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
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Date
1984
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Massey University
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Abstract
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.
Description
Irregular pagination: missing pages 86, 208
Keywords
Energy analysis, Linear equations, Linear models, Energy use