6. STOCHASTIC ANALYSIS, MODELLING AND SIMULATION OF
7.6 Optimal operation policies based on historical annual time series
However, the storage targets suggested by Figures 7.8, 7.9 and 7.10 can only be regarded as indicative and not representative of a situation where long term persistence is prevalent in annual time series such as Lake Victoria levels.
7.6 Optimal operation policies based on historical annual time series of net basin
outflows to exceed the historically observed limits, ostensibly to alleviate damage to shoreline infrastructure.
The rationale for experimenting with Option 2 is derived from a review of the work of Kite (1984) who utilised the Hydrologic Model of the Upper Nile Equatorial Lake Basin (Nemec and Kite, 1979) to simulate and test several previously designed regulation plans for Lakes Victoria, Kyoga and Albert. The regulation plans deemed to have been successful when evaluated in terms not violating dead storage constraints during the period 1912 – 1974, indicated that Lake Kyoga outflows should be allowed to exceed the historically observed limits so as to maintain the allowable limits on Lake Kyoga levels. These trial plans also permitted Lake Albert maximum recorded level to be exceeded. However, the plans tested by Kite (1984) were deemed successful in spite of the fact that the range of allowable levels prescribed were greater than the historical range in the case of Lake Victoria.
Within the context of the results obtained from the evaluation of historical regulation plans by Kite (1984), Option 2 is an attempt to draw lessons from these findings through specification of system constraints that avoid deviation from the historically observed range of lake levels for Lake Victoria and Lake Kyoga by permitting a wide range of releases and allowing Lake Albert to have a wider range of storage level variation since it can be utilised as a balancing reservoir in the system. Figures 7.11, 7.12 and 7.13 illustrate the beginning of period lake levels for the period 1899 – 2008 that result in maximum hydropower generation as prescribed by the IDP optimisation algorithm in the setup of the CSUDP model for the case study. The figures also illustrate the impact of the optimum operating policies on natural unregulated long-term lake levels i.e.. Agreed Curve end of year lake level records.
Figure 7.11 Optimal operating policies for Lake Victoria (1899 – 2008).
Figure 7.12 Optimal operating policies for Lake Kyoga (1899 – 2008).
Figure 7.13 Optimal operating policies for Lake Albert (1899 – 2008).
1133.0 1133.5 1134.0 1134.5 1135.0 1135.5 1136.0 1136.5
1899 1909 1919 1929 1939 1949 1959 1969 1979 1989 1999
Lake level (m.a.s.l)
Impact on Lake Victoria levels
Agreed curve operation policy Option 2 regulation policy Option 1 regulation policy
1030.0 1030.5 1031.0 1031.5 1032.0 1032.5 1033.0 1033.5 1034.0
1899 1909 1919 1929 1939 1949 1959 1969 1979 1989 1999
Lake level (m.a.s.l)
Impact on Lake Kyoga levels
Agreed curve operation policy Option 2 regulation policy Option 1 regulation policy
618.0 619.0 620.0 621.0 622.0 623.0 624.0
1899 1909 1919 1929 1939 1949 1959 1969 1979 1989 1999
Lake level (m.a.s.l)
Impact on Lake Albert levels
Agreed curve operation policy Option 2 - regulation policy Option 1 - regulation policy
In Figure 7.11, it is demonstrated that the magnitude of beginning of period Lake Victoria levels that would have yielded maximum hydropower generation is not significantly different under Options 1 and 2. As expected, in many instances the beginning of period lake levels prescribed by regulation with Option 1 or 2 are significantly higher than the natural lake levels that would have occurred. It is also striking to note that the beginning of period lake levels associated with maximum hydropower tends to mimic the shape of the variation of natural unregulated lake levels.
In Figure 7.12, it is evident that the beginning of period Lake Kyoga levels prescribed by regulation in accordance to Option 1 or 2 are approximately the same from the year 1900 up to 1952. After that, the beginning of period Lake Kyoga levels prescribed by Option 1 regulation are higher than those prescribed by Option 2. Both tend to suggest that Lake Kyoga should be maintained at a constant elevation of 1032.12 m.a.s.l after the year 1962 in the case of Option 1 and at 1030.31 after 1967 in the case of Option 2. Under both options, a deviation is evident in 1980 but it is short lived. In general Options 1 and 2 are associated with lake levels that are lower than the historically observed record with the natural variation being significantly altered, particularly after 1962. It is also interesting to note that some of the historical plans reviewed by Kite (1984) included trials that suggested that Lake Kyoga be regulated to maintain a constant elevation of 1031.62 m.a.s.l or 1035.23 m.a.s.l without being successful.
