Complex energy flow dynamics following an untoward event has a direct impact on the responses of the protective and stabilization control systems of the power grid, in defending the power grid against from large-scale cascading failures or network fragmentation.

In this dissertation, a non-classic view and an analytical framework on electro-mechanical dynamics are proposed, which is different from the electric circuit-based ones built up classic physics.

Inspired from some recent advances in port-Hamiltonian formulism in control systems and random work interpretation of energy flows in electric circuit, a hypothetical but well-grounded unitary view on power grid is postulated, which leads to the new concept of many-body delocalization. The power grid with n ports of synchronized components can be transformed into a unitary electromagnetic field, which can be mathematically described by a complete graph that couples the active and passive resources and boundaries. Thus, the energy flow becomes the manifestation of an underlying unitary electromagnetic field.

A quantum number-based analytical framework is built based on several principles related to the unitary field view, such as Hermitian symmetry, Heisenberg uncertainty principles and general relativistic effect. With the intrinsic properties of the quantum number-based model, a new network property is developed, namely z-direction radical distance. This is a new concept about the projection of angular quantum number and the unit reference potential. This novel radical distance concept describes the fundamental connection between the energy flow in a complex network and its structure: it stands for the fraction of system energy surging at various spots as the result of l-motions along the z-direction, later found very useful for understanding the energy flow in power grid. An evidential experiment is carried out using a real world power grid model of electro-mechanical stability. With mathematical tools from tensor analysis of network, the estimation of distribution of network energy flow in the power grid is derived. By comparing the radical distance based estimation of electromagnetic waves in the power grid to the one calculated with the complete dynamic system model of the power grid, a remarkable consistency is observed. This dissertation presents a unique perspective for complex network analysis, which is drastically different from the current “small-world” one. Based on its analytical root and the evidential experiments, we discover that radical distance is a metric that penetrates the boundary between the microscopic quantum world and real-world macroscopic power and energy systems. Such a discovery suggests the possibility of the coupling of active resources of power grid could be of the entangled particles type, authoring the usage of quantum effects in explaining and dealing with the states at a macroscopic scale, at least from a modeling/analytical perspective.