A distributed solar micro-grid connects its inverters through communication links…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Complex and collective systems · Complex and collective systems

Many Parts, One Behaviour, Ch Synchronisation, cascades and the resilience of networks

Problem

A distributed solar micro-grid connects its inverters through communication links forming an Erdos-Renyi random network with mean degree ⟨k⟩=20\langle k\rangle = 20. Each inverter's output phase behaves as a phase oscillator; the all-to-all coupling that would entrain every inverter is K0=15 rad s−1K_0 = 15\,\mathrm{rad\,s^{-1}}. ((a)) Estimate the coupling KcK_{\rm c} at which the real communication network begins to entrain the inverters. Use κ1≈⟨k⟩+1\kappa_1\approx\langle k\rangle+1 for an Erdos-Renyi graph and Kc≈K0/κ1K_{\rm c}\approx K_0/\kappa_1. ((b)) Panels fail at random with age. Using the random-failure percolation threshold, find the fraction of inverters that must fail before the communication network's giant component disappears.

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