Optimal Pump Scheduling Research Articles

Optimal scheduling of variable speed pumps with mixed integer linear programming

ABSTRACT Mixed integer linear programming (MILP) has been gaining traction as a method for solving optimal pump scheduling problems in water distribution networks (WDNs). However, inclusion of variable speed pumps (VSPs) in MILP pump scheduling frameworks has not been given adequate treatment. This article addresses this gap by describing a methodology for formulating and solving optimal pump scheduling problems with VSPs using MILP and piece-linear approximations of network components. The methodology proceeds in four steps: (a) WDN simulation with initial pump schedule(s), (b) approximation of network components, including VSP, using linear and piece-linear functions around the chosen operating points, (c) formulation of a fully parameterised mixed integer linear programme, and (d) solution of the optimisation problem and WDN simulation with optimal pump schedule(s). The methodology is coded in MATLAB/OCTAVE and Python and is publicly available on GitHub. It was applied to solve a pump scheduling problem on a two variable speed pump single-tank network that allows the reader to easily understand how the methodology works and how it is applied in practice. The results show that the formulation is robust and the optimiser is able to return a globally optimal solution for a range of operating points.

Code and Data Repository for Polyhedral Relaxations for Optimal Pump Scheduling of Potable Water Distribution Networks

This archive is distributed in association with the INFORMS Journal on Computing under a BSD license as part of the Multi-Infrastructure Control and Optimization Toolkit (MICOT) project at Los Alamos National Laboratory, LA-CC-13-108. The software and data in this repository comprise a snapshot of similar artifacts used in the production of the article Polyhedral Relaxations for Optimal Pump Scheduling of Potable Water Distribution Networks by B. Tasseff, R. Bent, C. Coffrin, C. Barrows, D. Sigler, J. Stickel, A. S. Zamzam, Y. Liu, and P. Van Hentenryck. This snapshot is based on the specific inputs and software found in the data and src directories, respectively. Snapshots of unprocessed experimental outputs are provided in the subdirectories of results. Finally, various precompilation, execution, batch cluster submission, and analytical postprocessing utilities are provided in the scripts directory.

Polyhedral Relaxations for Optimal Pump Scheduling of Potable Water Distribution Networks

The classic pump scheduling or optimal water flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally challenging mixed-integer nonlinear program (MINLP). It is complicated by nonlinear equality constraints that model network physics, discrete variables that model operational controls, and intertemporal constraints that model changes to storage devices. To address the computational challenges of the OWF, this paper develops tight polyhedral relaxations of the original MINLP, derives novel valid inequalities (or cuts) using duality theory, and implements novel optimization-based bound tightening and cut generation procedures. The efficacy of each new method is rigorously evaluated by measuring empirical improvements in OWF primal and dual bounds over 45 literature instances. The evaluation suggests that our relaxation improvements, model strengthening techniques, and a thoughtfully selected polyhedral relaxation partitioning scheme can substantially improve OWF primal and dual bounds, especially when compared with similar relaxation-based techniques that do not leverage these new methods. History: Accepted by David Alderson, Area Editor for Network Optimization: Algorithms & Applications. Funding: This work was supported by the U.S. Department of Energy (DOE) Advanced Grid Modeling project, Coordinated Planning and Operation of Water and Power Infrastructures for Increased Resilience and Reliability. Incorporation of the PolyhedralRelaxations Julia package was supported by Los Alamos National Laboratory’s Directed Research and Development program under the project Fast, Linear Programming-Based Algorithms with Solution Quality Guarantees for Nonlinear Optimal Control Problems [Grant 20220006ER]. All work at Los Alamos National Laboratory was conducted under the auspices of the National Nuclear Security Administration of the U.S. DOE, Contract No. 89233218CNA000001. This work was also authored in part by the National Renewable Energy Laboratory, operated by the Alliance for Sustainable Energy, LLC, for the U.S. DOE, Contract No. DE-AC36-08GO28308. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0233 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0233 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Implementation and Field Test of Optimal Pump Scheduling in the Multiproduct Refined Oil Transmission System

Optimal pump scheduling ensures the safe and economic operation of the oil pipelines, which is also of vital significance for energy conservation as well as carbon emission reduction. This article proposes a framework adapting the data-driven pressure loss estimation with the long short-term memory neural network (LSTM-NN) and pump characteristics fitting with quadratic polynomials to model-based optimal pump scheduling for the multiproduct refined oil transmission system. The data-driven methods are data-adaptive with periodical field data in a rolling-training manner, and thus can reflect actual working conditions in the transmission pipelines. The presented LSTM-NN for pressure loss estimation integrating the characteristics of multiproduct refined oil pipeline transmission has good performance with an acceptable mean squared error of 0.016 MPa <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> in real applications. The optimization model makes the time precision down to the minute level, which is more convenient for the system dispatchers to operate the pumps following the optimal schedule. Practical implementation and field test are carried out in a real-world pipeline system, which verifies that the proposed framework is more practical and better-performed than the manual schedule.

