I have a 5 V 5 A power source which is connected to a simple development board with a processor that draw current dependent on utilization. I use a multimeter that measure 1000 samples / s to measure energy consumption. I measure a voltage drop across a shunt resistor coupled in series with the input power to calculate average power and energy consumption of the development board. My question is : What can we say about error in this case ? Between two samples with a 1 ms interval, how frequent and how much can the power fluctuate in this interval ? Is there any way to find this out ? It would be unfortunate if there are several violent spikes between the samples.
In order to overcome these sort of sampling measurement errors you can make the problem "easier" by adding a large electrolytic capacitor on the power feed to the development board after the series measurement resistor. This is an "attempt" to measuring average current taken by the dev board. OK, I say you are measuring "average" but it depends how big your capacitor is in uF terms and how long your "violent spikes" are.
If you have a 1 ohm series resistor and a 100uF capacitor, the time constant of this is 0.1ms so you'll need more capacitance or more resistance. To get reasonably decent measurements go for a time constant of about 10ms - this should suit your multimeter.
As an aside, your multimeter may be perfectly capable of averaging over a 1ms period and giving you the results you think you may not be getting.