Dynamic Circuit Specialization (DCS) is a technique for optimized FPGA implementation and is built on top of Partial Reconfiguration (PR). Dynamic Partial Reconfiguration (DPR) provides an opportunity to share the silicon area between different Partially Reconfigurable Modules (PRMs) and therefore results in smaller and faster designs that potentially also reduce the power consumption. In this paper, we show that energy consumption is an important factor that has to be considered while implementing a parameterized design using DCS. In order to make a good choice for implementing a parameterized design with the goal of power optimized implementation, it is important to have a good power consumption estimate of the Dynamic Circuit Specialization. In this context, our paper presents a detailed investigation of the power consumption of a parameterized design implemented using DCS on the Xilinx Zynq-SoC FPGA. We propose an energy analysis of DCS and investigate the benefits of the use of DCS in comparison with a classic static FPGA implementation. We see that the power needed for the reconfiguration is much higher than the gain in power using the reconfiguration over the static implementation. An important reason is because of the CPU involved during the reconfiguration and the interface between the AXI bus and the HWICAP. To reduce the reconfiguration power, we include a clock gating technique to the reconfiguration interface AXI-HWICAP that makes DCS more power efficient. We also relate the power gain to the size of the implementation and to the allowed time to reconfigure versus the useful run time. We conclude that for an implementation with 10 FIR filters, the reconfiguration time should not take more than 30.3% of the total time in order to remain energy efficient. Considering a specific use case with 10 FIR filters at a reconfiguration rate of 0.01, the energy consumption using DCS implementation is 20.5% lower than using the static FIR.