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This thesis is concerned with the optimal scheduling of hydro-thermal power generation systems. This problem, usually referred to as the unit commitment and economic dispatch problem, manifests itself as a large scale mixed integer programming problem. In the first instance a linear model is built and solved using branch-and-bound. This approach is, however, very expensive in terms of computational time. Using Lagrangian relaxation the original primal problem may be written in a dual formulation: the problem then admits decomposition into more tractable subproblems. Furthermore, the primal solution can be approximated closely from the dual solution using the duality gap as a termination criterion. A heuristic is used to construct nearly optimal solutions to the primal problem based on the information provided by the dual problem. The decomposition is such as to allow an implementation on a transputer array with significant reductions in the computational time. An investigation into the application of genetic algorithms to power scheduling shows that this approach is feasible although expensive in terms of computational time. Lagrangian relaxation is next used to solve a nonlinear model incorporating the purchasing and selling of electricity. The information provided by the Lagrange multipliers which can be interpreted as shadow prices, is used to determine the best strategy for the purchasing and selling of energy. Nonconvex programming problems such as this may exhibit a duality gap, that is a difference between the optimal solution of the primal and dual problems. An investigation of this problem for power scheduling linked the existence of this gap to the operating constraints of the system.

The prediction of mass oscillation behaviour is an important part of the hydraulic design of a hydro-electric power scheme containing one or more surge chambers. Currently design practice is to employ computational models. However, the use of hydraulic models in the design of large or complex surge systems provides a useful means of corroborating results from computational studies. This thesis is concerned with the development of techniques for improving the accuracy of both methods. The first part of the thesis deals with the formulation of equations and techniques required for the development of a computer program capable of analysing a wide range of chamber configurations. The majority of these techniques are employed in a computational model, the salient features of which are discussed in some depth. The second section is concerned with the derivation of scaling relationships between prototype schemes and their corresponding hydraulic models. This is supplemented by a discussion of some practical aspects in the design and construction of models. The study culminated in the construction of a hydraulic model of the 1800 MW Dinorwig scheme. Advances in microcomputer technology have enabled them to be used, at reasonably low cost, in customised monitoring/control systems which improve the quality of hydraulic model tests. A number of techniques were developed which were incorporated in a program package for a 32 kilobyte microcomputer for use with the Dinorwig model. Further techniques are discussed in which monitored data is susbjected to further computational analysis. This includes a technique for combining results from hydraulic and computational models to produce a more accurate prediction. These techniques were used in a study of the Dinorwig scheme which revealed that as a result of an amendment to the chamber design, the original specification for the limits of surge amplitude are not satisfied.

In this thesis a mathematical and computer model is formulated to accurately represent the behaviour of the hydraulic and mechanical systems in a hydro power plant. It includes the elastic behaviour of the hydraulic system and the actual operating characteristics of the hydromachines under consideration. After verifying the accuracy of this detailed hydraulic/mechanical model, frequency response tests are conducted to enable a comparison to be made with the IEEE transfer function model. This transfer function although widely used and accepted as a hydro power scheme model in power system and governor studies (1-5) does not represent waterhammer in the hydraulic system or the actual behaviour of the hydromachines. The frequency response tests which are reported in this thesis clearly highlight the severe practical limitations of this model at both low and high frequencies of governor operation. The frequency response results for the detailed hydraulic/mechanical model also enable improved linear transfer functions to be derived. Finally, with the aid of an existing power system stability computer program, the responses of the detailed hyrdaulic/mechanical model, the derived linear transfer function model and the IEEE transfer function model to variations in load are compared in the time domain.