Abstract
Analysis of investment decisions in the electric sector is a subject with a long history of scholarship, with a rich literature, and extensive applications in practice. Many complex mathematical models are used by electric utilities for planning purposes, some of which, such as the WASP model, have found application in a number of developing countries.1 But given the existence of a number of excellent literature reviews, such as that of Anderson (1972), we shall not attempt to provide any detailed review here. Rather, the emphasis will be on an elaboration of the fundamental concepts involved, and an exposition of modelling approaches that lend themselves to integration with other energy sectors, or to integration with energy system-wide and economy-wide models. Thus, while many of the finer points of reliability analysis, and transmission line planning, are not taken up in any great detail here, we pay a great deal of attention to the interaction between investment requirements in the electric sector to investment flows throughout the economy — a subject taken up in some detail in Chapter 10.2 In this chapter, then, we develop the fundamental concepts; the linearization of load duration curves, formulation of the investment decision as a mathematical programming problem, the complications arising from the addition of a spatial dimension, and some environmental considerations.
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References
WASP (for Wien Automatic System Planning Package) is a series of six computer codes originally developed for a study of developing countries by the International Atomic Energy Agency (IAEA), and is designed to find the optimum power system expansion plan. By minimizing the discounted cash flow of all capital and operating expenses over the study period Dynamic programming techniques lie at the heart of the system. See IAEA (1973), Appendix A for details.
For an excellent presentation of the details of electric sector planning in the context of developing countries, see Munasinghe (1979).
Hydroelectric capacity, whether conventional or pumped storage, is less amenable to such generalizations, as we shall see in later sections.
When we ignore, for the sake of simplicity of notation, non-fuel operating costs (that may be a function both of installed capacity, or operating level, or both).
Anderson and Thanart (1972), for example, in their study of Turkey, used four segments, using a nine segment trial run only to identify the degree of error introduced by use of the four-segment scheme.
This is only one of several issues in computational optimality in very large linear programs, which, when both time and space dimensions are added, can quickly reach several thousand constraints and variables. Modern LP algorithms, mostly proprietary packages developed by the computer hardward manufacturers (such as the Control Data Corporation APEX-III code, or the IBM MPSX package) function best when the coefficient matrix is tridiagonal in structure (i.e., with as many zeros above the diagonal as possible) and with as few equality constraints as possible. Tridiagonality, as in the case of scaling, requires thought by the analyst (by rearranging the order of appearance of rows and columns in the matrix generator). Substitution of equality constraints by inequality constraints should also be done by the analyst whenever possible, although some automated options, such as the REDUCE option in the APEX code, automatically make such conversions (in addition to eliminating any redundant constraints and variables).
The controversy surrounding the discrepancy between ex ante expectations and actual reliability are well known, particularly for the larger baseload units whose economic depend critically on plant factors. The prudent analyst does a series of runs with different values of the plant factor in such situations, to determine the robustness of the predicted investment decision as a function of such assumptions.
The use of such transhipment model formulations for power system analysis appears to have been first used in the USSR-the earliest such reference in the literature known to the author is Makarova et al., (1966).
The assumption here is that baseload generated in one region is used in the baseload portion of the curve the other region, and so on. In the presence of diversity, this need not necessarily be so, and baseload generation in one region might serve intermediate load in the other. Indeed, diversity among adjacent systems is one of the reasons for interconnection — if the peaks are not coincident, then the peak of the interconnected system is less than the sum of the individual peaks, which lowers the total generation capacity required in the interconnected system to meet the same reliability criterion.
Even though this formulation includes a time dimension to capture seasonalities, such a model would not normally be classified as “dynamic.” Dynamic is a categorization generally applied only to models that attach a time dimension to the investment decision path — which the model being described here does not do.
Borenstein (1974) has explored a more sophisticated method of incorporating reliability issues using chance-constraints, but concludes that an adequate treatment within an LP framework is intractable. Almost all the electric sector spatial programming models in the literature use the formulation (8.18), or a close equivalent.
Pumped storage projects are assuming increasing importance in many developing countries: in India, several large projects in a number of Southern States are now underway including the Kadamparai project in Tamil Nadu, and the Nagar junasagar facility in Andrha Pradesh—see Ahamed (1975) and Subrahmanyam and Singh (1975).
For further discussion of the degree to which approximate methods accurately-simulate real power flows in a transmission grid, see Crevier (1972).
Some of the relevant discussion include Reger & Schwarts (1973) or Windsor (1975). For a good discussion of water resource screening models, that follows a general philosophy of approach similar to that discussed here, see Cohon, (1972). O’Laoghaire and Himmelblau (1974), is another excellent treatment.
The subject of conjunctive use of groundwater and surface water is another that has received extensive attention in the literature, with highly complex optimization models addressed to the details of system operation, see e.g. Yu and Haimes (1974).
For further discussion, see e.g. Loucks (1969) or Cohon (1972).
For example, the fact that such considerations are important in the Indian context is evidenced by the public concern over the emissions from the refinery under construction at Mathura, which could cause significant damage to famous monuments such as the Taj Mahal. In Bombay, public concern over environmental questions is reflected in controversies over industrial siting in the Bombay Metropolitan area (see, for example, numerous reports in the Times of India and other major Indian newspapers over the period September 1977 to June 1978 on the controversy over the proposed siting of a natural-gas based fertilizer plant utilizing the newly discovered gas from the Bombay High fields. The Bombay Bâchas Committee, an environmental group, was at the focal point of this controversy).
For a comprehensive discussion of Environmental Issues in Developing Countries, see e.g., Bowonder (1980).
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© 1984 Springer-Verlag Berlin Heidelberg
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Meier, P. (1984). Electric Sector Models. In: Energy Systems Analysis for Developing Countries. Lecture Notes in Economics and Mathematical Systems, vol 222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48337-0_8
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DOI: https://doi.org/10.1007/978-3-642-48337-0_8
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