Optimal scheduling of variable speed pumps with mixed integer linear programming

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).

Traditionally, pumping efficiency and pressure control have been studied as separate disciplines in water companies, with a focus on optimizing pump operation and managing leakage. Present-day siphons are frequently outfitted with variable speed drives; consequently, the siphon outlet tension could be constrained by controlling siphon speed. If there are siphons upstream from a tension-decreasing valve (PRV) with no moderate tank, the PRV gulf strain could be diminished by changing siphoning in the upstream piece of the organization. In addition, when optimizing pump operation, consideration should be given to the impact of pressure-dependent leakage on the resulting schedules. Thus, this article considers the streamlining of siphon and valve plans for complex huge-scope water circulation organizations (WDN). The review takes care of the siphoning booking issue, which tries to acquire the timetable of on/off switches for each siphon and valve that limits energy power cost, taking into account the energy consumed by the functioning siphons. This schedule generates the flow and pressure through the network and it has to satisfy the demand for all nodes, conserve energy, to minimize head loss. To execute and safeguard clean water assets, functional improvement of WDSs should consider both energy and upkeep costs while deciding the ideal timetable for siphons and valves. The point of this examination is to create and confirm an energy model that can work on the effectiveness of equal siphon frameworks. Accordingly, the research proposed the mathematical model of shaft power consumption using the quadratic polynomial fitting. Additionally, investigated the potential application of Variable Speed Pumps (VSPs) to improve pressure reliability, leakage, and electrical power consumption in Water Distribution Networks (WDNs). To execute and safeguard clean water assets, functional improvement of Water Circulation Frameworks (WDSs) should consider both energy and upkeep costs while deciding the ideal timetable for siphons and valves. The point of this examination is to create and confirm an energy model that can work on the effectiveness of equal siphon frameworks. The hybrid binary dragonfly-enhanced Particle Swarm Optimization (PSO) algorithm is proposed for joint pumping and valve scheduling problems in WDS. The optimal scheduling is conducted based on three different energy tariffs. The Matlab programming climate is utilized to demonstrate this strategy with the assistance of the EPANet Matlab tool compartment. Analyzing a range of scenarios with varying time frames, operational limitations, and network changes, the proposed WDN solution showed its capability to efficiently create and address optimization challenges tailored to diverse needs.

This work studies the power optimal dynamic scheduling problem in multi-channel multi-user wireless access networks. Users have quality-of-service (QoS) requirements on the minimum rates with statistical delay guarantees. Only one user is allowed to transmit over a channel in a given time slot. This work considers two scenarios: homogeneous and heterogeneous users. For the former scenario, the optimal scheduling policy can be derived, and an online scheduling algorithm for the optimal policy is proposed using online time-averaging without requiring a-priori known fading statistics. For the latter scenario, the optimal scheduling problem is combinatorially hard; hence, even when the fading statistics are available, computing the optimal policy is intractable. Consequently, this work develops a sub-optimal online scheduling algorithm with linear complexity which does not require a-priori known fading statistics. Moreover, the scheduling algorithm satisfies the QoS constraints for the users. Illustrative results demonstrate the performance of the proposed scheduling algorithms in various settings.

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.

We consider a class of k-server optimal task scheduling problems partitioning and scheduling N tasks with various real-time constrains and work loads on k servers with convex task processing cost function so as to minimize the total task processing cost while still guaranteeing satisfaction of all time constraints. This class has broad expressing power for practical scheduling problems in several areas such as real-time multimedia wireless transmission , CPU energy conservation, and warehouse order processing management, et. al. Our formulation is quite general such that most previous works can be readily reduced to a special case of the presented k-server optimal task scheduling problem. We show that, when k = 1, optimal solution can be obtained in computational complexity of O(N) and the corresponding optimal scheduling problem is equivalent to finding the shortest 2D Euclidean distance between two vertices inside a well-defined 2D polygon. However, when k 2, the optimal scheduling problem can be demonstrated to be NP-hard by reducing it to a well-known NP-complete bin-packing problem. Therefore, we conclude no polynomial time algorithm exists for a general k-server optimal task scheduling problem. We then construct approximation algorithms to solve the presented k-server problem in a practical way and illustrate its performance by simulation results and analysis.

SummaryModern power systems are being shifted its attention towards distributed generations (DGs). DGs have allured more concern as an auspicious opportunity with considerable economic profits. To minimize the power generation costs of DGs, day‐to‐day operation scheduling is essential. The role of this study is to offer an optimal operation schedule for DG with several energy sources including renewable energy sources (RES), considering economic facets. In order to achieve the cost minimization along with optimal scheduling, an objection function has been formulated and solved using the optimization algorithms. This study aims to present the applications of differential evolution (DE) algorithm and its variants such as opposition‐based differential evolution (ODE), self‐adaptive differential evolution (SaDE), improved differential evolution (IDE), and cultivated differential evolution (CuDE) for scheduling DG optimally. A scheme for optimal scheduling of thermal, wind power, and solar PV generators has been evaluated. The simulations have been carried out on IEEE 14 bus system, IEEE 30 bus system, IEEE 57 bus system, and Tamil Nadu Generation and Distribution Corporation Limited (TANGEDCO), as a real part of 62 bus Indian utility system (IUS). The novelty of this study lies in simulating a real‐time system for solving optimal scheduling problem, in that way helping decision makers to choose the optimal operation points. The results indicate that the SaDE outperformed other DE variants by giving the best fitness value and convergence rate.

