Pump Scheduling Optimization Research Articles

A Mixed‐Integer Linear Programming Framework for Optimization of Water Network Operations Problems

AbstractWater distribution systems (WDSs) are critical infrastructure used to convey water from sources to consumers. The mathematical framework governing the distribution of flows and heads in extended period simulations of WDSs lends itself to application in a wide range of optimization problems. Applying the classical mixed integer linear programming (MILP) approach to model WDSs hydraulics within an optimization framework can contribute to higher solution accuracy with lower computational effort. However, adapting WDSs models to conform to a MILP formulation has proven challenging because of the intrinsic non‐linearity of system hydraulics and the complexity associated with modeling hydraulic devices that influence the state of the WDS. This paper introduces MILPNet, an adjustable framework for WDSs that can be used to build and solve an extensive array of MILP optimization problems. MILPNet includes constraints that represent the mass balance and energy conservation equations, hydraulic devices, control rules, and status checks. To conform to MILP structure, MILPNet employs piece‐wise linear approximation and integer programming. MILPNet was implemented and tested using Gurobi Python API. Modeling accuracy was shown to be comparable to EPANET, a public domain software for hydraulic modeling, and sensitivity analyses were conducted to examine the impacts of the modeling assumptions on the performance of MILPNet. Additionally, application of the framework was demonstrated using pump scheduling optimization examples in single and rolling horizon scenarios. Our results show that MILPNet can facilitate the construction and solution of optimization problems for a range of applications in WDSs operations.

Pump scheduling optimization in water distribution system based on mixed integer linear programming

The energy consumption in water distribution systems (WDSs) is significant. Improving the efficiency of pump operation can significantly reduce energy costs. However, optimal pump operation is a nonconvex mixed-integer nonlinear programming (MINLP) problem, which can be challenging to solve. A feasible approach is to linearize the problem and convert it into a mixed-integer linear programming (MILP) problem. However, this approach introduces many auxiliary variables, which can lead to inefficiency in finding the optimal solution due to the expanded search space. To address this issue, we propose a novel method for linearization of the original MINLP problem and a strategy that can adaptively adjust the number of piecewise linearization breakpoints. By reducing the number of auxiliary variables, our approach achieved competitive computing efficiency and the ability to save energy costs, as demonstrated in two benchmark instances. Furthermore, in a realistic large-scale WDS, our approach saved 9.83% more energy costs than the genetic algorithm and achieved a gap of only 7.36% from the lower bound.

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

Effect of proppant deformation and embedment on fracture conductivity after fracturing fluid loss

Fracture conductivity after fracturing fluid loss is significant for the optimization of pumping schedule and the productivity modeling. A new model was established to evaluate the fracture conductivity under closure pressure, considering the proppant deformation and the mechanical properties of the shale. The deformation of proppants and formation rock and the embedment of proppants were calculated by the contact mechanics. The average pore radius in the fracture was calculated. After matching the simulated embedment with experimental data, the mechanical properties of shale after fluid loss were obtained. Based on that, a mathematical model combined with Kozeny-Carman correlation was established. The accuracy of this model was also verified by experimental data. The simulation shows that the change of the mechanical properties of shale leads to more nonlinear variation of the fracture conductivity. Improving the fracture aperture is a better way to improve the fracture conductivity compared with raising the fracture permeability.

Improving energy efficiency in water supply systems with pump scheduling optimization

Water supply systems have a significant environmental and energetic impact due to the large amount of energy consumed in water pumping and water losses. The safe and efficient operation of these systems is crucial, where digital tools, such as monitoring, hydro-informatics, and optimization algorithms, are key approaches that can play an important role on support decisions.This paper presents a hybrid optimization method to improve the energy efficiency of a water supply system towards a more sustainable water management concerning the water-energy nexus. A genetic algorithm was used to optimize the pumping schedule during the day. Knowing the water consumption a priori, it is possible to define the optimal pump status for a specific timeframe (e.g. every 1 h), minimizing the operation costs, and also the energy consumption and associated carbon dioxide emissions. Knowledge-based mechanisms, like introducing known feasible solutions in the population and selective mutation mechanisms, were introduced in order to boost the algorithm convergence. A model of the water network developed in the hydraulic simulator EPANET was used to evaluate the solutions. All the physical constraints of the water supply system (e.g. hydraulic compliances) and water demands must be met for each solution, including the level limits of the water storage tanks.From the obtained solutions, it is found that optimizing the pump scheduling can improve the energy efficiency up to 15% in average (maximum of 25%) comparatively to the real operation, although this value can severely decrease if a conservative approach is assumed of maintaining more water stored in the tanks (low-risk approach). Similar improvements were achieved for cost and carbon dioxide emissions. Besides knowledge-based mechanisms, the analysis of the water storage risk was also an innovative outcome of this paper.Finally, digital tools can be used to optimize the system with minimal investment in equipment or physical intervention, although optimal solutions depend on water availability, water demand, and water storage risk.

