Optimal operation of power systems.
Thesis DisciplineOperations Research
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
This thesis is primarily concerned with the solution of the long-term scheduling problem for mixed hydro-thermal systems such as that of the former New Zealand Electricity Department (NZED - now the Electricity Division of the Ministry of Energy). Chapters 2 to 6 describe our model for the solution of the deterministic version of this problem. This model, an adaptation of the Electricité de France (EDF) models outlined in Appendix A, involves the use of "energy prices" (Lagrange multipliers) to decompose the problem into manageable sub-problems. Our model differs from that of the EDF in the following ways. Firstly, instead of dealing with aggregate national loads, it is a multi-load model in which losses and restrictions in the transmission system are explicitly modelled. Secondly, we have adopted a more flexible scheme to ensure that short-term requirements are met. In particular we have developed a new approach to the scheduling of river chains in the short-term. Thirdly, we have generalised their approach so as to handle more realistic (non-convex) cost (and loss) functions. Finally, the nature of the NZED system (and of our model) has required the adoption of a more sophisticated approach to the adjustment of the "prices". Chapter 7 describes the application of this approach to the NZED system. Chapter 8 uses some recent results on the optimal recourse problem to generalise this model into a stochastic framework. Chapter 9 uses this abstract stochastic model to analyse some earlier approaches and to suggest a new method for the solution of realistic stochastic scheduling problems. Finally, Chapter 10 shows how the prices developed in the solution of the scheduling problem may be used in other contexts. In particular, a simple adaptation allows the "optimal tariff problem" to be solved exactly.