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We study the problem of distributed optimal resource allocation on networks with actions defined on discrete spaces, with applications to adaptive under-frequency load-shedding in power systems. In this context, the primary objective is to identify an optimal subset of loads (i.e., resources) in the grid to be shed to maintain system stability whenever there is a sudden imbalance in the generation and loads. The selection of loads to be shed must satisfy demand requirements while also incorporating criticality functions that account for socio-technical factors in the optimization process, enabling the algorithms to differentiate between network nodes with greater socio-technical value and those with less critical loads. Given the discrete nature of the state space in the optimization problem, which precludes the use of standard gradient-based approaches commonly employed in resource allocation problems with continuous action spaces, we propose a novel load-shedding algorithm based on distributed root-finding techniques and the novel concept of cumulative criticality function (CCF). For the proposed approach, convergence conditions via Lyapunov-like techniques are established for a broad class of time-varying communication graphs that interconnect the system's regions. The theoretical results are validated through numerical examples on the Quebec 29-bus system, demonstrating the algorithm's effectiveness. |
