Riadh Zorgati

Supply Shortage Hedging: Estimating the Electrical Power Margin for Optimizing Financial and Physical Assets With Chance-Constrained Programming

This paper deals with estimating the maximal production capacity of a hydrothermal system. We will show why this is of interest and how such a problem arises in a context of hedging against supply shortage, using financial and physical assets. Therefore, we will formulate the supply shortage hedging as a stochastic optimization problem with chance constraints and show on an example why introducing physical assets in the hedging problem is of economical interest. We then highlight the inherent mathematical difficulties, introduced by optimizing physical assets. Using maximal production capacities of the hydrothermal system improves tractability of the hedging problem. However, focusing on the hydraulic production maximal capacity, we illustrate the combinatorial and nontrivial nature of this subproblem. Finally, we show how our problem formulation may lead to embedded chance constraints.

Stochastic nuclear outages semidefinite relaxations

This paper deals with stochastic scheduling of nuclear power plant outages. Focusing on the main constraints of the problem, we propose a stochastic formulation with a discrete distribution for random variables, that leads to a mixed 0/1 quadratically constrained quadratic program. Then we investigate semidefinite relaxations for solving this hard problem. Numerical results on several instances of the problem show the efficiency of this approach, i.e., the gap between the optimal solution and the continuous relaxation is on average equal to 53.35 % whereas the semidefinite relaxation yields an average gap of 2.76 %. A feasible solution is then obtained with a randomized rounding procedure.

Eddy-Current Modeling of a Continous Conductivity Profile Resulting From a Diffusion Process

This paper deals with the modelization of eddy-current measurements over combustion turbine blade coatings affected by depletion of aluminum. First, we model the response of an eddy-current coil over a layered metallic structure with a top over-aluminized coating by extending the analytical Uzal-Roses model for one hyperbolic tangent conductivity profile to a conductivity profile using two hyperbolic tangents for taking inward and outward depletion of aluminum inside the coating into account. Results obtained with this model are similar to those obtained with a numerical multilayer model but with a reduced computing time.

Semidefinite relaxations for mixed 0-1 second-order cone program

We investigate semidefinite relaxations for mixed 0-1 Second-Order Cone Programs. Central to our approach is the reformulation of the problem as a non convex Quadratically Constrained Quadratic Program (QCQP), an approach that situates this problem in the framework of binary quadratically constrained quadratic programming. This allows us to apply the well-known semidefinite relaxation for such problems. This relaxation is strengthened by the addition of constraints of the initial problem expressed in the form of semidefinite constraints. We report encouraging computational results indicating that the semidefinite relaxation improves significantly the continuous relaxation (112% on average) and that it often provides a lower bound very close to the optimal value. In addition, the computational time for obtaining these results remains reasonable.

Uncertainties on Power Systems. Probabilistic approach and conic approximation

The global cost optimization problem in the electrical industry is stated as a chance-constraint problem for taking uncertainties on power systems into account. Using a probability measure on offer-demand equilibrium at each time step leads to a tractable problem by bounding the probability with Hoeffdings theorem. We show that such a bound can be written as a conic quadratic constraint, therefore giving a convex nature to the problem. The obtained problem can then be efficiently solved using an interior point method. Typical results obtained with this approach are reported. They concern a mid-term problem and illustrate the impact of uncertainties on power systems composed of an energy mix made up of nuclear, coal, fuel, gas and hydro production units.

Eddy-current {NDE} of combustion turbine blade coatings. Determination of conductivity profiles in the presence of a diffusion process

This paper deals with the estimation of conductivity profiles using Eddy- Current measurements over combustion turbine blade coatings affected by depletion of aluminium. First, we model the response of an Eddy-Current coil over a layered metallic structure with a top over-aluminized coating by extending the analytical Uzal-Roses model for one hyperbolic tangent conductivity profile to a conductivity profile using two hyperbolic tangents for taking inward and outward depletion of aluminum inside the coating into account. Results obtained with this model are similar to those obtained with a numerical multi-layer model with a reduced computing time.