Abstract:
A continuous-time model is formed of a hydro-electric scheduling problem, and recent advances in the theoretical understanding of separated continuous linear programs are used to develop several continuous-time algorithms robust enough to solve this model. The algorithms that we develop are based on a general principle we have called adaptive discretisation. A generalisation of the finite-dimensional Out-of-Kilter algorithm to continuoustime network programming is developed. This algorithm proves to be only partially successful. An adaptive discretisation approach to separated continuous linear programs yields two new algorithms. One algorithm solves a class of problems which have been previously addressed in the literature, and the second solves a variation of this problem class for which no algorithm previously existed. Numerical results show that these adaptive discretisation algorithms are all computationally efficient and produce accurate optimal solutions. A continuous-time model of the Waitaki Power Development of New Zealand is constructed and solved by an application of a continuous-time algorithm employing adaptive discretisation. This model differs from previous work by allowing the station output to vary as a piecewise linear function. In this way the power development can respond more naturally to the timevarying demand giving new insights into the forms of solutions to these problems. Techniques for addressing the unit commitment problem using a continuous-time model are discussed.