Water Allocation Under Uncertainty – Potential Gains from Optimisation and Market Mechanisms
Thesis DisciplineManagement Science
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
This thesis first develops a range of wholesale water market design options, based on an optimisation approach to market-clearing, as in electricity markets, focusing on the extent to which uncertainty is accounted for in bidding, market-clearing and contract formation. We conclude that the most promising option is bidding for, and trading, a combination of fixed and proportionally scaled contract volumes, which are based on optimised outputs. Other options include those which are based on a post-clearing fit (e.g. regression) to the natural optimised outputs, or constraining the optimisation such that cleared allocations are in the contractual form required by participants. Alternatively, participants could rely on financial markets to trade instruments, but informed by a centralised market-clearing simulation.
We then describe a computational modelling system, using Stochastic Constructive Dynamic Programming (CDDP), and use it to assess the importance of modelling uncertainty, and correlations, in reservoir optimisation and/or market-clearing, under a wide range of physical and economic assumptions, with or without a market. We discuss a number of bases of comparison, but focus on the benefit gain achieved as a proportion of the perfectly competitive market value (price times quantity), calculated using the market clearing price from Markov Chain optimisation. With inflow and demand completely out of phase, high inflow seasonality and volatility, and a constant elasticity of -0.5, the greatest contribution of stochastic (Markov) optimisation, as a proportion of market value was 29%, when storage capacity was only 25% of mean monthly inflow, and with effectively unlimited release capacity. This proportional gain fell only slowly for higher storage capacities, but nearly halved for lower release capacities, around the mean monthly inflow, mainly because highly constrained systems produce high prices, and hence raise market value. The highest absolute gain was actually when release capacity was only 75% of mean monthly inflow. On average, over a storage capacity range from 2% to 1200%, and release capacity range from 100% to 400%, times the mean monthly inflow, the gains from using Markov Chain and Stochastic Independent optimisation, rather than deterministic optimisation, were 18% and 13% of market value, respectively.
As expected, the gains from stochastic optimisation rose rapidly for lower elasticities, and when vertical steps were added to the demand curve. But they became nearly negligible when (the absolute value of) elasticity rose to 0.75 and beyond, inflow was in-phase with demand, or the range of either seasonal variation or intra-month variability reduced to ±50% of the mean monthly inflow. Still, our results indicate that there are a wide range of reservoir and economic systems where accounting for uncertainty directly in the water allocation process could result in significant gains, whether in a centrally controlled or market context. Price and price risk, which affect individual participants, were significantly more sensitive. Our hope is that this work helps inform parties who are considering enhancing their water allocation practices with improved stochastic optimisation, and potentially market based mechanisms.