On the integration of unit commitment and optimal power flow

For over twenty years, Lagrangian relaxation has been the algorithm of choice for solving the unit commitment problem in the electric power industry. This is because it is the only algorithm that exploits the problem structure and results in separation with price coordination when the dual problem is posed. The advantage is that the computational cost of a given iteration becomes linear in the number of discrete variables, whereas without separation the combinatoric complexity of the problem soon becomes overwhelming. However, classical Lagrangian relaxation requires linear constraints to insure separation, and only linear network models can be used. As a result, classical Lagrangian relaxations can be inaccurate and require post-processing and redispatching which adds to the actual cost of operation. This work proposes a formulation and solution algorithm that retains the advantages of classical Lagrangian relaxation while allowing the use of a nonlinear AC network model. The algorithm retains the good scalability properties of classical Lagrangian relaxation techniques, as well as the parallelizable structure of the computation. This property has been exploited and a parallel code has been written in order to test the algorithm on the larger problems. The numerical experiments all indicate that the algorithm converges in a manner similar to that of classical Lagrangian relaxation.