Approximate optimal periodic scheduling of multiple sensors with constraints

A field problem involving pumping of groundwater from a series of existing skimming wells to meet drinking water needs from a river flood plain is examined within a conceptual framework. A simplified hypothetical aquifer system that is representative of a study area, skimming wells, input variables, and aquifer parameters is solved using a simulation-optimization (S/O) approach. The S/O model proposed in this study is solved as a nonlinear, nonconvex problem using a simulated annealing algorithm and a variable density flow simulator. An artificial neural network is used to replace the simulator to reduce the computational burden. An optimal pumping schedule in terms of location and pumpages is presented that controls up coning from underlying saline water. The study suggests that an increased number of skimming wells do not necessarily yield more water, and that the pumping schedule must be staggered in space and time.

Pricing function plays an important role in optimal energy scheduling problem in smart grid systems. In this paper, we propose a novel real time pricing strategy named proportional and derivative (PD) pricing strategy. An optimal energy scheduling problem is then formulated by minimizing the total social cost of the overall power system. A distributed optimization algorithm based on finite-time consensus and projected gradient method is provided for each agent to iteratively determine an optimal solution to the problem. As iteration increases, the solutions from all the agents reach consensus and this solves the formulated optimal problem. A case study of heating ventilation and air conditioning (HVAC) system shows efficiency of the proposed algorithm.

We present a jointly optimal selection and scheduling scheme for the lossy transmission of frames governed by a dependency relation and a delay constraint over a link with limited capacity. A main application for this is scalable video streaming. Our objective is to select a subset of frames and decide their transmission schedule such that the overall video quality at the receiver is maximized. The problem is solved for two of the most common classes of dependency structures for video encoding, which include as a special case the popular hierarchical dyadic structure. We formally characterize the structural properties of an optimal transmission schedule in terms of frame dependency. It is shown that regardless of the subset of frames selected for transmission, any optimal schedule has an equivalent canonical form that is a subsequence of a unique universal sequence containing all frames. The canonical form can be computed efficiently through the construction of a dependency tree. This leads to separable but jointly optimal frame selection and scheduling algorithms that have quadratic computational complexity in the number of frames. Simulation with video traces demonstrates that the optimal scheme can substantially outperform existing suboptimal alternatives.

Existing optimal scheduling packages for water distribution systems (WDS) calculate the time schedules for control elements such as pumps, valves and treatment works following the idea of open loop control. The calculations take into account the hydraulic model of WDS, operational constraints and the time dependent electrical tariff. The time horizon is typically one day or one week depending on the network storage capacity and the structure of the electrical tariff. If such a schedule is applied to a physical system the predicted and the physical reservoir levels diverge due to uncertain demands and as a result the calculations need to be repeated at some time using updated demand prediction and the current measured reservoir levels. The aim of this paper is to investigate the feasibility of synthesising continuous feedback from reservoir levels to pump and valve operation, taking into account the operational constraints and the electrical tariff. This attempt can be seen as a generalisation of a simple practical rule where a pump is controlled by the level of an associated reservoir, e.g. the rule `if the tank is full switch the pump OFF, if the tank is empty switch the pump ON'. The proposed methodology relies on preparing a control law in an off-line mode which is subsequently used in a real time situation. The traditional optimal scheduling problem is solved many times for typical initial reservoir levels in the system and a family of reservoir and corresponding control trajectories is generated. These trajectories are approximated by a hyper-surface which represents an optimal control law ready to use in the field. The control action will follow the sequence: log the time, measure the current reservoir levels, evaluate from the hyper-surface the corresponding operation for pumps and valves and finally apply the control action to the pumps and valves. The approach avoids time-consuming online-recalculation of pump schedules, and additionally the feedback control is much more robust with respect to uncertain demands. The limitation of the approach is dictated by the number of reservoirs and number of initial reservoir levels which need to be considered. In the worst case the computational complexity may increase exponentially with the number of reservoirs.^ Initially this approach was applied to a simple system containing a single reservoir fed by one pump station with a time varying tariff and subsequently to a medium-size system with four reservoirs and four pump stations. This paper was presented at the 8th Annual Water Distribution Systems Analysis Symposium which was held with the generous support of Awwa Research Foundation (AwwaRF).

