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You can make some useful estimates on short time peak power requirements from known energy use over a known time with some additional information.
Consider kwired's example of a church. Suppose the monthly energy consumption is 2000 kwh, the church has heavy usage of 8 hours per week, and and there is a base load of 1 kW. Next assume a 31 day month and 4 weekends per month. Base load is 1*24*31 = 744 kWh. This may be a good guess for a refrigerator and gas fired furnace plus some incidentals. Subtract this from the 2000 total and the result is 1256 kWh. There are 32 hours that produce this 1256 load or 39 kW is the added load. Thus, over some short time periods we can expect about 40 kW loads.
With a few measurements at some specific times you should be able to get some reasonable estimates. Summer, winter, and spring-fall will all have different values. You need to use some intelligent techniques plus some fudge factors and the results can be quite good.
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