First Advisor

Harold Linstone

Term of Graduation

Spring 1977

Date of Publication

Spring 5-12-1977

Document Type


Degree Name

Doctor of Philosophy (Ph.D.) in Systems Science


Systems Science




Electric power production -- Mathematical models



Physical Description

x, 179 pages


The energy resource planning process for electric utilities in the Northwestern United States is unique because the region relies upon a mix of hydro and thermal resources. Consequently, methods used to study predominantly thermal or predominantly hydro systems are not applicable. Methods are needed to determine if a particular configuration of resources will be adequate to meet future energy load, taking into account various sources of uncertainty. A literature survey of presently available methods is described, and one method is studied in some detail. A new method for analyzing systems that rely upon a mix of hydro and thermal resources is then described.

The primary contributors to uncertainty in a hydro/thermal electricity supply system are: (1) uncertain rainfall and snowfall, which results in uncertain availability of hydro energy; (2) the uncertain arrival times of planned nuclear and coal plants; (3) uncertain capacity factors for thermal plants; and (4) the uncertain amount of energy that customers will require in future years. The new model, called CHANCE, characterizes each of these uncertain phenomena with a probability density function.

Mathematical convolution and an algorithm developed by the author are then used to determine the probability density function for the energy margin--the difference between supply and demand. Measures of the "energy adequacy" of the supply system are then computed from the energy margin probability density function. A computer program was designed so that the conceptual model can be easily applied to any desired electrical supply system. Once an appropriate set of input assumptions h2ve been determined, they are easily entered into the computer via a question and answer sequence and stored for future use. The computer program then computes the energy adequacy of the system. The user can then change assumptions and/or resource schedules via a question and answer sequence, and recompute the energy adequacy. The computer then prepares a report showing how the alternative assumptions and/or schedules compare.

CHANCE has been applied to Pacific Power and Light Company, Portland, Oregon. At the present time, about half of their energy is generated by hydro plants and the other half is generated by coal plants. Only a small fraction is generated by nuclear plants. All planned additional generation is either coal-fired or nuclear-fired. The results of applying CHANCE indicate that planned resources are not likely to be adequate to meet the needs in the early 1980's.

Several evaluation exercises have also been carried out. First, CHANCE was calibrated against other electrical energy planning models used by Pacific Power and Light. Next, the sensitivity of the CHANCE model to changes in input assumptions was measured. As was anticipated, the model is highly sensitive to the assumed energy load forecast, to the assumed potential delays in the arrival of resources, and to the assumed thermal plant capacity factors. Thus, more research in these areas is warranted.

Research that might lead to improvements in the CHANCE model is then outlined, and final conclusions are drawn. The final conclusions are that the CHANCE model: (1) is valid relative to the outlined scope, (2) is quite versatile and flexible, and (3) fulfills an important need in electrical energy planning.


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