Optimal pump scheduling in multi-phase distribution networks using Benders decomposition

With the growing adoption of renewable energy resources in the power grid, co-optimizing the operation of water and power distribution networks (WDNs and PDNs) increases the flexibility of both systems. The optimal water power flow problem (OWPF) is formulated to manage resource utilization across the WDNs and multi-phase PDNs. The nonlinear WDN hydraulic constraints and PDN ac power flow equations render the OWPF problem nonconvex. This paper formulates a convex optimal water power flow (C-OWPF) problem adopting successive approximations in WDNs and branch-flow relaxations in PDNs. The C-OWPF problem is a mixed-integer semidefinite program, which is computationally challenging even for small instances. Additionally, privacy considerations of WDN and PDN operators motivate the need for solving the C-OWPF in a distributed fashion. This paper develops a C-OWPF solver based on Benders decomposition that overcomes computational complexity challenges and preserve the privacy of the respective operators. The merits of the Benders decomposition-based solver are demonstrated on the IEEE 4-bus PDN coupled with a 3-node WDN and the IEEE 123-bus PDN coupled with the 36-node WDN.

A Chaotic Sobol Sequence-based multi-objective evolutionary algorithm for optimal design and expansion of water networks

The design of a water distribution network (WDN) is an optimization problem that is computationally challenging with conflicting objectives. This study offers an enhanced Chaotic Sobol Sequence-based Multi-Objective Self-Adaptive Differential Evolution (CS-MOSADE) algorithm for multi-objective WDN design. The CS-MOSADE algorithm was tested on two benchmark WDNs, and a real WDN. Optimization results indicate that the CS-MOSADE algorithm converged two to three times faster than the MOSADE and NSGA-IIalgorithms and led to better output in terms of even distribution of solutions and convergence towards the true Pareto-optimal front. Smaller spacing metric indicated better uniformity in the obtained solutions; and larger hyper-area and coverage function values depicted better convergence towards the true Pareto-optimal front for the CS-MOSADE algorithm compared to the other algorithms. The CS-MOSADE algorithm was then applied to solve a WDN expansion problem for optimal pump scheduling and minimization of Life Cycle Cost, maximization of reliability and minimization of Green House Gas (GHG) emissions. A significant reduction in GHG emissions of 2.17 x 106 kg was achieved at an additional cost of $0.55 x 107 when optimal pump scheduling was incorporated in the model of the real WDN over service life of 50 years.

Development of optimal pump schedules for improved energy efficiency in water supply systems (case of NWSC)

The water utility in Uganda (NWSC) was under pressure from regulators, environmentalists and board members to reduce energy costs. However, achieving energy efficiency in the water distribution systems of Kampala that is characterized by variable demands and prescribed pressures would be impossible if this utility continued operating on trial and error methods. This research was undertaken in the year 2016-2017 and aimed at exploring how pump schedule optimization could enable NWSC to deal with the challenge of high energy costs and improve water utility performance. In this research, the energy consumption of existing pumps was obtained from historical data, data was diagnosed and based on the diagnostic findings, decision variables were selected and optimal pump schedules were formulated. The formulated schedules were applied to the Gabba Muyenga supply system of National Water and Sewerage Company (Uganda) as a proof of concept. The formulated pump schedules when applied on different pumps classified as models 1, 2 and 3 based on pump flow ratings and motor voltage ratings, results show that scheduling pump operations based on time of the day tariffs enabled NWSC to save about 0.373 Million kWh annually. On the other hand pump scheduling based on pressure, modulation had the potential to reduce water losses enabling NWSC to save 12 m3/hr equivalent to 0.068 million kWh per year in energy terms without compromising customer service levels and this was only for the established DMA within the case study area and not for the entire NWSC water distribution network. The data presented were obtained through field measurements, statistical analysis and hydraulic design calculations

