Phase locking of wind turbines leads to intermittent power production

Wind energy, inserted into the power grid by wind turbines, is strongly influenced by the turbulent fluctuations of wind speed in the atmospheric layer. Here we investigate the power production of a wind farm and show that due to the presence of large-scale and long-time correlation in wind velocity, turbines interact with each other. This interaction can result in phase locking in pairs of turbines. We show that there are time intervals during which some pairs of turbines are temporally phase locked. This intermediate phase locking leads to the statistical effect that the short-time fluctuations of the cumulative power output of the wind farm become non-Gaussian, i.e., intermittent power production occurs. Contrary to phase-locked states, there are some time intervals where all turbines are phase unlocking and consequently the probability density function of the temporal increment of cumulative power production of the wind farm has almost Gaussian distribution. The phase-locked states, which can be distinct from phase-unlocked states by their dynamical features, are evaluated by reconstructed stochastic differential equations.