During the course of execution of the IDP optimisation algorithm, many more infeasible and/or inferior initial storage volume scenarios occur, in the case of Lake Kyoga, during the post 1961 hydrological regime. Constant lake level elevations tend to be prescribed by the optimisation model over this period as these are the transitions that result in feasible releases and superior hydropower generation capacity for a given set of release constraints. Sustained high regulated releases from Lake Victoria typically in the range of 1200 m3.s-1 tend to limit the range of existing feasible solutions. For example, an outflow of 1000 m3.s-1 would lower the level of Lake Victoria by 37 mm after one month, but the same inflow would raise Lake Kyoga by nearly 700 mm because of its smaller surface area (Swenson and Wahr, 2009).
This argument can also be extended to Lake Albert. Sene (2000) demonstrated that at high flow, a 1 m increase in Lake Victoria is capable of exerting a 1.57m rise in Lake Kyoga and a
extra constraints on the feasible region within which it has been designed to operate. In Figure 7.13, it is shown that regulation of Lake Albert would entail maintaining it at a constant elevation of about 621 m.a.s.l in the case of Option 1 and at a much lower elevation of 618.76 m.a.s.l in the case of Option 2. Clearly the variation associated with the unregulated natural lake levels would be drastically altered.
The pattern of total annual maximum hydropower generation over the period 1899 – 2008 that would have resulted if all hydropower plants considered were online is shown in Figure 7.14 below. It is approximately the same under Options 1 and 2. The simulation shows that annual hydropower generation in Options 1 and 2 is extremely variable prior to 1961 when lake levels were much lower in Lake Victoria and more stabilised thereafter when lake levels rose. Figure 7.14 clearly demonstrates the beneficial aspects of lake regulation in terms of enhancement of hydropower generation when compared against unregulated conditions i.e. Agreed curve operation. It also quantitatively illustrates the desirability of maintaining the post 1961 hydrological regime for the lakes if the objective is to maximise hydropower generation.
Figure 7.14 Variation of hypothetical annual hydropower generation (1899 – 2008).
0 200 400 600 800 1000 1200 1400 1600 1800
1899 1920 1941 1962 1983 2004
Energy generation (MW)
Option 1 regulation policy Option 2 regulation policy Agreed curve operation
Under regulated lake conditions, power generation can be enhanced in the short term by as much as 64% in certain years when compared against operation using naturalized lake levels or unregulated conditions. However, over the whole the planning period considered (1899 – 2008), the average gain in power produced under regulated lake conditions was a modest 13%
(Table 7.10).
Table 7.10 Statistics of energy generation for the period 1899 – 2008 under various regulation options
Regulation policy Mean annual energy generation (MW)
Total energy generation (MW)
Option 1 1287 141598
Option 2 1287 141596
Agreed curve 1144 125828
Table 7.11 contains a summary of the hydraulic statistics for regulation with Options 1 and 2.
They are largely similar in terms of minimum and maximum values reached. However, the maximum withdrawals are significantly higher when the lakes are regulated with Option 2.
Table 7.11 Hydraulic statistics of flow (m3.s-1) for regulation Options 1 and 2
Limits Option 1 Option 2
Victoria Kyoga Albert Victoria Kyoga Albert
Minimum 261 280 343 261 280 344
Mean 861 864 981 861 866 986
Maximum 1718 1864 2057 1761 1908 2059
To attain convergence of the IDP algorithm in its application for Lake Victoria, the minimum flow constraint had to be relaxed for the initial two years of the model run i.e. in 1899 and 1900. In these two years the minimum flow constraint was relaxed from 347 m3.s-1 at all times to 261 m3.s-1 in 1899 and 274 m3.s-1 in 1900. Under these conditions, Options 1 and 2 violate the minimum flow constraint in Lake Victoria in the years 1899 and 1900. No violation of minimum flow constraints occurs in subsequent years of the near optimal trajectories. The reasons as to why minimum release constraints have to be violated in these years are related to the fact the initial lake reservoir conditions are very close to the minimum lake level.
Furthermore, years 1899 and 1990 were notably dry years. Year 1899 recorded the lowest net basin supply value of – 12,975 MCM in the Lake Victoria Basin.