Methods and apparatus for reducing peak power consumption of a grid connected power plant having a plurality of wind turbines. In response to determining that a power production value of the power plant is below a power threshold, one method includes: after a first time delay of a first group of one or more wind turbines, control the first group to operate in a power saving mode for a predefined first power saving period; and after a first time delay of a second group of one or more other wind turbines, control the second group to operate in the power saving mode for a predefined second power saving period. The first time delay of the first group is less than the first time delay of the second group and the power saving mode inhibits a power consuming activity for the wind turbines operating in the power saving mode.