This paper looks into the voltage stability and network scalability of self-contained converter-based DC MG under an innovative control approach, namely a nonlinear adaptive droop-based controller with overcurrent protection, devised for HEA applications. Apart from guaranteeing tight voltage regulation and accurate adaptive distribution of load power across parallel batteries proportional with their current SoC, the controller features an inherent overcurrent protection. Notably, the applied nonlinear adaptive droop-based controller introduces a virtual voltage and a constant virtual resistance, placed in series with the inductance and parasitic resistance of each DC/DC bidirectional boost converter. Moreover, the voltage stability for the n-dimensional system is subsequently investigated, providing valuable insights into the voltage dynamic behaviour, followed by a network scalability study based on the system's passivity properties. Finally, numerical simulations replicating various in-flight scenarios align with and validate our theoretical developments in the pursuit of minimising emissions, environmental impact, and operational costs.