We study robust control policies for DC power networks with flexible line susceptances, or weights, subject to perturbations in supply-demand vector. The margin of robustness for a given control policy is defined as the radius of the largest `1 ball in the space of balanced perturbations under which the link flows can be asymptotically contained within their specified limits. We propose an optimization framework to compute universal upper bound on the margin of robustness for multiplicative perturbations, and a projected gradient descent heuristic for solution. An explicit expression for the sensitivity of link flows with respect to link weights is provided as part of the heuristic, and could be of independent interest. We propose decentralized control policies which are provably maximally robust for parallel networks in several scenarios. Simulation results are also presented to compare the empirical robustness of the proposed control policies with respect to heuristics on a benchmark non-parallel IEEE network.
['Qin Ba', 'Ketan Savla']
On decentralized robust weight control for DC power networks