Representing flow mixing demands in a multi-nodal CDDP model of a mixed used catchment

Abstract

Constructive dual dynamic programming (CDDP) can be used to optimise a multi-nodal water system, or to clear a multi-nodal water market in the presence of competing consumptive demands, such as irrigation for farming, and non-consumptive demands, such as hydro-power generation. In this setting, CDDP is used in a two-stage process. First a deterministic multi-node version of the algorithm is used to construct a series of demand curves for release (dcr) under various catchment inflow scenarios. This is termed the 'intra-period' problem. Then a stochastic version of the algorithm uses the constructed dcr's to optimise the system, or clear the market over multiple periods, under uncertainty. This paper outlines the intra-period multi-node CDDP algorithm, and shows how to adapt this to address uses with water-mixing requirements, such as water returned to the river after being used for cooling a thermal power plant. All cost and benefit functions at the nodes are converted to net demand functions, i.e., marginal net benefit as a function of water supplied. For this, the nodal marginal value (or bid) information is re-cast to form net demand curves, and the arcs re-oriented towards the reservoir. Then the algorithm constructs the intra-period demand curve for release (dcr) by sequentially forming marginal water value curves at each node, passing these curves towards the reservoir. Arc flow bounds may limit the opportunities for using water at the nodes. Consumptive users extract water from the system, so each unit of water flow can only be used for a single consumptive use. A non-consumptive user transfers water from one node to another, extracting some benefit (e.g. from hydropower generation), or incurring some cost (e.g. for a pump). Costs can be associated with arc flow bounds and distributary demands to represent in-stream and environmental reserve flows enforced using penalty costs. High temperature return flows from thermal power plant cooling can affect the downstream ecosystem. As a result an additional flow past the thermal station is needed to control the temperature. The mixing flow required can be modelled as a fixed ratio of heated to unheated water. The paper explains how to extend a CDDP model to incorporate flow mixing externalities into the model, using multiple parallel arcs. The model assumes a single long-term storage reservoir embedded in a catchment with a “tree-like” topology. Consumptive demands occur at the nodes. Non-consumptive demands appear on arcs. Cooling and temperature control flow demands are represented as parallel arcs assuming that an upstream flow unit can be diverted to any arc of our choice, but other types of flow splitting are discussed. The deterministic CDDP algorithm then forms a net conditional dcr for each node that implicitly trades off the marginal value of all uses, to maximise total value, or clear the intra-period market. That dcr can then be incorporated into a stochastic CDDP algorithm to construct (inter-period) marginal storage values for the reservoir (and implicit release/allocation schedules for the entire catchment) over the entire planning horizon.