Statistics of voltage drop in radial distribution circuits: a dynamic programming approach

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.