Mohammadreza Chamanbaz — Research — Optimal Power Flow Design

Optimal Power Flow Design Under Renewable Generation and Load Uncertainty

We consider AC optimal power flow (OPF) problems in the presence of uncertain loads and renewable generators. Goal of OPF design is to guarantee that controllable generation is dispatched at minimum cost, subject to operational constraints on generation and transmission. The high variability of renewable generation, such as wind power, and the presence of uncertain loads, requires the use of new methodologies to guarantee that the proposed solutions continue to work for the different possible uncertain scenarios.

We employ an approach based on a randomized technique recently developed, which allows to tackle the problem without assuming any a-priori dependence of the voltages in the network from the uncertain generators/loads. The proposed solution can exploit the usually available probabilistic description of the uncertainty and variability, and provides solutions with a priori probabilistic guarantees.

This work is done in collaboration with Dr. Fabrizio Dabbene and Prof. Constantino Lagoa.

Line loading percentage for 10,000 random samples extracted from the uncertainty set. In this figure the dispatch policy is designed based on randomized approach. The line loading does not exceed its limits in almost all scenarios. In the boxplots, the red line represents the median value, edges of each box correspond to the 25th and 75th percentiles, whereas the whiskers extend to 99% coverage. The magenta marks denote the data outliers.

This figure represents a scanario where the solution to standard optimal power flow design is used (where no uncertainty is taken into account in the design) but some uncertainty appears in the renewable power generators. The line loading exceed its limits very frequently. This can lead to line trip or even casdading failures.

Comparing the two figures one can observe that ignoring the uncertainty in renewable power generator in the design of dispatch policy can lead to significant dammage to the power grid.


  • M. Chamanbaz, F. Dabbene, C. Lagoa, “AC Optimal Power Flow in the Presence of Renewable Sources and Uncertain Loads”, IEEE Transactions on Control of Networked Systems, Submitted PDF.