Stochastic, Computational and Convergence Aspects of Distribution Power Flow Algorithms

This paper discusses uncertainties in distribution system analysis. Special emphasis lies with distributed generation (DG) units. Both backward-forward sweeps and Newton-Raphson based current injection updates are discussed. A first class of stochastic modeling is of probabilistic nature. In analytic probabilistic methods a linearization of the power flow equations is applied. Non-linearities are respected in numerical Monte Carlo analysis when using the appropriate convergence criteria. The second class uses qualitative uncertainty descriptions in boundary and fuzzy power flow methods. Correlation of loads and DG is always a crucial aspect. These aspects are elaborated with regard to robust methodologies for setting benchmarks of DG performance based on stochastic programming and evolutionary algorithms.