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

TL;DR

This paper presents a dynamic programming algorithm to efficiently compute the probability distribution of maximum voltage drops in radial distribution circuits with high variability and uncertainty, aiding risk assessment.

Contribution

It introduces a novel dynamic programming approach to calculate voltage drop probabilities in distribution lines with uncertain loads, assuming load independence.

Findings

Algorithm achieves linear complexity in the number of buses.

Effectively models voltage drop risks under load variability.

Demonstrated on a 4-bus system with high load fluctuations.

Abstract

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.