  We investigate the influence that adding a new coupling has on the linear
stability of the synchronous state in coupled oscillators networks. Using a
simple model we show that, depending on its location, the new coupling can lead
to enhanced or reduced stability. We extend these results to electric power
grids where a new line can lead to four different scenarios corresponding to
enhanced or reduced grid stability as well as increased or decreased power
flows. Our analysis shows that the Braess paradox may occur in any complex
coupled system, where the synchronous state may be weakened and sometimes even
destroyed by additional couplings.
