Bradley J. Eck

A Lagrangian decomposition approach for the pump scheduling problem in water networks

Dynamic pricing has become a common form of electricity tariff, where the price of electricity varies in real time based on the realized electricity supply and demand. Hence, optimizing industrial operations to benefit from periods with low electricity prices is vital to maximizing the benefits of dynamic pricing. In the case of water networks, energy consumed by pumping is a substantial cost for water utilities, and optimizing pump schedules to accommodate for the changing price of energy while ensuring a continuous supply of water is essential. In this paper, a Mixed-Integer Non-linear Programming (MINLP) formulation of the optimal pump scheduling problem is presented. Due to the non-linearities, the typical size of water networks, and the discretization of the planning horizon, the problem is not solvable within reasonable time using standard optimization software. We present a Lagrangian decomposition approach that exploits the structure of the problem leading to smaller problems that are solved independently. The Lagrangian decomposition is coupled with a simulation-based, improved limited discrepancy search algorithm that is capable of finding high quality feasible solutions. The proposed approach finds solutions with guaranteed upper and lower bounds. These solutions are compared to those found by a mixed-integer linear programming approach, which uses a piecewise-linearization of the non-linear constraints to find a global optimal solution of the relaxation. Numerical testing is conducted on two real water networks and the results illustrate the significant costs savings due to optimizing pump schedules.

Simulation-optimization approaches for water pump scheduling and pipe replacement problems

Network operation and rehabilitation are major concerns for water utilities due to their impact on providing a reliable and efficient service. Solving the optimization problems that arise in water networks is challenging mainly due to the nonlinearities inherent in the physics and the often binary nature of decisions. In this paper, we consider the operational problem of pump scheduling and the design problem of leaky pipe replacement. New approaches for these problems based on simulation-optimization are proposed as solution methodologies. For the pump scheduling problem, a novel decomposition technique uses solutions from a simulation-based sub-problem to guide the search. For the leaky pipe replacement problem a knapsack-based heuristic is applied. The proposed solution algorithms are tested and detailed results for two networks from the literature are provided.

Tailoring Seasonal Time Series Models to Forecast Short-Term Water Demand

AbstractThis paper presents a methodology to forecast short-term water demands either offline or online by combining seasonal autoregressive integrated moving average (SARIMA) models with data assimilation. In offline mode, the method frequently reestimates the models using the latest historical data. In online mode, the method applies a Kalman filter to optimally and efficiently update the models using a real-time feed of data. The tailoring process consists of identifying, estimating, and validating the models, along with exploring how the length of demand history used in fitting can improve forecast performance. A suite of models are obtained that are adequate for 15-min, hourly, and daily demands having daily and weekly periodicities. The model output is analyzed across temporal resolutions, periodicities, and forecasting modes. The study finds that the normalized forecast deviations range from approximately 4.2 to 1.3%, in correspondence to a decrease in temporal granularity. Models of the weekly-sea...

Fast non-linear optimization for design problems on water networks 1

As water infrastructure ages and repair costs increase, optimization techniques are increasingly used for the design and operation of water networks. A key challenge for optimization on water systems is the fast and accurate simulation of hydraulic equations. Conventional simulation tools such as Epanet are fast but cannot perform optimization alone and so must be coupled to an optimization engine, typically a metaheuristic such as a genetic algorithm. In contrast, mathematical optimization methods take into account hydraulic equations as constraints. The energy equation for pipe ow is a challenging constraint because it is non-linear and given by an explicit function with a rational exponent (Hazen-Williams) or an implicit function (Colebrook-White). This paper uses a quadratic approximation for pipe head loss that provides very good accuracy. The approximation is applied to pose and solve a mixed integer non-linear program (MINLP) for placing and setting pressure reducing valves. The problem is addressed using both local and global solvers. Computational results show accuracy comparable to Epanet and signicant potential to reduce non revenue water by deploy

An R package for reading EPANET files

The EPANET software for modeling piping networks is widely used for the design and analysis of water systems. This short communication describes epanetReader, an R package for reading EPANET files. The package reads network and simulation data in text-based file formats into R and provides summary and plotting functionality. epanetReader also introduces sparklines as a visualization of water network simulations. The package is available through the Comprehensive R Archive Network and GitHub.com. The paper documents an R package for water network data.Files from the EPANET and EPANET-MSX simulators are supported.Package functions visualize data as maps and sparklines.