A hybrid time MILP model for the pump scheduling of multi-product pipelines based on the rigorous description of the pipeline hydraulic loss changes

As the primary means of transporting refined products, multi-product pipelines play a significant role in ensuring downstream energy supply. The pump scheduling optimization of multi-product pipeline can significantly lower the energy consumption of the pipeline. With the input parameters of pipeline flowrates and batch interface locations, which are determined by a specific detailed schedule, this paper first proposes an innovative method for a rigorous description of pipeline hydraulic loss changes during the multi-batch sequential transportation process. Based on the hybrid time representation, the scheduling horizon is divided into two levels of time windows and a mixed-integer linear programming (MILP) model for the pump scheduling of multi-product pipelines is established according to the proposed method. Various technical and operational constraints are considered. Finally, the established model is successfully applied to a real-world multi-product pipeline, with three operation modes, in China. The superiority, accuracy, and applicability of this model are validated in detail through comparison with a previous model.

Bayesian optimization of pump operations in water distribution systems

Bayesian optimization has become a widely used tool in the optimization and machine learning communities. It is suitable to problems as simulation/optimization and/or with an objective function computationally expensive to evaluate. Bayesian optimization is based on a surrogate probabilistic model of the objective whose mean and variance are sequentially updated using the observations and an “acquisition” function based on the model, which sets the next observation at the most “promising” point. The most used surrogate model is the Gaussian Process which is the basis of well-known Kriging algorithms. In this paper, the authors consider the pump scheduling optimization problem in a Water Distribution Network with both ON/OFF and variable speed pumps. In a global optimization model, accounting for time patterns of demand and energy price allows significant cost savings. Nonlinearities, and binary decisions in the case of ON/OFF pumps, make pump scheduling optimization computationally challenging, even for small Water Distribution Networks. The well-known EPANET simulator is used to compute the energy cost associated to a pump schedule and to verify that hydraulic constraints are not violated and demand is met. Two Bayesian Optimization approaches are proposed in this paper, where the surrogate model is based on a Gaussian Process and a Random Forest, respectively. Both approaches are tested with different acquisition functions on a set of test functions, a benchmark Water Distribution Network from the literature and a large-scale real-life Water Distribution Network in Milan, Italy.

A precision pump schedule optimization for the water supply networks with small buffers

The study addresses the problem of finding an energy-efficient pump and valve configuration of a water supply network. It is motivated particularly by scantily buffered networks which require both method precision and algorithm efficiency that tightly chase notably dynamic water demand. The model unprecedentedly comprehends physical and hydraulic laws that govern pump-valve configuration along with ensuing flow and energy level. The solution method combines hydraulic relaxation of individual pump characteristic curves to a station curve and an LP-based search performing optimal trade-off between water head and discharge beyond the minimum energy level for each station. With a hamming-distance-type shortest path formulation incorporated into the search steps, it can also minimize both frequency and magnitude of pump-valve reconfiguration. The proposed method achieved an energy-cost saving of 5.9% and did so more consistently than manual operation, while retaining computation time suitable for unit period as short as 15 min.

Extending EPANET Capabilities with Add-In Tools

EPANET is probably the most widespread model for water distribution network (WDN). More than twenty years after its appearance, it has become a global reference both for hydraulic and quality analysis of water networks. In 2000, EPANET 2 appears, which includes as most important computational feature a new Toolkit. This toolkit was a library of functions allowing the modification of network data and reading results without access to the appropriate files. Over time, the use of this library has been the communication protocol for every application developers who use the method propose by Todini and Pilati to analyze the behavior of WDN. This library also provides interface tools that allow the execution of a simulation from an external application, as long as the network characteristics had been previously defined.This paper presents a change in the original EPANET model, including a new menu in the graphical user interface (GUI). This menu allows users to set up a personal collection of Add-In tools, which use both project data and simulation results. These tools can be customized and allows to extend the analysis capability of EPANET. All of them can access EPANET functions through the Toolkit and were developed by the authors during the Spanish translation of EPANET, taking into account the homologous Add-in tools developed for SWMM model. As an example of the operation and capabilities of this new menu, several applications integrated as EPANET add-in tools are presented. These tools perform tasks such as importing data network from both CAD and GIS systems, the design of WDNs using genetic algorithms, automatic assignment of initial water quality to network nodes; the skeletonization of a network or optimization of pumping schedule in the network in order to achieve a minimum energy cost.

Investigation of Cost and Energy Optimization of Drinking Water Distribution Systems.

