  We analyze a power distribution line with high penetration of distributed
generation and strong variations of power consumption and generation levels. In
the presence of uncertainty the statistical description of the system is
required to assess the risks of power outages. In order to find the probability
of exceeding the constraints for voltage levels we introduce the probability
distribution of maximal voltage drop and propose an algorithm for finding this
distribution. The algorithm is based on the assumption of random but
statistically independent distribution of loads on buses. Linear complexity in
the number of buses is achieved through the dynamic programming technique. We
illustrate the performance of the algorithm by analyzing a simple 4-bus system
with high variations of load levels.
