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Unformatted text preview: the S-curve is most-frequently used to predict the product life
cycle. The curve characteristics are normally a slow start, a steep growth and
then a plateau. Sometimes, in the plateau part section, the curves are replaced by new curves. 36 Selecting the right form of S-curve in technological forecasting is sometimes
quite difficult. Mathematically there are many different equations that can be
used to represent an S-shaped curve. The solution to the problem depends
on the technology or the product being forecast and its characteristics. Many researchers have shown that population growth tends to follow a similar
pattern as the growth of biological organisms. This concept has been applied
to growth patterns of particular technologies, life cycles of individual products
and of government spending. 
The S-curve characteristics are normally a slow start, a steep growth and then
a plateau. The question is: are there any similarities between the S-curve and
the maximum system loads?
In 1951 the maximum system demand started with 1.2 GW. From the sixties,
the maximum system demand showed a steep growth due to new iron and
steel plants, chemical plants and municipalities being electrified. In the nineties, new aluminium and stainless plants have been commissioned, but
during that same period a steep decline in the gold mining loads occurred.
Recently the platinum mines and ferro-chrome smelters have shown
significant growths in their loads. Exports to neighbouring states have increased significantly over the last seven years. Negative annual growths
also occurred twice, in 1989/1990 and again 1997/1998. This is a possible
sign that the growth rate is slowing down.
A number of S-curves are available, but the generalised logistic curve shows
the more promising curve. The generalised logistic curve parameters are
given: Y = A+ C
(1 + Te − B ( x− M ) 1 / T ) where A the lower asymptote (starting point) (3.2.1) 37 C the upper asymptote (mature level) M the time of maximum growth (point of inflexion) B the growth rate T near which asymptote maximum growth occurs  It is important to determine the end of the horizon figure as accurately as
possible. The S-curve results are close to the moderate scenario re sults, but,
unfortunately, those results cannot be published.
The results are discussed in Chapter 5. Joubert’s forecasts could easily be
criticised, but to predict loads at the end of a twenty-year horizon is almost
impossible. The only reason for doing this is to benchmark the area and substation forecasts. The reasons for the twenty-year area and substation
forecasts are discussed later. Three “graphical measures” are used to verify the S-curve’s expected loads.
The first graph displays the fluctuation of the actual loads and the expected
loads (results from the balancing algorithm) around the S-curve results as a
cycle. The actual loads and the expected loads are divided by the results of
the S -curve and the results are plotted over time. The second graph displays the annual load increases. The results are based
on the actual and the expected (results from balancing algorithm) loads.
Referring to the results, from 1971, approximately every twelve years, a
number of large load increases occur. During those years, large steel plants
and aluminium smelters have been commissioned. Even the first twelve years of expected loads show such step load increases.
The last graph shows the percentage growths. The growth for each year is
determined as follows: Loadt + p % Growtht + p
= Loadt × 1 + 100 p (3.2.2) 38 where
Load t the actual load for 1951
p the number of years later than 1951 For further reading on system peak prediction, refer to the next articles:
1) Jordan’s energy consumption is described by an exponential model.
Oil provides 95 % of Jordan’s total energy needs and the remaining
5 % comes from gas fields. All the gas is used for electricity generation. Jordan assumed that the rate of change of energy
consumption per year is usually proportional to the current rate of
2) The electrical energy growth in Mauritius is predicted by the GNP
growth. The ratio of electricity to GDP is given as an empirically
determined elasticity coefficient. 
3) In 1989, Zimbabwe developed a non-linear dynamic model to
forecast the country’s maximum system.
macroeconomic and demographic The model relates variables to electricity consumption.  Mathematically based growth curves, such as a multivariate analysis of
variance models, based on theory when the parameters are stochastic, is a
further option for modelling the system peaks. [9 – 11]
3.2.2 Generation Pattern
The three questions, when, where and how much, must be answered for the
generation pattern. The question about how much is not about the actual net
sent out, but the maximum available net sent out.
The factor about regulatory aspects is important. This includes new agreements between neighbouring countries and the utility to import
electricity. The possibility is that privately owned p...
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This document was uploaded on 03/04/2014.
- Spring '14