The solution of the power flow equations is of paramount importance for the design, operation, and control of (linear) electrical networks. The objective of the so-called power flow problem is to find operating conditions for a set of connected power generating units given load specifications. It is well-known that power flow equations are subject to uncertainty. Typical sources of uncertainty in power flow problems are generation or load profiles, line parameters, or network conditions. With increasing penetration of renewable energy sources a structured approach to solve uncertain power flow problems is desirable, especially for later use in context of power dispatch. When uncertainties in the power network are treated as random variables, the problem is referred to as stochastic power flow or probabilistic power flow.
The objective of the research project is to compare different (numerical) solution approaches to solve the stochastic power flow problem with respect to accuracy and simulation times. Viable approaches include (Markov chain) Monte-Carlo, two-point estimate methods, and/or unscented transforms.