Line failure probability bounds for power grids

We develop upper bounds for line failure probabilities in power grids, under the DC approximation and assuming Gaussian noise for the power injections. Our upper bounds are explicit, and lead to characterization of safe operational capacity regions that are convex and polyhedral, making our tools compatible with existing planning methods. Our probabilistic bounds are derived through the use of powerful concentration inequalities

Optimization of stochastic lossy transport networks and applications to power grids

Motivated by developments in renewable energy and smart grids, we formulate a stylized mathematical model of a transport network with stochastic load fluctuations. Using an affine control rule, we explore the trade-off between the number of controllable resources in a lossy transport network and the performance gain they yield in terms of expected power losses. Our results are explicit and reveal the interaction between the level of flexibility, the intrinsic load uncertainty and the network structure.Comment: 30 pages, 10 figure

On the optimal selection and integration of batteries in dc grids through a mixed-integer quadratic convex formulation

This paper deals with the problem of the optimal selection and location of batteries in DC distribution grids by proposing a new mixed-integer convex model. The exact mixed-integer nonlin-ear model is transformed into a mixed-integer quadratic convex model (MIQC) by approximating the product among voltages in the power balance equations as a hyperplane. The most important characteristic of our proposal is that the MIQC formulations ensure the global optimum reaching via branch & bound methods and quadratic programming since each combination of the binary variables generates a node with a convex optimization subproblem. The formulation of the objective function is associated with the minimization of the energy losses for a daily operation scenario considering high renewable energy penetration. Numerical simulations show the effectiveness of the proposed MIQC model to reach the global optimum of the optimization model when compared with the exact optimization model in a 21-node test feeder. All the validations are carried out in the GAMS optimization software.Fil: Serra, Federico Martin. Universidad Nacional de San Luis. Facultad de Ingeniería y Ciencias Agropecuarias. Laboratorio de Control Automático; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Investigaciones en Tecnología Química. Universidad Nacional de San Luis. Facultad de Química, Bioquímica y Farmacia. Instituto de Investigaciones en Tecnología Química; ArgentinaFil: Montoya Giraldo, Oscar Danilo. Universidad Distrital Francisco José de Caldas; Colombia. Universidad Tecnológica de Bolívar; ColombiaFil: Alvarado Barrios, Lázaro. Universidad Loyola Andalucia; EspañaFil: Álvarez Arroyo, Cesar. Universidad de Sevilla; EspañaFil: Chamorro, Harold R.. Royal Institute of Technology; Sueci