The accurate measurement of power consumption by dielectric barrier discharge plasma actuators is a challenge due to the characteristics of the actuator current signal. Microdischarges generate high-amplitude, high-frequency current spike transients superimposed on a low-amplitude, low-frequency current. A high-speed digital oscilloscope was used to measure the actuator power consumption using the shunt resistor method and the monitor capacitor method. The measurements were performed simultaneously and compared to each other in a time-accurate manner. It was found that low signal-to-noise ratios of the oscilloscopes used, in combination with the high dynamic range of the current spikes, make the shunt resistor method inaccurate. An innovative, nonlinear signal compression circuit was applied to the actuator current signal and yielded excellent agreement between the two methods. The paper describes the issues and challenges associated with performing accurate power measurements. It provides insights into the two methods including new insight into the Lissajous curve of the monitor capacitor method. Extension to a broad range of parameters and further development of the compression hardware will be performed in future work.