Due to its relatively high total energy efficiency, the application of cogeneration, i.e. simultaneous exploitation of power and heat from the energy transformation process, is receiving increased attention. In many countries cogeneration is today an essential element in the energy supply system. In order to improve the operation of such systems, it is necessary to have detailed and reliable optimization models and methods available. The same is also desirable for pure heating systems, and for pure power systems. However, finding the optimal plan for production of heat and power, possibly also taking into account the optimal use of storage devices, is a difficult optimization problem.

Finding the optimal production schedule for the near future is known as the short-term planning problem or the unit commitment and economic dispatch problem. Typically a time horizon of up to one week, partitioned into one-hour time intervals, is considered. The problem may be characterized as a nonlinear mixed integer optimization problem, often large scale. In line with the development of optimization tools, a large number of optimization methods have been applied to obtain the solution. In recent years, methods based on Lagrangian relaxation have become the dominant ones, motivated by the separable structure of the problem.

The present thesis deals with mathematical models and Lagrangian relaxation based algorithms for short-term planning of cogeneration and power systems. Both deterministic and stochastic models are discussed. Using Lagrangian multipliers, Lagrangian relaxation is applied to the problem by either relaxing all unit-coupling constraints or all time-coupling constraints, which will decompose the (relaxed) problem into independent subproblems. This will also generate a corresponding dual problem. make the algorithms successful, it is necessary to have reliable methods for the solution of the dual problem and for the independent subproblems. The aim with the thesis is to present ideas and theories that may be exploited in such algorithms to make them more efficient.