Development of optimal water distribution system design and operation approach considering hydraulic and water quality criteria in many-objective optimization framework

Abstract Water distribution systems (WDSs) are major infrastructure, and it needs to consider economic, hydraulic stability, and water quality safety to optimal design and operation of WDSs. However, the previous studies related to WDS design and operation were focused on each field (i.e. design: optimal pipe diameter, pump sizing, and valve location; operation: optimal pump scheduling, etc.) even though the WDS design and operation have a correlation. Therefore, to achieve economic feasibility, hydraulic stability, and water quality safety under WDS design and operation process, this study develops an optimal WDS design and operation approach considering hydraulic and water quality criteria in the many-objective optimization framework. To consider design and operation, this study applies three objective functions to minimize the total design and operation cost (i.e. the pipe cost, pump construction, and pump operation cost), maximize system robustness, and minimize the amount of chlorine requisition simultaneously under the hydraulic and quality constraints. The proposed optimal WDS design and operation model was applied to the two-stage optimization procedures. The first process determined the optimal pipe diameter set. The second process determined the optimal pump construction and scheduling considering three objective functions such as the total pump cost, the system robustness, and the quantity of the required residual chlorine for determining optimally the available number of pumps, capacity, and scheduling. For the optimization, the self-adaptive multi-objective harmony search is used and a famous benchmark network for the optimal design and pump operation of WDSs is applied to verify the proposed approach. This study can provide a new perspective on WDS design and operation technique considering the essential design factors to the water utility.

Staged energy and water quality optimization for large water distribution systems.

Simultaneous optimization of energy and water quality in real-time large-sized water distribution systems is a daunting task for water suppliers. The complexity of energy optimization increases with a large number of pipes, scheduling of several pumps, and adjustments of tanks' water levels. Most of the simultaneous energy and water quality optimization approaches evaluate small (or hypothetical) networks or compromise water quality. In the proposed staged approach, Stage 1 uses a risk-based approach to optimally locate the chlorine boosters in a large distribution system based on residual chlorine failures and the associated consequences in different land uses of the service area. Integrating EPANET and CPLEX software, Stage 2 uses mixed integer goal programming for optimizing the day-ahead pump scheduling. The objective function minimizes the pumping energy cost as well as the undesirable deviations from goal constraints, such as expected water demand. Stage 3 evaluates the combined hydraulics and water quality performances at the network level. The implementation of the proposed approach on a real-time large-sized network of Al-Khobar City in Saudi Arabia, with 44 groundwater wells, 12 reservoirs, 2 storage tanks, 191 mains, 141 junctions, and 17 pumps, illustrated the practicality of the framework. Simulating the network with an optimal pumping schedule and chlorine boosters' locations shows a 40% improvement in water quality performance, desired hydraulics performance with optimal pump scheduling, and an average 20% energy cost reduction compared to the normal (unoptimized) base case scenario.

Optimal pumping schedule with high-viscosity gel for uniform distribution of proppant in unconventional reservoirs

Hydrocarbon recovery from a hydraulic-fractured unconventional reservoir can be enhanced by replacing slickwater with non-Newtonian high-viscosity gel as a fracturing fluid. However, in the literature, the role of gel rheology on hydrocarbon production from a fractured reservoir is not very well understood. This lack of understanding makes it difficult for the industry to choose appropriate viscosity parameters of fracturing gels. Motivated by these limitations, first, we have developed a high-fidelity model of non-Newtonian fluid flow to simulate fracture propagation, fluid leak-off, and gel flowback processes to predict the oil production from a hydraulic fractured reservoir. Simulation results of the high-fidelity model show how fracture geometry, formation damage, and gel cleanup process varies with the fracturing fluid rheology. Hence, the developed model is used to understand the effect of gel rheology on hydrocarbon production via a sensitivity analysis, which provides a set of rheological parameters that maximize the cumulative amount of oil production. Finally, utilizing this optimal high-viscosity gel, a model predictive controller is designed to obtain an optimal pumping schedule necessary for producing a target fracture geometry and proppant concentration. The closed-loop simulation results demonstrate that the obtained pumping schedule successfully achieved the desired fracture geometry and proppant concentration at the end of pumping, leading to the maximum oil production from an unconventional reservoir.

