Claus Davidsen

Optimizing Wellfield Operation in a Variable Power Price Regime

Wellfield management is a multiobjective optimization problem. One important objective has been energy efficiency in terms of minimizing the energy footprint (EFP) of delivered water (MWh/m(3) ). However, power systems in most countries are moving in the direction of deregulated markets and price variability is increasing in many markets because of increased penetration of intermittent renewable power sources. In this context the relevant management objective becomes minimizing the cost of electric energy used for pumping and distribution of groundwater from wells rather than minimizing energy use itself. We estimated EFP of pumped water as a function of wellfield pumping rate (EFP-Q relationship) for a wellfield in Denmark using a coupled well and pipe network model. This EFP-Q relationship was subsequently used in a Stochastic Dynamic Programming (SDP) framework to minimize total cost of operating the combined wellfield-storage-demand system over the course of a 2-year planning period based on a time series of observed price on the Danish power market and a deterministic, time-varying hourly water demand. In the SDP setup, hourly pumping rates are the decision variables. Constraints include storage capacity and hourly water demand fulfilment. The SDP was solved for a baseline situation and for five scenario runs representing different EFP-Q relationships and different maximum wellfield pumping rates. Savings were quantified as differences in total cost between the scenario and a constant-rate pumping benchmark. Minor savings up to 10% were found in the baseline scenario, while the scenario with constant EFP and unlimited pumping rate resulted in savings up to 40%. Key factors determining potential cost savings obtained by flexible wellfield operation under a variable power price regime are the shape of the EFP-Q relationship, the maximum feasible pumping rate and the capacity of available storage facilities.

Erratum for “Using Stochastic Dynamic Programming to Support Water Resources Management in the Ziya River Basin, China” by Claus Davidsen, Silvio J. Pereira-Cardenal, Suxia Liu, Xingguo Mo, Dan Rosbjerg, and Peter Bauer-Gottwein

23 Water scarcity and rapid economic growth have increased the pressure on water 24 resources and environment in Northern China causing decreasing groundwater tables, 25 ecosystem degradation and direct economic losses due to insufficient water supply. We 26 applied the water value method, a variant of stochastic dynamic programming, to optimize 27 water resources management in the Ziya River basin. Natural runoff from the upper basin 28 was estimated with a rainfall-runoff model auto-calibrated with in-situ measured discharge. 29 The runoff serial correlation was described by a Markov Chain and used as input to the 30 optimization model. This model was used to assess economic impacts of the middle route of 31 South-North Water Transfer Project (SNWTP), ecosystem minimum flow constraints and 32 limited groundwater pumping. A regional climate shift has exacerbated water scarcity and 33 increased water values, resulting in stricter water management. Our results show that the 34 SNWTP reduces the impacts of water scarcity and impacts optimal water management in the 35 basin. The presented modelling framework provides an objective basis for development of 36 tools to avoid over-pumping of groundwater resources at minimum costs. 37 38 Subject headings: Water resources management, China, Water shortage, River basins, 39 Optimization models, Economic analysis, Stochastic models, Reservoir operation 40 41