The work presented in this thesis concerns the optimisation of the hour-to-hour generation schedule (over a scheduling interval of 24 hours) of the generating stations in an all-hydro electric - system. The day-to-day system storage policy is assumed known from the long-term schedule. System load demand is first treated as deterministic. Later, attempts are made to treat it as stochastic. Throughout the text, system transmission losses are represented by means of the B-coefficient loss formula. Chapter 1 presents brief discussions on various topics which may play - a part in the optimization process. In particular, the concept of frequency control and the distinction between long-term and daily scheduling are outlined. The optimization objective is then formulated and some of the known methods of obtaining the solution are briefly discussed. In chapter 2, the optimization problem is first formulated . as that of minimizing the instantaneous total power drawn from the system subject to satisfying a . predetermined time-varying load demand.This is analogous to the minimization of the instantaneous total cost rate in thermal systems. Station characteristic curves are approximated by straight line segments and head variations are assumed negligible. The optimising - conditions are derived using the Lagrange multiplier technique. A small system consisting of 4 stations is studied, where optimisation is achieved by means of an analogue computer. By introducing weighting factors in the objective function, the storage policy can be satisfied. (Analysis carried out in chapter 3 later reveals that this is the correct measure which must be taken to meet the storage policy). Problems do arise, however, when - there are multi-unit stations present in the system. Due to the non-monotonic nature . of the incremental Output curves' of such stations, a. number of solutions would satisfy the optimising conditions. The optimum solution can only be established after testing each possible solution, a prohibitive task for large systems. Approximating the incremental output curves of such stations may create undesirable errors. Another weakness of the method is that it cannot readily take into account the effects of head variations. The application of Pontryagin's Maximum Principle is attempted in chapter 3. It is shown that, for systems with fixed‚ÄövÑvÆ head stations, the optimising conditions are exactly identical to that derived using the Lagrange multiplier technique with weightings being introduced in the objective function. Unfortunately, those problems associated with the presence of multi‚ÄövÑvÆunit stations are still unsolved. Under ideal system conditions, it is shown that optimum generation schedule would result if all stations; except the frequency control station, were step loaded. Step loading mode is defined as an operating mode where the instantaneous station discharge rate is only allowed to take one of two discrete values with stepwise transitions. The analysis indicates that the switching instants do not play any part, except they must be so chosen that the output of the frequency control station is kept within its limits. When step loading technique is applied to non‚ÄövÑvÆideal systems, the optimisation. becomes that of searching for the optimum switching instants of the step loaded stations. This is discussed in chapter 4. For practical reasons, only two step loading modes are assumed admissible. A system consisting of 18 stations is studied. Experimental results indicate that the optimum step loading modes can be established within - a reasonably short computation time. One striking feature of the step loading technique is that it can handle the optimal scheduling problem where the load demand is treated as being stochastic. The effects of head variations can be estimated fairly accurately. The application of the principle of dynamic programming is discussed in chapter 5. Due to the multi-dimensional nature of the problem, this principle must be combined with the relaxation principle to minimise the computation time and computer storage requirements. A good initial guess for the optimum schedule may be obtained using step loading technique. The step loading modes are then modified by applying the combination of dynamic programming and relaxaxtion principles. Finally, chapter 6 outlines the general conclusions drawn from the work presented in the preceeding chapters. The possibility. of applying Pontryagin's Maximum Principle to obtain the long-term storage policy is also studied. Related future research areas are suggested. To the author's best knowledge, the materials presented in chapters 3, 4 and 5 are original. Chapter 2 is based on the work of Chandler Jr. and Gabrielle, where the mathematical error found in their text has been corrected and the weighting procedure, among other materials has been included.

Novel cyber-physical architecture for optimal operation of renewable-based smart city considering false data injection attacks: Digital twin technologies for smart city infrastructure management

To attain the highest performance of energy supply systems, it is necessary to rationally determine design specifications in consideration of operational strategies corresponding to energy demands. Mixed-integer linear programming (MILP) approaches have been applied widely to such optimal design problems. A MILP method utilizing the hierarchical relationship between design and operation variables have been proposed to solve them efficiently. However, it cannot necessarily be effective to multi-objective optimal design problems because of the existence of a large number of competing design candidates. In this paper, the hierarchical MILP method is revised from the viewpoint of computation efficiency so that it can be applied practically to multi-objective optimal design problems. At the lower level, the order of the optimal operation problems to be solved is changed based on incumbents obtained previously to increase a lower bound for the optimal value of the combined objective function and reduce the number of the optimal operation problems to be solved. At the upper level, a lower bound for the optimal value of the combined objective function is incorporated into the solution method to reduce the number of the design candidates to be generated. This revised hierarchical MILP method is applied to a multiobjective optimal design of a gas turbine cogeneration plant, and its validity and effectiveness are clarified.

Optimal (short-term) pump schedule detection for water distribution systems by neutral evolutionary search