Active network management for electrical distribution systems: problem formulation, benchmark, and approximate solution

With the increasing share of renewable and distributed generation in electrical distribution systems, active network management (ANM) becomes a valuable option for a distribution system operator to operate his system in a secure and cost-effective way without relying solely on network reinforcement. ANM strategies are short-term policies that control the power injected by generators and/or taken off by loads in order to avoid congestion or voltage issues. While simple ANM strategies consist in curtailing temporary excess generation, more advanced strategies rather attempt to move the consumption of loads to anticipated periods of high renewable generation. However, such advanced strategies imply that the system operator has to solve large-scale optimal sequential decision-making problems under uncertainty. The problems are sequential for several reasons. For example, decisions taken at a given moment constrain the future decisions that can be taken, and decisions should be communicated to the actors of the system sufficiently in advance to grant them enough time for implementation. Uncertainty must be explicitly accounted for because neither demand nor generation can be accurately forecasted. We first formulate the ANM problem, which in addition to be sequential and uncertain, has a nonlinear nature stemming from the power flow equations and a discrete nature arising from the activation of power modulation signals. This ANM problem is then cast as a stochastic mixed-integer nonlinear program, as well as second-order cone and linear counterparts, for which we provide quantitative results using state of the art solvers and perform a sensitivity analysis over the size of the system, the amount of available flexibility, and the number of scenarios considered in the deterministic equivalent of the stochastic program. To foster further research on this problem, we make available at http://www.montefiore.ulg.ac.be/~anm/ three test beds based on distribution networks of 5, 33, and 77 buses. These test beds contain a simulator of the distribution system, with stochastic models for the generation and consumption devices, and callbacks to implement and test various ANM strategies.