Unit commitment in oligopolistic markets by nonlinear mixed variable programming

In the paper we consider the unit commitment problem in oligopolistic
markets. The formulation of the problem involves both integer and continuous variables
and nonlinear functions as well, thus yielding a nonlinear mixed variable programming
problem. Our formulation takes into account all technical constraints for
the generating units, such as ramp rate and minimum up and down time constraints,
considers the uncertainty related to the selling prices and allows modeling their dependence
on the total output of a producer. The objective function is the expected
value of the revenue over the different scenarios minus a term which takes into account
the risk related to the decision. To solve the problem we adopt a recently proposed
method for mixed integer nonlinear programming problems and use a derivative
free algorithm to solve the continuous subproblems. We report results for two
operators: one managing a single unit and the other managing three units. Numerical
results give evidence to the features of the modeling and show viability of the adopted
algorithm.