Hedging rule for reservoir operations: 2. A numerical model

TLDR

Reservoir operation optimization typically relies on heuristic algorithms to search for hedging rules. This study introduces a method that derives a hedging rule from theoretical analysis using a two‑period Markov hydrology model, a nonlinear utility function, and a specified inflow probability distribution. The method embeds marginal‑utility‑based hedging rule derivation into reservoir‑operation simulation, eliminating trial‑and‑error inaccuracies and the dimensionality curse of traditional optimization models. Numerical results show that the hedging policy improves utility and water‑supply reliability relative to the standard operation policy across varying reservoir capacities, inflow uncertainty, price elasticity, and discount rates, confirming the theoretical conditions.

Abstract

Optimization models for reservoir operation analysis usually use a heuristic algorithm to search for the hedging rule. This paper presents a method that derives a hedging rule from theoretical analysis (J.‐Y. You and X. Cai, 2008) with an explicit two‐period Markov hydrology model, a particular form of nonlinear utility function, and a given inflow probability distribution. The unique procedure is to embed hedging rule derivation based on the marginal utility principle into reservoir operation simulation. The simulation method embedded with the optimization principle for hedging rule derivation will avoid both the inaccuracy problem caused by trail and error with traditional simulation models and the computational difficulty (“curse of dimensionality”) with optimization models. Results show utility improvement with the hedging policy compared to the standard operation policy (SOP), considering factors such as reservoir capacity, inflow level and uncertainty, price elasticity and discount rate. Following the theoretical analysis presented in the companion paper, the condition for hedging application, the starting water availability and ending water availability for hedging, is reexamined with the numerical example; the probabilistic performance of hedging and SOP regarding water supply reliability is compared; and some findings from the theoretical analysis are verified numerically.