It will help us answer your question if you explain in more detail. For example, we do not know if you are exploring the usage of individual consumers or of the entire market. How will the estimates of the usage each minute be used?
It sounds like the amount of electricity used over a give hour is available. If it is not available over shorter time periods, then it could be estimated; however, caution is urged. The accuracy of 59 estimates each hour, in conjunction with one actual observation, leads to all kinds of issues depending on how you might be using these estimates.
If you average the data by dividing by 60, you will lose its variation. Since you seem familiar with simulation, you can randomly fit the hourly data into 60 slots using simulation. Let the data for one hour be “n”. Imagine you have 60 cells to fill, then for 1 to n, make a random draw with a probability of 1/60 and put it randomly into the one of the 60 cells. (You may want to make a distinction of cells during peak and non-peak hour of usage). You will also have to specify a probability distribution from which to draw the data. Note that Excel has many random distribution that you can use.