Computationally inexpensive robust design of run-of-river hydropower plants

Run of River hydropower plants (RoR) are characterised by a negligible storage capacity and by generation almost completely dependent on the quantity and variability of river flows. RoRs designed today will be deployed in a world characterised by a changing climate and uncertain economic conditions (electricity prices, interest rates, cost overruns). Investments need to be financially robust to these perturbations, but both design optimisation and robustness analyses traditionally incur large computing times and resources to explore a large range of potential futures. This hinders widespread uptake of these methods, and the emissions associated with large computing costs mitigate the environmental benefits of an otherwise renewable energy source.

Here we demonstrate a computationally inexpensive method for the optimisation (including multi-objective optimisation) and robustness analysis of run-of-river plants. It is based on the remark that the daily flow duration curve (FDC) can be approximated by a limited number of points, supporting a much faster evaluation of performance for a given FDC. Our method carries out the following steps:  (1) we approximate the daily FDC with N regularly spaced points, (2) we couple a multi-objective evolutionary algorithm with our state-of-the-art toolbox to optimise technical and financial indicators of performance, (energy production and economic profit) and generate design alternatives, (3) we sample uncertain factors to generate an ensemble of plausible future states of the World (SOWs), (4) we approximate the future FDC of each ensemble member with N points, (5) we quantify the robustness of selected alternative designs across the entire ensemble of SOWs.

We test our method with N=25, 50, 100, 250 and 500 points. We compare these results with traditional analysis (TA) done without approximating the FDC, and evaluated the trade-off between quality of results and required computational resources. Computational time required for performing optimisation with historical record (27 years of daily discharge) using 100,000 function evaluations is reduced by 98% and 92% for N = 25 and 500 respectively. The resulting Pareto optimal set has a good diversity and hypervolume performance for N ≥ 50 points is close (> 95%) to that of the set found by using 1,000 years of synthetic data for the optimisation. Likewise, the time required for analysing robustness across S = 500 SOWs is 98% less than TA in which we use an HPC platform and take 1,000 (synthetic stream flow) years into account. The performance evaluation of alternatives across the entire ensemble of SOWs is very similar to the robustness values based on TA. These preliminary results suggest that optimisation and robustness analysis can be performed with the proposed methodology for RoRs by using far less computational resources.