Holistic management of water and energy resources through energy and water quality management systems (EWQMSs) have traditionally aimed at energy cost reduction with limited or no emphasis on energy efficiency or greenhouse gas minimization. This study expanded the existing EWQMS framework and determined the impact of different management strategies for energy cost and energy consumption (e.g., carbon footprint) reduction on system performance at two drinking water utilities in California (United States). The results showed that optimizing for cost led to cost reductions of 4% (Utility B, summer) to 48% (Utility A, winter). The energy optimization strategy was successfully able to find the lowest energy use operation and achieved energy usage reductions of 3% (Utility B, summer) to 10% (Utility A, winter). The findings of this study revealed that there may be a trade-off between cost optimization (dollars) and energy use (kilowatt-hours), particularly in the summer, when optimizing the system for the reduction of energy use to a minimum incurred cost increases of 64% and 184% compared with the cost optimization scenario. Water age simulations through hydraulic modeling did not reveal any adverse effects on the water quality in the distribution system or in tanks from pump schedule optimization targeting either cost or energy minimization.

Optimization of pumping schedule based on water demand forecasting using a combined model of autoregressive integrated moving average and exponential smoothing

Stable water supply to end users is the most important element in water supply systems (WSSs). The portion of energy used by the water distribution system is up to 40% of the total energy consumed by WSSs. To save energy cost for pumping systems, a number of attempts have been made. Especially, an optimization scheme for scheduling the water-pumping operation has attracted the interest of water engineers. In this paper, a binary integer program was applied to optimize pumping schedule of a WSS in Polonnaruwa, Sri Lanka based on the hourly water demands for the next day. The water demands were forecasted by a combined model consisting of an autoregressive integrated moving average (ARIMA) model and an error compensation routine based on exponential smoothing technique. The result showed that the optimization system could reduce the operation cost of the WSS by minimizing electricity for water pumping; electricity cost for pump operation could be reduced by 55%.

A simple forecast technique for estimating the statistical characteristics of water consumption

The forecast water consumption values are the most critical input data in the pump schedule optimization of water distribution systems. The aim of this paper is to present a simple technique which is able to estimate the mean consumption and its distribution for a given demand zone with an hourly resolution. Simplicity (low computational cost) is advantageous since the forecast model needs to be run for any optimization computation. The proposed technique uses a recorded hourly consumption database and consists of two steps. First, the database content is automatically grouped based on the similarity of the elements (more precisely, their normality). This step is time-consuming but is performed only once for a given database independently of optimization. The second step – which is quick but has to be performed before the actual optimization – makes use of this grouping for forecasting mean value and standard deviation. The proposed technique provides hourly water consumption predictions independently; that is, the neighbouring hours do not effect each other, which prevents the accumulation of prediction errors. The daily overall consumption is computed a posteriori. The test results presented in this paper prove the applicability of the technique for real-life problems. Moreover, it is demonstrated that the confidence interval provided by the technique includes the actual measured data.

Concurrent Pump Scheduling and Storage Level Optimization Using Meta-models and Evolutionary Algorithms

In spite of the growing computational power offered by the commodity hardware, fast pump scheduling of complex water distribu- tion systems is still a challenge. In this paper, the Artificial Neural Network (ANN) meta-modeling technique has been employed with a Genetic Algorithm (GA) for simultaneously optimizing the pump operation and the tank levels at the ends of the cycle. The generalized GA+ANN algorithm has been tested on a real system in the UK. Comparing to the existing operation, the daily cost is reduced by about 10 − 15%, while the number of pump switches are kept below 4 switches-per-day. In addition, tank levels are optimized ensure a periodic behavior, which results in a predictable and stable performance over repeated cycles.

Comparison of deterministic and heuristic optimization solvers for water network scheduling problems

This paper presents a novel approximate dynamic programming technique for solving the pump schedule optimization of real-water distribution networks. The method is based on the significant decreasing of the search space by splitting the optimization problem into smaller units. In addition, the state space of the main distribution system was further reduced to the most important reservoirs. The capabilities of the proposed technique are demonstrated on a real-life problem, the water distribution system of the town of Sopron, Hungary. Nine test cases were defined which represent different initial water level scenarios, thus the new application was easy to compare to a former developed genetic algorithm and to some world-leading optimization solvers which are available on the NEOS Server. The benefits and drawbacks of these deterministic and heuristic methods are highlighted.

