Networks of unidirectionally coupled electromechanical oscillators / Resilience of power grids under delayed feedback control

Networks of unidirectionally coupled systems exhibit complex dynamical behaviors. Here we focus on the propagation and amplification of an input signal in networks of micro-electro-mechanical systems (MEMS). Considering the case of sinusoidal signal input, the amplification appears up to a saturation level which depends on the transmission rate. However, increasing the number of MEMS, there is an instability that leads to chaotic behavior which is triggered by the amplification of the harmonics generated by the nonlinearities. For stochastic input signals, the MEMS array acts as a band-pass filter. One of the applications of this work is to solve the problem of energy supply for a chain of micro machines or micro robots which is seen as a real challenge encountered in industry.



This work investigates the resilience of an elementary electricity system (power plant - consumer) under proportional and derivative (PD) control when subject to large perturbations. A particular attention is paid to small power grids, representative of power grid structure in some developing countries. The considered elementary electricity system consists of a consumer (machine), a power plant (generator) and a transmission line. It is found that the controller increases the resilience of the system. We also show that time delays associated to the feedback loop of the controller have a negative impact on the performance.