Abstract
This document presents an analysis in the development of a new mathematical formulation with which it will be possible to determine, through probabilistic approaches, the cost that can be generated if a diversified electricity market existed, in which the demand is able to actively participate. For this, it is considered that the electrical demand in a moment of time has associated a probability distribution and a system that makes it controllable. The cost of uncertainty of demand is mathematically developed by calculating the expected cost of supplying the most convenient demand value for the power system. The validation of the analytical formula is done through the Monte Carlo method, which allows us to compare the penalty costs in the case of underestimating or overestimating the demand for electrical energy. 
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