated under different operating scenarios and compared with a nonlinear sliding mode controller (SMC). Simulation results demonstrate that the NBC provides faster stabilization, improved steady-state response, and superior power-sharing capability, making it a reliable solution for dynamic stability enhancement in grid-connected DC microgrids.