Practical real-time optimization for energy efficient water distribution systems operation

The production, treatment and delivery systems of drinking water and wastewater is one of the largest energy consumers in the US with about 4% of the nation’s power consumption. Roughly 80% of the water treatment and distribution costs are associated with electricity, mainly for pumping. Increasing the efficiency of drinking water pumping systems could benefit both the energy- and water-sectors. Despite the advancement of optimal pump scheduling technology, most water utilities are relatively small, and thus lack the funds, hardware and technical personal to support the use of sophisticated and computer intensive pump optimization programs. This study presents a simple and practical model predictive control methodology for real-time pump scheduling. This methodology can be deployed on a standard hardware (e.g., PLCs in pumping stations), which is currently in use by most water utilities. As such, it provides optimal pump scheduling benefits without necessitating large investment in new computational hardware (e.g., advanced controllers). The proposed methodology reduces both the energy consumption (by selecting the most efficient pumps’ combinations) and the operation cost (by optimizing the pumps’ operation according to electricity tariff periods). The results show that our practical methodology, which could be implemented in simple controllers, can provide near optimal decisions comparable with sophisticated optimization methods that require advanced hardware. To the best of our knowledge, there is no available methodology with such capabilities which is specifically designed for local control schemes. Thus, the novelty of this study is the utilization of this optimization methodology on a simple PLC hardware. Our results are of high importance for both academic and practical reasons, as it shows that the proposed methodology could be a kernel for a low-cost pumps’ optimization technology.

Impact of Optimized Pump Scheduling on Water Quality in Distribution Systems

AbstractPump scheduling can improve performance of water supply systems, but it may have a different effect on water quality. The target of this article is to examine optimized pump schedules’ impa...

Optimal Regulation of Pumping Station in Water Distribution Networks Using Constant and Variable Speed Pumps: A Technical and Economical Comparison

Greenhouse gas emission is one of the main environmental issues of today, and energy savings in all industries contribute to reducing energy demand, implying, in turn, less carbon emissions into the atmosphere. In this framework, water pumping systems are one of the most energy-consuming activities. The optimal regulation of pumping systems with the use of variable speed drives is gaining the attention of designers and managing authorities. However, optimal management and operation of pumping systems is often performed, employing variable speed drives without considering if the energy savings are enough to justify their purchasing and installation costs. In this paper, the authors compare two optimal pump scheduling techniques, optimal regulation of constant speed pumps by an optimal ON/OFF sequence and optimal regulation with a variable speed pump. Much of the attention is devoted to the analysis of the costs involved in a hypothetical managing authority for the water distribution system in order to determine whether the savings in operating costs is enough to justify the employment of variable speed drives.

Short-Term Water Demand Forecasting Using Nonlinear Autoregressive Artificial Neural Networks

AbstractShort-term water demand forecasting models address the case of a real-time optimal water pumping schedule. This study focuses on developing artificial neural network (ANN) models to forecas...

Optimal water intake and supply pump scheduling considering water quality safety in multiple water intake system

Optimal water intake and supply pump scheduling considering water quality safety in multiple water intake system

Efficient optimization of pump scheduling for reduction of energy costs and Greenhouse gas emissions

Optimal pump scheduling has been applying to decrease operating costs of water distribution systems (WDSs). However, the operations of pumping stations will result in an increase of Greenhouse gas emission (GHG). To reduce GHG, pumping stations should be operated with high efficiency. For this reason, optimal pump cheduling should take into account both energy cost savings and pumping station efficiency. The aim of this article is to suggest an efficient multi-objective optimization solution or minimizing pumping energy cost and maximizing pumping station efficiency. As a result, a trade-off solution compromising pumping energy cost and pumping system efficiency will be achieved. The Genetic Algorithm (GA) combined with a WDS simulator, EPANET will be applied to solve the pump scheduling problem in one benchmark WDS and the results from our solution will be compared to the ones in the literature in terms of pumping energy cost and efficiency.

