Invited Session Tue.1.MA 550

Tuesday, 10:30 - 12:00 h, Room: MA 550

Cluster 18: Optimization in energy systems [...]

Nonlinear and combinatorial aspects in energy optimization


Chair: Antonio Frangioni



Tuesday, 10:30 - 10:55 h, Room: MA 550, Talk 1

Sofia Zaourar
Prices stabilization for inexact unit-commitment problems

Coauthor: Jérôme Malick


Unit-commitment (UC) problems in electricity production are well-suited for constraint (or price) decomposition techniques: by dualizing the linking constraints, the large-scale nonconvex problem decomposes into smaller independent subproblems. The dual problem consists then in finding the best Lagrangian multiplier (the optimal price); it is solved by a convex nonsmooth optimization method.
Realistic modeling of technical production constraints makes the Lagrangian subproblems themselves difficult to solve. It is possible for bundle algorithms to cope with inexact solutions of the subproblems. In this case however, the computed optimal dual variables show a noisy and unstable behaviour, that could prevent their use as price indicator.
In this talk, we present a way to stabilize dual optimal solutions by penalizing the noisy behaviour of the prices in the dual objective. After studying the impact of a general stabilization term on the model and the resolution scheme, we present total variation stabilization and its primal interpretation. We illustrate our approach on the real-life UC problem of Electricite de France (French Electricity Board).



Tuesday, 11:00 - 11:25 h, Room: MA 550, Talk 2

Antonio Frangioni
Exploiting structure in MIQP approaches to unit commitment problems

Coauthor: Claudio Gentile


The unit commitment problem in electrical power production is naturally formulated as a mixed-integer quadratic program; as such it could be solved with general-purpose MIQP tools, but direct application of this approach using the standard formulation is not efficient. Yet, the problem presents several (possibly nested) sources of structure, from the space decomposability usually exploited by Lagrangian Relaxation approaches (leading to smaller, very structured MIQP subproblems for which efficient specialized methods exist) to the presence of very many semicontinuous variables with convex nonlinear cost (which suggests the use of perspective reformulation techniques to strengthen the lower bound). We discuss novel ways of exploiting some of these structures, possibly in combination, reporting computational results to help gauging their potential effectiveness.



Tuesday, 11:30 - 11:55 h, Room: MA 550, Talk 3

Maria Teresa Vespucci
A procedure for minimizing variations of an initial operating point in medium-voltage AC network with distributed generation and storage devices

Coauthors: Alberto Gelmini, Mario Innorta, Diana Moneta, Dario Siface


An optimization algorithm is described for the voltage control of medium voltage distribution networks in presence of distributed generation. Given the current operating point and the forecasted load and generation, the algorithm computes the changes to be requested to the controllable resources in order to ensure fulfillment of technical constraints (voltage at nodes, current in branches) with the lowest overall cost. Distributor's redispatching costs, modelled by means of binary variables, are minimized while satisfying service security requirements and ensuring service quality, represented by nonlinear constraints. Storage devices are modeled by means of constraints that relate adjacent time periods. The proposed two-step solution procedure is based on decoupling active and reactive variables. In step 1 a MILP model determines the active power production and the use of storage devices that minimize redispatching costs over all periods in the time horizon: in this step a DC network representation is used. In step 2, given the optimal active power productions computed in step 1, reactive variables in each time period are computed by solving an AC optimal power flow model.


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