In certain cases load power is described by discrete distribution rather than normal distribution in the general literature. Which kind of actual load does it corresponds to in the real power system?
There is a considerable difference between stochastic and random. Stochastic is not complete random, and it is the combination of deterministic and random nature. I don't think any load (component level/ aggregate load at bus level) can vary too randomly and its not feasible to assume them as such since the load is always varies slightly across the means so normal distribution is the better option.
May be components operating at very LV lelvel (e.g. electronic circuuits) fit the random distribution ....