Minimizing the energy consumption and silicon area are usually two major challenges in the design of battery-powered embedded computing systems. Dynamic and Partial Reconfiguration (DPR) opens up promising prospects with the ability to reduce jointly performance and area of compute-intensive functions. However, partial reconfiguration management involves complex interactions making energy benefits very difficult to analyze. In particular, it is essential to realistically quantify the energy loss since the reconfiguration process itself introduces overheads. This paper addresses this topic and presents a detailed investigation of the power and energy costs associated to the different operations involved with the DPR capability. From actual measurements considering a Xilinx ICAP reconfiguration controller, results highlight other components involved in DPR power consumption, and lead to the proposition of three power models of different complexity and accuracy tradeoffs. Additionally, we illustrate the exploitation of these models to improve the analysis of DPR energy benefits in a realistic application example.