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. Advanced ANM strategies imply that the system operator has to solve large-scale optimal sequential decision-making problems under uncertainty. For example, decisions taken at a given moment constrain the future decisions that can be taken and 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

A Gaussian mixture approach to model stochastic processes in power systems

peer reviewedProbabilistic methods are emerging for operating electrical networks, driven by the integration of renewable generation. We present an algorithm that models a stochastic process as a Markov process using a multivariate Gaussian Mixture Model, as well as a model selection technique to search for the adequate Markov order and number of components. The main motivation is to sample future trajectories of these processes from their last available observations (i.e. measurements). An accurate model that can generate these synthetic trajectories is critical for applications such as security analysis or decision making based on lookahead models. The proposed approach is evaluated in a lookahead security analysis framework, i.e. by estimating the probability of future system states to respect operational constraints. The evaluation is performed using a 33-bus distribution test system, for power consumption and wind speed processes. Empirical results show that the GMM approach slightly outperforms an ARMA approach.GREDO