Decomposition Approach for Background Leakage Assessment: BBLAWN Instance

AbstractThis paper summarizes an approach for the assessment and control of background leakage on water distribution networks. The methodology was developed for the battle of background leakage assessment for water networks (BBLAWN) held at the Water Distribution System Analysis Conference 2014 in Bari, Italy. The problem instance posed for the conference considers an aging water network with high levels of background leakage. A range of operational and design changes including new valves, pipes, pumps, tanks, and controls are available to reduce the expenditure needed to operate the system. Constraints are imposed on nodal pressures and tank levels to meet service level requirements. The solution methodology proposed in this paper decomposes the problem according to the type of intervention, considering each type separately. An initial diagnosis of the network informs the manner and order of evaluating the various interventions. Custom implementations of network simulation, heuristic algorithms, and opti...

Polynomial optimization for water networks: Global solutions for the valve setting problem

This paper explores polynomial optimization techniques for two formulations of the energy conservation constraint for the valve setting problem in water networks. The sparse hierarchy of semidefinite programing relaxations is used to derive globally optimal bounds for an existing cubic and a new quadratic problem formulation. Both formulations use an approximation for friction loss that has an accuracy consistent with the experimental error of the classical equations. Solutions using the proposed approach are reported on four water networks ranging in size from 4 to 2000 nodes and are compared against a local solver, Ipopt and a global solver, Couenne. Computational results found global solutions using both formulations with the quadratic formulation having better time efficiency due to the reduced degree of the polynomial optimization problem and the sparsity of the constraint matrix. The approaches presented in this paper may also allow global solutions to other water network steady-state optimization problems formulated with continuous variables.

Temperature dynamics and water quality in distribution systems

Quality assurance strategies for water distribution systems often include the application of chemical disinfectants to limit the growth and transmission of pathogens. Characteristics of water quality in individual systems, and the type of disinfectant employed, create significant complexity in understanding and quantifying the impact of disinfectants in different networks. An additional challenge is that disinfection byproducts (DBPs), created through the breakdown of disinfectants, can be detrimental to human health. Therefore, it is necessary to maintain the correct level of disinfectant to control microbial pathogens while also limiting formation of DBPs to acceptable levels. Limiting formation of DBPs is an ongoing challenge for operators. We examined the impact of ground surface temperature and changes in network operations on disinfectant breakdown. As drinking-water utilities encourage customers to conserve water, water residence times within networks increase. In addition, as surface temperatures increase, heat transfer into the drinking water in subsurface pipes can also increase. Here, we review the literature on ways in which temperature affects disinfection rates and the production of DBPs and select one pathway for more detailed assessment. Numerical modeling is used to examine the changes in DBP production as a function of residence time, ground surface temperature, and heat transfer through the soil to the pipe.

Bad Data Analysis with Sparse Sensors for Leak Localisation in Water Distribution Networks

Traditional bad data detection and localisation, based on state estimation and residual analysis, produces misleading results, with high rates of false positives/negatives, in the case of strongly-correlated residuals arising from a low redundancy of sensors. By clustering the measurements according to the structure of the residuals covariance matrix, a method is proposed to extend bad data analysis to the localisation and estimation of anomalies at the coarser resolution of clusters rather than single measurements. The method is applied to the problem of water leak localisation and a realistic test-case, on the water distribution network of a major European City, is proposed.

Pump Scheduling for Uncertain Electricity Prices

Water utilities have optimized pump schedules to take advantage of day/night electricity pricing plans for several decades. As intermittent renewable energy sources such as solar and wind power provide an increasingly large share of the available electricity, energy providers are moving to dynamic pricing schemes where the electricity price is forecast 24 hours in advance on 30-minute time steps. The customer only knows the actual price several days after the electricity is used. Water utilities are uniquely positioned to take advantage of these dynamic prices by using their existing infrastructure for pumping and storage to respond to changing costs for power. This work develops an operational technique for generating pump schedules and quantifying the uncertainty in the cost of these schedules. With information about the pumping schedules and the distribution of possible costs, a system operator can pump according to her desired level of risk. To develop this information, a representative sample of electricity price forecasts covering nearly the full range of possible price curves must be created. Forecasts from the energy supplier and historical data on actual prices are used to condition stochastic sampling of daily energy price trajectories using covariance decomposition methods. From this ensemble of realizations, electricity price profiles are classified into a handful of scenario classes. The optimal pumping schedule for each price class is then computed. Once the pumping schedule is known, the price of that schedule is evaluated against all other price classes to determine the robustness of the schedule. The method is applied on a simple real-world network in Ireland. In this application, electricity prices vary every half hour and range from 5 to 262 €/mWh. Optimizing the pumping schedule proved to be the slowest step in the process so selection of proper price scenarios on which to generate the schedule was critical to obtaining results in an operational time-frame.