Partially rated DC interlinking converters are recognized for their high-gain power regulation capabilities, which effectively synergize active power across DC microgrids (DCMGs). Integrating energy storage units (ESUs) to address the intermittent nature of renewables in DCMGs has become an enhanced requirement for these converters. This article proposes a partially rated multiport interlinking converter (PMIC) that incorporates a distributed ESU. The PMIC controls a floating voltage and a bidirectional shunt current on the DC line, ensuring full galvanic isolation for the ESU while operating at a low DC-link voltage. It regulates multidirectional power flow and balances power during peak and off-peak periods. A decentralized droop-based power flow control strategy is proposed for the PMIC, which distributes renewable energy generation, load consumption, and ESU utilization proportionally across the system. The control strategy includes two tailored continuously differentiable activation functions, Sigmoid and Hyperbolic Tangent, to facilitate autonomous global power-sharing and seamless ESU engagement. Simulation and experimental case studies confirm the PMIC's capability to smooth renewable energy fluctuations and enhance the power and voltage profiles of DCMGs.