Ant-colony optimization of pumping schedule to minimize the energy cost using variable-speed pumps in water distribution networks

Despite considerable pumping energy costs in pumping stations of water distribution networks (WDNs), there are not many studies offering pumping schedule in order to optimize pumping energy costs regarding the WDN design. This paper aims to focus on the optimization of the WDN pumping station schedule by means of variable-speed pump (VSP) and using a combination of the ant system iteration best algorithm (ASib) and EPANET2.0. In fact, the VSP is implemented to increase the flexibility of pumping station and obtain the pumping schedule with optimized energy cost as the water demand changes during a day. Given that vast search space in optimization process leads to a decrease in the quality of final results, in this study, two heuristic methods coupled with ASib are proposed in order to reduce the number of feasible solutions in the search space. The optimization results showed that the proposed heuristic approaches have considerably improved the quality of solutions produced by the ASib and enhanced the navigation of the optimization process. The results of optimization for the Richmond network, similar to the genetic algorithm (GA), showed that the ASib was capable of improving pumping energy costs. Besides, using the variable-speed pump in an optimized pump scheduling could lead to greater savings (about 10%) in pumping energy costs compared with the single-speed pump (SSP).

Finding Least-Cost Pump Schedules for Reservoir Filling with a Variable Speed Pump

AbstractThis paper presents a simple and straightforward technique to solve the problem of least-cost reservoir filling with the help of a variable speed pump in the case of a highly simplified hydraulic system. Although artificial performance curves are used, the presented technique is directly applicable for real-life hydraulic systems of the same topology. The technique is based on keeping the specific energy consumption of the pump as low as possible and uses easy-to-implement control policy. Because of the simplicity of the model, it is believed that it can serve as a tutorial or benchmark problem for pump-schedule optimization problems. The near optimality of the results is demonstrated numerically by comparing them to the solution of a general-purpose global optimization software.

Short-term pump schedule optimization using MDP and neutral GA

The choice of a pump schedule has a great influence on the cost efficiency of a system, when the energy consumption charge changes during the day. The pump scheduling problem for a simplified regional water network is considered, and the formulation of the problem as a Markov decision process is given. The experimental section shows computer simulations and compares the results with a novel evolutionary approach based on neutral genetic algorithm techniques.

Neutral Search Technique for Short-Term Pump Schedule Optimization

This paper deals with the computation of short-term (typically 1 day ) least-cost pump schedule for water distribution systems with on-off type pumps and well-defined operating points. The objective function is to minimize the overall energy charge for a prescribed water consumption while several constraints are considered, such as storage and source limitations, pump setting bounds, nodal mass balances, and the power demand charge. In this study a neutral search technique with genetic algorithms (GAs) is proposed to solve the least-cost pump schedule problem where neutrality is achieved through objective-fitness mapping instead of representational redundancy. We introduce a fitness assignment technique for groups of individuals where grouping is based on objective similarity. As a consequence two different individuals can be equally fit (belonging to the same group) which implies the neutrality. We compare the neutral search technique to two conventional GA approaches on a hypothetical water distribution...

The energy-efficiency benefits of pump-scheduling optimization for potable water supplies

Water utilities across the developed world have been installing and operating telemetry and SCADA (supervisory control and data acquisition) facilities for at least three decades. They have amassed substantial quantities of historical operational data held in databases called data warehouses. Significant interest exists for extracting the underlying value from this data to support decision making and performance improvement. The water industry uses approximately 3% of total electricity production in developed countries such as the United Kingdom and the United States. Up to 90% of this electrical energy is consumed by pumps. Small improvements in pump efficiency will yield significant reductions in energy consumption with consequential reductions of carbon emissions to the atmosphere. Technologies to initially select a pump to match the expected performance requirements and then maintain optimal performance through periodic refurbishment are well established. Dynamically optimizing the scheduling of pump operation to improve efficiency under changing diurnal and seasonal water demand patterns is far more complex. This paper summarizes 20 years of progress in the development of pump efficiency improvement techniques and focuses on real-time dynamic optimization technologies and data-mining techniques to improve energy efficiency. Case study results from an automated real-time commercial pump-scheduling system, Aquadapt™, are presented.

Optimization of pumping schedule based on forecasting the hourly water demand in Seoul

In modern water distribution systems, pumping accounts for a large portion of the costs; therefore, water utilities need to reduce the pumping cost. The purpose of this study was to reduce and optimize the pumping costs. The study area was composed of one filtration plant, five reservoirs and 3 pumping stations. The IP (Integer programming) method used for the optimization, as it gave a global solution, with the pump controlled as either on or off. It is necessary to correctly forecast the hourly water demand to obtain an IP solution as both the optimized pumping schedule and low limitation of the reservoir are dependent on this factor. Therefore, three methods (time index, multiple regression + time index & Fourier series + transfer ARIMA) were compared to forecast the hourly water demand. As a result of these comparisons, the multiple regression + time index model was selected. The low limitation of the reservoir was also determined depending on the correction of the hourly water demand model. The optimization of pumping in the water distribution system had previously been simulated for 3 months using the IP. As a result of this simulation, it was found that the pumping cost could be reduced by 12.2%∼38.7%.