# Transmission of Energy

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## Abstract

In this chapter we provide exact and approximate results for the problem of the Transmission of Energy in Complex Networks. The problem is the understanding of how the energy transmission between the providers of energy (such as power plants, renewable sources, or any type of supplying entity) and the consumers of energy (such as factories, homes, or any type of demand entity) depends on the topology and the structure of a network that inter-connects the two sets of entities and the dynamical behaviour of all the entities in the network, such as depicted in Fig. 1.4. Moreover, we want to provide safe strategies to create self-controlled and stable systems (i.e., resilient to failures, structural modifications, and dynamical changes) that have an optimal (i.e., with less cost and power dissipation) and smart (i.e., allowing the decentralisation of large power-plants into small fluctuating renewable energy-sources) energy transmission.

## Keywords

Power Grid Model Erdos-Renyi Network (ERNs) Generator Terminal Bus Laplacian Matrix Network Flow Conservation## References

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