A Lagrangian Decomposition Algorithm for Optimal Emergency Voltage Control

Voltage control problems typically involve large networks comprising diverse components extending over considerable areas and interconnecting different grids and operators. To deal with such systems, there has been over the past few years a steadily increasing interest in model predictive/optimal control techniques as a viable solution. In such a setting, it is essential to be able to coordinate the control actions among the various grids while preserving sensitive local system data that regional operators are often not willing to disclose. In view of these discordant factors, centralized and decentralized control schemes, respectively, yield advantages and drawbacks: the former require global system data to be accessible whereas the latter may prove to be difficult to effectively implement or might achieve suboptimal performance. The present paper therefore proposes a centralized control scheme that is solved however in a distributed fashion through a Lagrangian decomposition algorithm, thus reaping the benefits of both approaches: the control problem is global, therefore intrinsically more reliable and comprehensive, but only local information is employed to achieve the overall optimum control input. The computational delay associated with the additional iterations required by the algorithm is shown to be viable for the considered application and can furthermore be inherently accounted for within the proposed optimal control scheme.