On a flexible model for New Zealand's hydro-thermal electricity generation system : a thesis presented in partial fulfilment of the requirements for the degree of Ph.D. in Operations Research at Massey University
This thesis investigates the modelling of the New Zealand hydro-thermal electricity generation system in order to determine an optimal strategy for generation, in terms of minimizing fuel costs. The model currently used by ECNZ (Electricity Corporation of New Zealand) uses an SDP (Stochastic Dynamic Programming) method for solution; this allows little detail of the physical system, and models two explicit hydro reservoirs. The model developed in this thesis is flexible, in order to allow the balance between ensuring stochastically stable solutions and the detail of the physical system, to be altered, whilst ensuring computational tractibility. The areas of the system which are important to be modelled accurately are isolated, as are those which may lead to computational intractibility if they are modelled in too much detail. The flexibility in the model also allows the effects of the approximations used on solutions to be explored in a wider framework. The time horizon of the model is one to two years, with time steps of the order of a week. The time horizon describes the level to which many aspects of the system are to be modelled. Transmission is modelled explicitly so as to include information on the geographical locations of power stations and power users; this takes the form of a network structure underlying the model. The load at each geographic location is represented by a Load Duration Curve (which is more robust, in terms of forecasting, than a direct representation of load with respect to time). Hydro river chains are modelled as single power stations with a single reservoir and connect the model temporally; we model six explicit hydro river chains. Thermal stations are modelled individually, and the generation from run-of-river and geothermal stations is removed from load before solution begins. The initial approach considers a model which, upon further investigation, is unacceptable. However, examination of the issues highlighted by this approach provide insight into the system. The resultant re-modelling of the problem leads to a linear model which does not explicitly model the uncertainty in the generating capacity of stations due to forced outages. This accentuates the reason why the usual approach to explicitly modelling the uncertainty of supply (within a week) cannot be used in the case where the geographic distribution of generation has been explicitly modelled. The deterministic model may then be formulated as a Generalized Network with side constraints. The deterministic model developed can be extended stochastically in many ways. The stochastic extension investigated uses Rockafellar and Wets' Progressive Hedging Algorithm. This takes a scenario approach, in which the stochastic variables are approximated by a number of scenarios of observed values. A policy is required which minimizes the expected cost of generation over these scenarios, ensuring that information on the observed values of the stochastic variables is not used before it would be available in practice. Results and implementation issues are discussed for both the deterministic and stochastic models. Consideration is given to the implementation of a finished product, as well as implementation for the purposes of investigating the feasibility and examining the computational effectiveness of approximations made in the model.