An improved approach to the development of operating policies for multiple reservoir systems

The diminishing potential for development of further reservoirs, coupled with environmental awareness about the negative environmental impacts of reservoir construction and operation, has not only necessitated the need for improved operation of reservoirs through better planning, but has also created an additional demand on reservoirs in the form of instream flow requirements to preserve the ecological integrity of the rivers. The combination of these factors has lead to a considerable interest in both private and government water resources engineering practice in the use of mathematical models for optimisation of reservoir operations.

The optimisation approaches which have been most commonly used for planning the operation of reservoirs are dynamic programming (DP), linear programming (LP) and non-linear programming. While all of these techniques are reasonably effective for optimisation of operation of single reservoirs, dynamic programs are by far the most frequently used partly because of the ease with which they can handle stochasticity of inflow regimes. However, while all the techniques, including dynamic programming techniques, are relatively easily applied to optimisation of single reservoirs, serious theoretical and computational issues arise when they are applied to the optimisation of the operations of multiple reservoir systems, particularly when stochastic issues related to inflow regimes or variation in demands are considered. For this reason, none of the above techniques have been able to be applied directly to the simultaneous optimisation of the operation of multiple reservoir systems. Instead, the optimisation processes have relied upon approximations such as decomposition of a system or joint simulation-optimisation approaches.

The research reported in this thesis proposes a new approach to optimisation of the operation of reservoir systems, particularly multiple reservoir systems. This approach enables improved levels of consideration of the stochasticity of the inflow process while also significantly reducing the computational requirement and permits a more detailed and accurate representation of the system within the optimisation process. The approach is based on consideration of the stochasticity of inflows through the concept of Limiting State Probabilities. These Limiting State Probabilities rely on an assumption of stationarity of monthly transition probability matrices, an assumption which is also commonly used in stochastic reservoir operation models and define a probability distribution of inflows which, for each time period, are independent of the flows in the previous month, but which implicitly incorporate the time period to time period correlations normally captured by Markov processes. The Limiting State Probability vectors for each time period are obtained by a process of multiplication of the transition probability matrices associated with the inflows in that time period and the time period immediately preceding it. These Limiting State Probability vectors are the same as the marginal probabilities of inflows derived from steady state solutions in stochastic dynamic programs. The ability of Limiting State Probability vectors to remove the explicit temporal correlations is derived from the close relationship of Limiting State Probabilities to the long term steady state conditions of optimal reservoir operation. The elimination of temporal correlation also enables the spatial correlation between the inflows to reservoirs at different locations to be considered implicitly rather than explicitly. The spatial correlation is able to be eliminated from explicit consideration in the inflows to the model because the removal of the time period to time period correlation means that the results of a deterministic optimisation of reservoir using an inflow sequence generated by and conforming to the Limiting State Probability are independent of the actual order of inflows in that inflow series. This non-dependence of the results of the optimisation on the order of inflows enables the Limiting State Probability generated inflow sequences to be used as input to each reservoir in a multiple reservoir system with a diminished need to consider spatial correlation of inflows explicitly. The approach is validated first by application to the optimisation of the operation of a single reservoir wherein it is shown that the same results, i.e., optimal operating policies, are obtained when Limiting State Probabilities rather than traditional transition probability matrices are used in the recursive equations of the stochastic dynamic program. Optimal operation of the same single reservoir was then performed by the deterministic modelling technique network linear programming using inflow sequences generated by Limiting State Probabilities. The results obtained from the optimisation technique were similar to those obtained by stochastic dynamic programming with some of the differences being due to use of discrete variables in stochastic dynamic programming and continuous variables in the network linear program. Use of the Limiting State Probability concept was then extended to simultaneous optimisation, using network linear programming, of a multiple reservoir system comprising six reservoirs and seventeen demand centres, plus instream flow requirements. The deterministic inflow inputs, i.e., inflow sequences to each reservoir required by network linear programming were generated on the basis of Limiting State Probabilities relevant to each reservoir. The results of the application of the NLP technique using the inflows generated by Limiting State Probabilities showed the approach to be a computationally tractable and effective means to improved level of consideration of stochasticity of inflows in the optimisation of the operation of multiple reservoir systems.