Computing Optimal Control of Cascading Failure in DC Networks
This work addresses the problem of controlling cascading failures in power networks, which is important for system reliability, but the proposed methods are limited to specific network topologies and the results are theoretical without empirical validation on realistic benchmarks.
The paper tackles optimal control of cascading failure in DC networks, proposing two approaches to compute optimal control actions that steer the network to a feasible state. The first approach decomposes the problem for tree-reducible networks and achieves optimality in two iterations, while the second searches over a finite representation of the reachable set.
We consider discrete-time dynamics, for cascading failure in DC networks, whose map is composition of failure rule with control actions. Supply-demand at the nodes is monotonically non-increasing under admissible control. Under the failure rule, a link is removed permanently if its flow exceeds capacity constraints. We consider finite horizon optimal control to steer the network from an arbitrary initial state, defined in terms of active link set and supply-demand at the nodes, to a feasible state, i.e., a state which is invariant under the failure rule. There is no running cost and the reward associated with a feasible terminal state is the associated cumulative supply-demand. We propose two approaches for computing optimal control. The first approach, geared towards tree reducible networks, decomposes the global problem into a system of coupled local problems, which can be solved to optimality in two iterations. When restricted to the class of one-shot control actions, the optimal solutions to the local problems possess a piecewise affine property, which facilitates analytical solution. The second approach computes optimal control by searching over the reachable set, which is shown to admit an equivalent finite representation by aggregation of control actions leading to the same reachable active link set. An algorithmic procedure to construct this representation is provided by leveraging and extending tools for arrangement of hyperplanes and polytopes. Illustrative simulations, including showing the effectiveness of a projection-based approximation algorithm, are also presented.