Applications of linear modelling in energy analysis : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Technology at Massey University
The primary objective of this study was to explore the use of classical linear models in Energy Analysis; so as to resolve some of the methodological problems associated with Energy Analysis, and to extend the scope and potential of Energy Analysis as a scientific discipline. This was undertaken in the form of two separate yet related discourses. The first discourse provided a basis for resolving the energy quality problem encountered in Energy Analysis. A general equation was hypothesized and tested: [Equation] The matrix of simultaneous linear equations represented by this equation is usually overdetermined. Therefore, an appropriate solution method is a fitting procedure, such as regression. Further, in order to solve this general equation, one coefficient must arbitrarily be given a value equal to unity. Hence, all estimated coefficients are expressed in terms of multiples of that coefficient (termed quality equivalents). The general equation was first tes ted for the 1 97 6 New Zealand economy, so as to estimate 'actual' quality coefficients. Subsequently, the general equation was tested for a notional 'energy efficient' New Zealand economy, so as to estimate 'long run' quality coefficients, which reflected thermodynamic limits. Generally very accurate estimates of the coefficients were obtained. The solutions to the equations indicated that hydroelectricity was the highest quality primary energy source, followed by natural gas, oil, coal and then wood. The second discourse examined the 'optimal' use of primary energy resources in the New Zealand food system, using the formalism of Linear Programming. A preliminary discussion concluded that the concept of 'optimality' had greater potency than the concept of 'efficiency' in evaluating the use of energy resources, particularly in food systems. For each food sector (Production, Processing, Export-Import, Distribution, Catering and Household), coefficient matrices were assembled, drawing on literature data. Various combinations of constraints and objective functions were applied, in different Runs. The main objective functions used were minimising energy inputs for providing a nutritionally adequate diet , or maximising net energy gain from exporting agro-food products. The most critical constraints were found to be land area and market demand constraints. Detailed results of the Linear Programming runs are presented and discussed. An energetically 'optimal' diet was found to consist of large amounts of cereals, significant amounts of fresh fruit and vegetables and dairy products, and a very small amount of meat. Such a diet provided the Recommended Daily Allowances, for all nutritional elements, for the New Zealand population. Meat, Fish and Dairy products were found to have a particularly important function as commodities to be traded for imports of oil and energy intensive goods. A final discussion reviewed the use of Linear Models in Energy Analysis, and future directions for growth and development in Energy Analysis.
Energy analysis, Linear equations, Linear models, Energy use
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