UBC Theses and Dissertations

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UBC Theses and Dissertations

Stochastic dynamic programming optimization model for operations planning of a multireservoir hydroelectric system Ayad, Amr


This thesis presents a Stochastic Dynamic Programming (SDP) modeling algorithm to model six hydropower plants in British Columbia (BC), Canada. The main output of the algorithm is the water value function for the two biggest reservoirs in BC, Williston and Kinbasket reservoirs. The AMPL programming language was used to implement the algorithm. Extensive testing has shown that the program is able to solve the problem producing acceptable water value and marginal value functions up to a problem size of ~ 164 million states per time step using the computing resources available on one of the BC Hydro’s servers. The objective of the work presented here was to assess the sensitivity of solution efficiency and precision for several storage state and decision space discretizations. The impact of introducing a storage state-space corridor, as an alternative of the traditional fixed storage state-space, was investigated. In addition, the sensitivity of the modeling results to different spill penalty values was analyzed. It was found that finer state-space increments give more precise results but the granularity was limited to the computing resources available. Introducing the storage state-space corridor provided several advantages; nevertheless, care should be taken in the design of such corridors so that the solution efficiency and accuracy are not jeopardized. Also, recommendations on the use of suitable spill penalty value are provided. Flexibility is one important feature of the modeling algorithm. This flexibility is a result of optimizing the algorithm and the organization of the code, which provided control over the increment of the state-spaces and the storage corridor, the ability to run the problem for one storage reservoir while fixing the state of the other storage reservoir and the ability of the user to run the model either directly on a personal computer/server using the command prompt or by using a scheduling program to optimize the use and sharing of computing assets. Further enhancements of the algorithm will enable the model developed in this thesis to handle much larger problems but will likely still suffer from the limitations due to the inherent curse of dimensionality in modeling using the SDP algorithm.

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