This book introduces several novel contributions into the current literature. Firstly, given that microgrid topologies are paramount in theoretical analysis, the author has proposed a rigorous method of computing the network’s admittance matrix and developed to facilitate the stability analysis of DC microgrids supplying nonlinear loads. This unique approach enabled the factorisation of the admittance matrix in a particular way that facilitates a rigorous theoretical analysis for deriving the stability conditions.
Secondly, author has proposed a unified control structure at the primary control layer that maintains the widely accepted droop-based approaches and additionally ensures crucial current- and voltage-limiting properties, thus offering an inherent protection to distributed energy resources. He has formalised the control design proofs using Lyapunov methods and nonlinear ultimate boundedness theory, for both parallel and meshed microgrid configurations. Moreover, he hasdeveloped a distributed secondary controller using a diffusive coupling communication network, on top of the primary control, to achieve voltage restoration and improve the power sharing. In this way, the author has formulated the complete hierarchical control scheme.

In this high-order nonlinear setting, he has analytically proven closed-loop system stability of the overall system, for the first time, using two-time scale approaches and singular perturbation theory, by formulating rigorous theorems that introduce straightforward conditions that guide the system and control design and demonstrate system stability at the desired equilibrium point. In addition, the author has provided a straightforward algorithm for simple testing of system stability and explored from a graphical perspective by giving an interpretation to the effect of the nonlinear load onto the system performance and stability.