3. METHODOLOGY
3.5 Identification of efficient reservoir operating rules
The beneficial and adverse effects of a regulation project are not all commensurable and may therefore be difficult to combine into a single objective. To have a clear definition of optimality in such situations, solutions to non-commensurable multi-objective problems are classified as either ‘inferior’ or ‘non-inferior’, (Vemuri, 1974; Cohon and Marks, 1973; Haimes et al., 1975). Roughly defined, an inferior solution to a maximisation problem is one that has an objective whose level of attainment is increased without necessitating a decrease in the level of attainment of any other objective. Conversely, a non-inferior solution is one where no objective’s level of attainment can be increased without another objective’s attainment level decreasing. Figure 3.1 illustrates the various terminologies associated with multi-objective optimisation. In this case, the problem considered is the minimisation of a function with two objective, f1 and f2, i.e. max (f1, f2), subject to a constraint set in the decision space that defines the feasible and infeasible regions. The non-inferior solution set is a sub-set of the feasible region and it can alternatively be referred to as the set of non-dominated solutions.
The method of generating non dominated solutions for large scale multi-reservoir operation through application of constraints on allowable releases and storage targets was applied in this study since it has been shown to be superior over other approaches, such as the weighting method (Cohon and Marks (1975); Ko et al., 1992). This approach is suitable for generating non-dominated solutions for a reservoir where the number of objectives and constraints is small in order to avoid prohibitive dimensionality (Tauxe et al., 1979a, 1979b; Georgakakos, 1993).
Objectives other than the primary objective were treated as constraints. By varying the minimum acceptable levels of the secondary objectives a set of trade-offs may be generated between all of the objectives. The hierarchy of primary and secondary objectives were defined in a participatory stakeholder consultative process (Zaake and McCartney, 2008).
Figure 3.1 Search for pareto-optimal solutions (Duckstein and Opricovic, 1980).
Since it is acknowledged that it is not possible to consider all the relevant management objectives within the scope of a single study, the objective was to define operating rules that are only a plausible alternative but not a compromise solution. In this case, a primary objective of maximising expected energy generation was investigated subject to satisfying historically observed minimum and maximum lake levels and outflows. Secondary objectives such as flood control around the lake shorelines, limiting the range of lake level variation to support navigation and water related infrastructure, minimum flows to support freshwater ecosystems etc., were taken care of within the imposed constraints. The consumptive water demands for other sectors such as ecosystems, irrigation, and domestic water supply were indirectly accounted for through the utilization of net inflows or net basin supplies to each lake reservoir.
The process of searching for efficient lake-reservoir operating rules was supported by application of the LVDST, Equatorial Lake Model, SAMS and CSUDP in a complimentary fashion where output from one or more models is utilised by another in a hierarchy illustrated by the flow diagrams shown in Figure 3.2 and 3.3. The method for deriving deterministic operating rules is shown in Figure 3.2. Similarly Figure 3.3 illustrates a slightly different method used for deriving stochastic operation rules.
Figure 3.2 Deterministic derivation of operation rules for the case study.
LVDST
CSUDP
IDP optimization algorithm
Regression Analysis Equatorial
Lake Model
Plant power functions Turbine curves Turbine availability
Tail water curves Head loss functions
Initial state trajectories Maximum and minimum lake levels and releases
Set of optimum monthly or seasonal initial storage volumes and releases resulting in maximum power generation Net basin supplies
Lake levels Lake outflows
Refinement
Lake level vs storage curves
System performance simulation & evaluation
Operating rules
Figure 3.3 Stochastic derivation of operation rules for the case study.
In Figures 3.2 and 3.3 the basic data input to the Equatorial Lake Model are lake levels, outflows and lake level vs. storage curves. The output from the Equatorial Lake Model are the net basin supply time series. The LVDST yields optimum plant power functions based on plant characteristic input data. In both cases, operating rules are prescribed with the support of the generalised dynamic programming tool i.e. CSUDP. The method of utilisation of statistical features of the net basin supply in CSUDP is described in detail in Chapter 8. The prescribed operating rules are associated with a certain level of performance of the system. Evaluation of the performance of the system is discussed in the next section.
LVDST
CSUDP
SDP optimization algorithm
SAMS Equatorial
Lake Model
Plant power functions Turbine curves Turbine availability Tail water curves Head loss functions
Transition probabilities Maximum and minimum lake levels and releases Optimal monthly or
Seasonal storage guide curves conditioned on current storage and previous net inflows that resulting in maximum power generation
Net characteristic inflows Lake levels
Lake outflows
Refinement
Lake level vs storage curves
System performance simulation & evaluation
Historical net basin supply time series
Synthetic net basin supply time series Statistical properties
of net basin supply time series