This next chapter of the thesis expands on the developed work of the previous chapter, adding a degree of complexity that improves the overall closed-loop system performance. First, tools from the field of geometric control are utilized to shed light on the operation of, and interaction between, different microgrid components such as constant power loads and power converters. Understanding the behaviour of the system in this level, allows the formulation of a control-theoretic analysis to characterize a robustly positive invariance set under the solution of the system dynamics and constant power load demand perturbations. It is shown that this approach allows us to reduce the inherent conservativeness of the control architecture developed in the previous chapter, reducing the computational burden and relaxing the sufficient conditions for recursive feasibility of the receding horizon control scheme.