Optimal Operation Rules for Parallel Reservoir Systems with Distributed Water Demands

This paper addresses the doubts regarding the spatial characteristics of the commonly used rules for parallel reservoir system operation. The rules based on aggregation-decomposition determine the system total release first and then assign this release to individual reservoirs, without considering the water demand distribution in the river network. In this paper, a conceptual model for parallel reservoir systems with distributed water demands is proposed. Three specific optimality conditions are derived for determining the optimal analytical solution. A rigorous proof shows that the aggregation-decomposition-based rules are a special case of the derived rules. An efficient algorithm is then developed based on the optimality conditions and shortage allocation index (SAI), in which a larger SAI indicates taking a higher percentage of the system water shortage, as release or storage. Unlike traditional algorithms that modify the violated variables empirically, we propose a criterion in terms of relative deviation indicators to determine the crucial priority of variable modification. This criterion can effectively address constraint violations. The optimal rules along with the solution algorithm are then demonstrated by the operation of a parallel reservoir system in the Shiyang River Basin, China. The results show that the proposed rules and algorithm are more efficient and effective than traditional algorithms and aggregation-decomposition-based rules, especially in dry seasons with more binding constraints.