While chip vendor still stick to Moore's law, and the performance per dollar keeps going up, the performance per watt has been stagnant for the last few years. Moreover energy prices continue to rise world-wide. This poses a major challenge to organisations running grids, indeed such architectures require cooling systems. Indeed the one-year cost of a cooling system and of the power consumption may outfit the grid initial investement. We observe , however, that a grid does not constantly run at peak performance. In this paper, we propose a workload concentration strategy to reduce grid power consumption. Using the Xen virtual machine migration technology, our power management policy can dispatch transparently and dynamically any applications of the grid. Our policy concentrates the workload to shutdown nodes that are unused with a neglectable impact on performance. We show through evaluations that this policy decreases the overall power consumption of the grid significantly