# Computing stuff tied to the physical world

## Measurement intervals and graphs

In Software on May 13, 2013 at 00:01

One more post about graphs in this little mini-series … have a look at this example: Apart from some minor glitches, it’s in fact an accurate representation of the measurement data. Yet there’s something odd: some parts of the graph are more granular than others!

The reason for this is actually completely unrelated to the issues described yesterday.

What is happening is that the measurement is based on measuring the time between pulses in my pulse counters, which generate 2000 pulses per kWh. A single pulse represents 0.5 Wh of energy. So if we get one pulse per hour, then we know that the average consumption during that period was 0.5 W. And when we get one pulse per second, then the average (but near-instantaneous) power consumption over that second must have been 1800 W.

So the proper way to calculate the actual power consumption, is to use this formula:

``````    power = 1,800,000 / time-since-last-pulse-in-milliseconds
``````

Which is exactly how I’ve been measuring power for the past few years here at JeeLabs. The pulses represent energy consumption (i.e. kWh), whereas the time between pulses represents estimated actual power use (i.e. W).

This type of measurement has the nice benefit of being more accurate at lower power levels (because we then divide by a larger and relatively more accurate number of milliseconds).

But this is at the same time also somewhat of a drawback: at low power levels, pulses are not coming in very often. In fact, at 100 W, we can expect one pulse every 18 seconds. And that’s exactly what the above graph is showing: less frequent pulses at low power levels.

Still, the graph is absolutely correct: the shaded area corresponds exactly to the energy consumption (within the counter’s measurement tolerances, evidently). And line drawn as boundary at the top of the area represents the best estimate we have of instantaneous power consumption across the entire time period.

Odd, but accurate. This effect goes away once aggregated over longer period of time.

1. “The pulses represent energy consumption (i.e. kWh), whereas the time between pulses represents estimated actual power use (i.e. W).”

This sentence is the whole truth. I searched long for a formula to compute the power of a S0-counter. So the result was: P (kW) = (3600/const of S0-counter ) / delta t

whereas const of S0-counter = counts for 1 kWh in above example: 2000 imp/kWh

thanks jcw for this “erhellend” article (sorry no dictionary near my hands).

2. For reference: http://dict.tu-chemnitz.de/ beolingus german/english online dictionary In this case the proper translation would “enlightening”, unfortunately not shown above, although “illuming” / “illuminating” should work and is shown.