Estimation of power system operation boundaries is an important issue in power system engineering. To make an adequate approximation of the operation boundary, not only the geometric properties of the boundary have to be taken under consideration but also the stochastic properties of the future injected power. In this paper two different distance functions on the power system operation boundary are suggested. The methods used to find the distance functions assumes that the future injected power can be modeled by a diffusion process. The proposed distance functions can be used when an approximation such as a Taylor's expansion of the power system operation boundary is needed. It is then suggested to use the point on the operation boundary that minimizes one of the proposed distance functions, as the basis for the approximation. Another possible application of the distance functions is when wanting to control power system equipment in order to increase stability margins.