Energy Meters

If I understand you question correctly, and you are referencing a "standard" watt hour meter, there is no way to calculate it other than the obvious one of taking readings at constant intervals over the period of time in question (for instance every hour) and then comparing the differences. The intervals don't have to be constant if you normalize them for the interval, but watt hour meters only record total usage occurring between successive readings.

The most active time of usage is when there is the greatest load turned on downstream of the meter.

Some things respond better to investigation and measurement rather than calculation. This may be one of them.

Log KW over the time period in question.

KW is the rate of energy use, so the highest kW reading over a time period would theoretically be the "MOST ACTIVE TIME OF [energy] USE" if I understand your question correctly.

The easiest and most accurate way would be to switch the watt meter to one of the types that takes continuous multiple readings at successive intervals to give you a record of power consumption over time. Some of the public utilities are going to these type of meters now so they can zap you for a lot more money for your consumption during peak usage hours. If you can't switch your meter, a good plan B would be to do like a few others mentioned above and take regular successive readings and do some math.

The simplest way is chart the current over several 24 hour periods. There is plenty of gear around to do this. A tong tester with proportional analogue output connected to a chart or a data logger makes it dead easy. If you want to do it permanently modern KWH meters for industrial customers have facilities built in, check with your supply authority regarding the cost of change over. Alternatively use a PLC to log the data permanently and upload it to something like Citect, which can trend it as long as you like.