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 Hoeffding´s 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.