Constantly growing power consumption of data centers is a major concern from environmental and economical reasons. Current approaches to reduce negative consequences of high power consumption focus on limiting the peak power consumption. During high workload periods, power consumption of highly utilized servers is throttled to stay within the power budget. However, the peak power reduction affects performance of hosted applications and thus leads to Quality of Service violations. In this paper, we introduce Power Shepherd, a hierarchical system for application performance aware power shifting. Power Shepherd reduces the data center operational costs by redistributing the available power among applications hosted in the cluster. This is achieved by, assigning server power budgets by the cluster controller, enforcing these power budgets using Running Average Power Limit (RAPL), and prioritizing applications within each server by adjusting the CPU scheduling configuration. We implement a prototype of the proposed solution and evaluate it in a real testbed equipped with power meters and using representative cloud applications. Our experiments show that Power Shepherd has potential to manage a cluster consisting of thousands of servers and limit the increase of operational costs by a significant amount when the cluster power budget is limited and the system is overutilized. Finally, we identify some outstanding challenges regarding model sensitivity and the fact that this approach in its current from is not beneficial to be used in all situations, e.g., when the system is underutilized.