Issue 
La Houille Blanche
Number 67, Octobre 1972



Page(s)  487  498  
DOI  https://doi.org/10.1051/lhb/1972032  
Published online  23 March 2010 
Moyens d'estimer la valeur économique des installations de transfert d'énergie par la simulation mathématique d'exploitation. Application de ces données à l'aménagement et au choix des sites
Chef de la Division ProjetsProspection au D.E.P.H., E.D.F., Paris
For the last several years Electricité de France have been assessing the economics of hydroelectric projects by comparing the project with a fictitious thermal power station which could be built on the same site and which would give equivalent service. Computer programmes now available can be used to determine the best overall combination of the various power production schemes which would satisfy a given demand at minimum total cost. In the work presented here a mathematical model is used to simulate operation of the entire French network with a view to finding the optimal amount and type of pumped storage which should be installed. Before giving the results of this overall model study, pumped storage and gas turbines are compared and several important general ideas are deduced from this comparison. Based on French prices, Figure 1 gives the comparative cost of pumping stations with daily (Revin) and weekly time cycles (Montézic). Excluding the storage structures, this cost is in the order of 300400 F. The difference is due to storage costs. This is expensive for the first type (30 F /kWh) but much less so for the second (2 F /kWh). With a day cycletime storage only occurs over 6 hours, the cost being 180 F /kW. For the second case, the cost is only 72 F /kW with a 36hour basin (weekly cycle which provides 60 hours per week at full capacity). However, inexpensive storage is only available in mountainous areas (high falls) and transport costs are high (200 F /kW) to the industrial powerconsuming regions situated in the main well north of the mountains. By and large, the sixhour supply delivered to the Paris area by a daytype scheme gives an inclusive cost of 650 F /kW whereas the twelvehour supply from a weekly scheme amounts to approximately 750 F/kW, transport included. We are now in a position to compare pumped storage with gas turbines and this is done in Figure 2 which shows (a) that the short supply time (4 or 5 hours) is undoubtedly the economical domain for pumping (white area) unless a large number of cycles (over a 100) are required each year, in which case the economics are in favour of the longer duration and (b) that the economical domain for the gas turbine (shaded area) corresponds to the longer duration supply, this being the case. However, only on a few occasions in any given year. Pumped storage and gas turbines are thus shown to be complementary. Seasonal timecycle pumping stations have also been considered (see Figure 3). These are of interest in that they are able to modulate the duration of their supply from one week to the next. However, seasonal stations do not solve the problem of variation from year to year : this remains the special field of the gas turbine. Figure 4 shows that, although on average the gas turbine is only used a few hours a year (Figure 4 c) and is the uppermost plant type on the load duration curve, a plot of this kind in fact expresses a mathematical expectancy which is the sum of a large number of weeks in normal years with no recourse to gas turbines (Figure 4 b) and abnormal weeks in difficult years during which the gas turbine is used for a long supply duration (Figure 4 a) according to the ideas given above. In order to calculate the best breakdown between pumping and gas turbines, it is therefore necessary to use mathematical models which simulate the entire network (thermal and hydraulic) on the basis of probabilities, i.e. demand probability, probability of availability of thermal and hydroelectric power and energy availability probability during slack hours. Figure 5 shows the result of such a test. Here the amount of peakhour plant is optimized by adjusting the number of gas turbines (xaxis) to achieve minimal total cast (yaxis), this being the sum of annual gasturbine cost (curve A), power consumption (B) and extent of power default (C). The "value" of a pumping scheme is given by the difference between the total cost obtained for the optimized network in which the scheme appears and the network cost without the scheme. Figure 6 shows how this "value" (yaxis) varies with the reserve associated with each GW of pump power (yaxis). The yvalue of A is the value of 1 GW for the daily cycle where as the yvalue of B is for 1 GW of the weekly cycle. Dashed letters A' and B' are for 2GW. MM' represents a 300MW daily pumping scheme which has been added, during the year in question, to the pump plant defined by point M ; its value is 15 X 10 6 F. MM" represents a 300MW weekly scheme, the value of which is 22 X 10" F. Shown on the same type of plot in Figures 7 to 10 is the overall pumping "value" inserted into the French network during years 1980, 1985, 1988 and 1995. By tracing on these plots the best pumpedstorage development strategy for France, it is found that quantities and types to be installed are as follows : (i) Quantities : 0.5 GW per year between 1975 and 1980, 0.75 GW per year between 1980 and 1985, approximately 1GW per year after 1985 and about half of all the preceding power in the form of gas turbines ; (ii) Type of pumping : mainly the weekly type up to 1985, changing gradually to a predominance of the daily type thereafter.
© Société Hydrotechnique de France, 1972