Watts [W] to Watt-Hours [Wh]

Questions
#1

My understanding is that a Watts is the value of energy at any given moment in time and that a Watt-Hour is the aggregation of each watt moment of time value generated in one hour.

In an application designed to continuously read and record watt energy generated by a PV Solar system what is the standard moment of time. For example is it every second or some other interval?

If the application is designed to sample individual moments of time at say 10 second intervals where the watts at those intervals might have different value what then would be the formula to calculate those individual readings into an watt-hours.

#2

My system reports power (W) at 5 minute intervals. To convert that to Wh you just multiply each 5 minute value by 5/60 (~ 0.08333) and sum the 12 results that constitute an hour.

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#3

Strictly speaking the Energy (Wh) is the area under the Power curve or plot of Power (Watt) vs. time (hour). Mathematically Energy or Watt-hours is a function of Power and time E=f(P,t). If you can express the Power as a function of time mathematically you could use integral calculus to solve the problem. However, there is no neat function of Power and time that you can easily determine. Therefore, you are left with an approximation by determining the average power over a small intervals of time such as five minutes. So every five minutes the average power over that period can be multiplied by 5/60 ths of an hour to get one increment of Energy produced. Accuracy is determined by the increment and is generally smaller with decreasing intervals. If the average power over a 5 minute increment is 4000 kW then the Energy produced is 4000 X 5 / 60 or 333 1/3 Watt-Hours or 0.333 kWh. Summing the 5 minute increments of Energy over the time your PV system is producing power will give you the Energy produced for that day.

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#4

The problem with that is that it is quite inaccurate. Power values are usually spot samples so you could say the reported value is a random number between the min and max power value that occurred in the period. You are then accumulating this random value over the period to compute a dubious energy counter. This is true for both generation and consumption although consumption usually varies more randomly so is more problematic to derive from a power value.

Collecting and plotting power values is a waste of time. It is only accurate to collect proper metered energy counters and if you want to see power values then you should simply derive the average power value from the start and end energy counters over the period (i.e. power is just the slope of the energy curve, i.e. rate of change of energy). Energy is what you actually pay for so is the fundamental quantity that matters.

OP, on posts here (and WP forum where I also visit) it is astounding how much confusion is seen regarding the difference between energy and power. Perhaps a simple analogy is that energy (kWh) is analogous to distance (km) and power (kWh per hour) is analogous to speed (km per hour). You pay for the energy you use, i.e. you pay for the distance you travel. The speed you travel to get there may vary quite a bit but is irrelevant to what you get charged at the end of the day.

#5

If your system is not reporting the power for each interval accurately then your calculations will (duh) not be accurate.
I have Enphase inverters and they report power at 5 minute intervals. (Although lately they seem to have switched to 15 minute intervals). I assume that they are reporting the average power for that interval. If not, then the data is bad.

#6

Enphase inverters, and probably most other inverters, also report energy generated in Wh. In this case, the inverter is acting as a digital Wh meter and is sampling the current and voltage at a very high rate internally to give you accurate energy values. Using the measured energy from your inverter or meter is the better way to get accurate energy data.