Effects of Frustrated Interactions on Synchronicity in Electrical Power Grids

For decades, electrical energy has been provided by relatively few and large power stations driven by fossil fuels or nuclear reactions. Recently, with the ever-increasing need for more power in combination with greater environmental awareness, there is a growing trend to incorporate also renewable energy sources; such as, wind, photovoltaic arrays, solar-thermal converters, biogas, etc. However, the incorporation of many smaller and often intermittent alternative energy sources into existing power grids can lead to loss of synchronicity in the grid. Therefore, the question of how the stability of power grids is affected by changes in the nature and topology of the coupling is currently of key importance. In the present study we consider the effects of frustrated coupling in such grids, by using a Kuramoto-Sakaguchi-type model that takes into account the frustration via a single frustration (or phase-lag) parameter. We study numerically how such frustrated disorder brings about strong hysteresis and multistability in the grid, thereby affecting its ability to remain synchronized. We compare our results to previous models in which the frustrated interactions were neglected.