Bayesian set pair analysis and machine learning based ensemble surrogates for optimal multi-aquifer system remediation design

Surrogate models are often adopted to substitute computationally intensive groundwater simulation models for aquifer management due to their high effectiveness and computing efficiency. However, solutions of using only one surrogate model are prone to large prediction uncertainty. This study compares individual surrogate models and an ensemble surrogate model in an optimal groundwater remediation design problem. Three machine learning based surrogate models (response surface regression model, artificial neural network and support vector machine) were developed to replace a high-fidelity solute transport model for predicting saltwater intrusion and assisting saltwater scavenging design. An optimal Latin hypercube design was employed to generate training and testing datasets. Set pair analysis was employed to construct a more reliable ensemble surrogate and to address prediction uncertainty arising from individual surrogate models. Bayesian set pair weights were derived by utilizing full information from both training and testing data and improved typical set pair weights. The individual and ensemble surrogate models were applied to the salinization remediation problem in the Baton Rouge area, southeast Louisiana. The optimal remediation design includes two conflicting objectives: minimizing total groundwater extraction from a horizontal scavenger well while maximizing chloride concentration difference to the MCL (maximum contamination level) at monitoring locations. NSGA-II (Non-dominated Sorting Genetic Algorithm II) was employed to solve the nonlinear optimization model and obtain Pareto-optimal pumping schedules. The optimal pumping schedules from ensemble surrogate models and individual surrogate models were verified by the solute transport model. The study found that Bayesian set pair analysis builds robust ensemble surrogates and accounts for model prediction uncertainty. The ensemble-surrogate-assisted optimization model provides stable and reliable solutions while considerably alleviating computational burden.

Multi-criteria analysis applied to multi-objective optimal pump scheduling in water systems

Abstract This work presents a multi-criteria-based approach to automatically select specific non-dominated solutions from a Pareto front previously obtained using multi-objective optimization to find optimal solutions for pump control in a water supply system. Optimal operation of pumps in these utilities is paramount to enable water companies to achieve energy efficiency in their systems. The Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (FTOPSIS) is used to rank the Pareto solutions found by the non-dominated sorting genetic algorithm (NSGA-II) employed to solve the multi-objective problem. Various scenarios are evaluated under leakage uncertainty conditions, resulting in fuzzy solutions for the Pareto front. This paper shows the suitability of the approach for quasi real-world problems. In our case-study, the obtained solutions for scenarios including leakage represent the best trade-off among the optimal solutions, under some considered criteria, namely, operational cost, operational lack of service, pressure uniformity and network resilience. Potential future developments could include the use of clustering alternatives to evaluate the goodness of each solution under the considered evaluation criteria.

Wastewater Pump Control under Mechanical Wear

With reference to a classical wet tank equipped with a wastewater submersible pump, in this research, an advanced numerical model has been used in order to obtain the optimal pump scheduling of on/off operation and variable pump speed. Then, in order to evaluate the time decay of pump performances, the mechanical wear has been artificially simulated and the performance curves have been experimentally obtained for different rotational speeds. Finally, the benefits, as well as the feasibility, of pump scheduling have been evaluated for differing operating conditions. According to the results, the optimal pump scheduling achieves large energy savings up to 43%, for soft mechanical wear. If the mechanical wear is considered, the energy savings are large as well, between 35.60% and 26.70%, for medium and hard mechanical wear, respectively. On the other hand, the limitation of such a strategy has been highlighted: the feasibility of pump scheduling is limited by the elevation of the downstream tank. According to the results, energy savings can be achieved until the elevation of the downstream tank is 67% of the pressure head at the best efficiency point, whereas such percentage decreases to 50% for hard mechanical wear. Finally, the results show that plant efficiency is strongly affected by the mechanical wear: an accurate maintenance of the pumping system is therefore recommended in order to attenuate the time decay of pump performances.

Utilization of Water Supply Networks for Harvesting Renewable Energy

Renewable surplus power is increasing due to the increasing penetration of these intermittent resources. In practice, electric grid operators either curtail the surplus energy resulting from renewable-based generations or utilize energy storage resources to absorb it. In this paper, we propose a framework for utilizing water pumps and tanks in water supply networks to absorb the surplus electrical energy resulting from renewable-based electricity generation resources in the electrical grid. We model water supply networks analytically, and propose a two-step procedure that utilizes the water tanks in the water supply network to harvest the surplus energy from an electrical grid. In each step, the water network operator needs to solve an optimization problem that is nonconvex. To compute optimal pump schedules and water flows, we develop a second-order cone relaxation and an approximation technique that enable us to transform the proposed problems into mixed-integer second-order cone programs. We then provide the conditions under which the proposed relaxation is exact, and present an algorithm for constructing an exact solution to the original problem from a solution to the relaxed problem. We demonstrate the effectiveness of the proposed framework via numerical simulations.