I after I encountered the same problems mentioned by @PeterKietzmann in this thread when conducting the experiments for my thesis I did some experiments independent from that. I post this as a RIOT issue since according to Peter, the IoT-LAB tutorials do not produce this kind of output so this might be a RIOT problem.

I used the energy consumption monitoring feature of the IoT-LAB to measure with a period of 140 μs and an average of 4.

I used to setups:

First, I setup an application that went into main and left it immediately for idling:

int main(void) {
    return 0;
}

I did not add any other modules to the binary and disabled auto_init (so no xtimer or anything is running in the background).

The energy consumption for this looks as follows:

Also with an disabled auto_init I had another application running which remained in main()

int main(void) {
    while(1);
    return 0;
}

The spurious peaks are a known IoT-LAB issue: iot-lab/iot-lab#148, the saw-toothing however is not. The frequency of the tooths isn't constant and differs from experiment to experiment. They can be very long or very short (as seen above with my two experiments), but up until now they always were more likely in a resolution of seconds, not milli- or microseconds.