Badrodin, Jamaliatul Badriyah
(2023)
Robust optimization technique for hydropower production.
*University of Southampton, Doctoral Thesis*, 80pp.

## Abstract

The aim of this thesis is to propose efficient methods for scheduling a long-term hy- dropower production. Managing hydropower is challenging, as it consists of various variables and constraints. The hydropower studied here consist of storage water, re- lease water, and pumping storage. Moreover, uncertainty regarding the amount of inflow water to the reservoir makes the problem more difficult. Therefore, it is essen- tial to model the problem which taking into account the uncertainty in the problem. Consequently, We model the problem using Robust Optimization (RO) and Stochastic Dynamic Programming (SDP) and compare the results. The result shows that RO per- forms better than SDP. Hence, we focus on solely using the RO model for the rest of the research.

We also investigate two types of decision making, namely risk averse and risk-neutral, then capture their behaviour in our model. Because of the uncertainty regarding inflow water, we want our decision to be able to adapt to any realisation of inflow. Therefore, we define the decision variables as an affine function of inflow water. These decision variables depend on a series of τ of inflow, where τ is the time window of how far we look back into the history of inflow. The result shows that an increase in τ causes an improvement in the result in training set. However, it is shown that there stops being an improvement at some point of τ and that too large of τ causes a degradation in the quality of the result when it is applied to validation set.

The phenomenon of the decreasing quality of result in validation set when τ is increas- ing prove that there is an overfitting on the model. Therefore, we add a regularisation to the model to prevent the overfitting. We add the constraints to restrict that the amount inflow water today give more effect to the decision on how much water should be re- leased today rather than the amount of inflow water yesterday. Adding this constraints to the model improves the quality of the solution in the validation set.

Furthermore, we add the spill variable to the problem. This variable is bounded by a function called as evacuation curve. The evacuation curve is a function of the max- imum amount of water to be spilled at specific level of storage at a specific time and scenario of inflow. This function is increasing and non-linear. However, we approxim- ate it to an affine function to keep the model linear. The numerical result suggests that the spill variable is not useful when the average water in the storage is not close to the maximum capacity.

Finally, we add the waterhead variable to the model. Previously, the problem assumes that the waterhead is constant. However, in reality, the waterhead is not fixed and de- pends on the water level in the storage. The variable waterhead then is described as an affine function of storage variable. Thus, this converts the model to a non-linear and non-convex model. We combine this non linear model with a rolling horizon algorithm to solve the problem. We propose two rolling horizon algorithms: Simple Rolling hori- zon (SRH) and Dynamic Rolling Horizon (DRH). The result shows that considering the rolling horizon algorithms, SRH and DRH, leads to better revenue and shorter time to run than when the problem is solved in full time horizon at once. Moreover, compar- ing the result of the model considering waterhead and the linear model with constant waterhead, it is found that considering waterhead gives better revenue. Lastly, by com- paring two rolling horizon algorithms, it can be shown that DRH produces better result rather than SRH.

**PhD_Thesis_Jamaliatul_Badrodin**

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