Gideon Sinai

OPTIMAL OPERATION OF MULTIQUALITY WATER SUPPLY SYSTEMS-III: THE Q-C-H MODEL

A new technique for optimal operation of multiquality water supply systems is proposed. The technique, which is known as a Q-C-H (flow-quality-head) model, combines previously developed Sow-quality (Q-C) and flow-head (Q-H) models for optimal operation of water supply systems. The decision variables in the model are the operation of treatment plants, pumps and valves. The model minimizes the cost of water at sources, treatment, energy, and loss of agricultural yield when water quality is low. The model uses an iterative modified projected gradient method combined with the Complex method. As in the Q-C and Q-H models, the solution method is based on decomposition, dis-aggregation/aggregation approach, involving internal and external optimization. The decision variables of the external model are the flows in the loops of the network and the removal ratios at the treatment plants. The operation of the pumps and valves are the decision variables of the internal model. The method is demonstrated by application to an example problem.

OPTIMAL OPERATION OF MULTI-QUALITY WATER SUPPLY SYSTEMS-I: INTRODUCTION AND THE Q-C MODEL

One of three complementary models for optimal operation of multi-quality water supply systems is presented. The other two models are the subject of companion papers. The model, which is known as the Q-C (flow-quality) model, includes mass continuity of water and constituents. However, the hydraulic constraints do not appear explicitly. To prevent infeasibilities or unreasonable hydraulic conditions arising from the lack of hydraulic constraints, limits and a cost are associated with the flow in each pipe. The constraints in the model include dilution conditions which depend on flow direction. These dilution conditions are introduced into the model by an exponential function, resulting in a smooth continuous nonlinear programming problem, which is transformed into an equivalent problem and solved by a modified projected gradient method. The method is insensitive to scaling of variables, and the computational complexity depends only slightly on the number of water quality parameters. The method is demonstrated by application to two examples: the solution for a small network is presented in detail, and main results are shown for a larger one. The results of these two applications indicate the methods applicability to real networks.

OPTIMAL OPERATION OF MULTI-QUALITY WATER SUPPLY SYSTEMS-II: THE Q-H MODEL

This paper describes the second in a series of three models for optimal operation of multi-quality water supply systems. This second model, which is termed the Q-H (flow-head) model, seeks to determine the optimal operation of pumps and valves, and does not consider water quality aspects. However, the model belongs to the group of three models Tor multi-quality systems because it is one of the two building blocks (the other is the flow-quality Q-C) of a full-llow-quality-head (Q-C-H) model. This Q-H model is based on continuous representations of the head-flow and power-flow functions of the pumping stations, which in turn results in a continuous non-convex optimization model. For a given flow distribution in the network, Q0, the Q0-H model is solved for the optimal operation of pumps and valves. The flow distribution is then modified by changing the circular flows, using a projected gradient method combined with the Complex Method which employs the results of the Q0-H solution, such that the locally optimal solution at the next point has a better value of the objective function. The process is continued until one of the termination criteria is satisfied. The circular flows thus serve as decision variables in an external problem, while in the internal problem the decisions are the operation of pumps and valves. The method is demonstrated by application to a sample problem.

Salinity control in multi-quality irrigation networks -- Kibbutz Hamadia feasibility study

Abstract A farm-scale water supply system of Kibbutz Hamadia in Israel has been analyzed to demonstrate the feasibility of controlling water quality by using a multi-quality network so as to meet the various water quality requirements at the consumer outlets. The irrigation network has been analyzed in steady-state and transient conditions. The results show the importance of the setting of the degree of opening of the control valves to prevent a shift in the dilution point. The quality of water supplied to the consumers was found to change significantly during the transition period and the consequences of this lag time have been shown. This method offers an alternative to a dual or even multiple water distribution system.

Comparison of models for optimal operation of multiquality water supply networks

The solution of models for the optimal operation of multiquality networks is difficult because both the objective function and the constraints are nonlinear. Methods of nonlinear optimization are sensitive to scaling, values of gain factors in the penalty terms, distance of the initial solution point from the optimal point, and the size of the network. The original nonlinear problem has been simplified by selecting proper variables as unknowns. An equivalent optimization problem with nonlinear objective functions and linear constraints is presented. A comparison is made between two methods: the suggested one, decomposed projected gradient (DPG), and sequential quadratic programming (SQP), on several case studies. It was found that SQP obtains slightly better solutions for small networks but is sensitive to the gain factor, to scaling, and to the choice of initial point. For networks containing 20–50 pipes and nodes, SQP did not reach a feasible optimal solution. To overcome the scaling problem, two projected gradient approaches—full mixing step (FMS) and partial mixing step (PMS)—are suggested and tested against the SQP and a unit adjustment (PMS-O) optimization methods. Both methods, PMS and FMS, result in good steady solutions even for a complicated case of a regional network with multiple water quality factors and treatment plants. The SQP and PMS-O methods failed due to scaling, size of network, and distance of initial points from the optimal solution.

Optimisation of complex water supply systems with water quality, hydraulic and treatment plant aspects

A model for optimal operation of a complex water supply system for drinking water and with water quality, hydraulic and desalination treatment plants developed by Cohen and others has been applied to a realistic regional network, in which water quality is defined by salinity, magnesium and sulphur. The model considers the hydraulics of the network, including pump stations, boosters and control valves. Solute transport in the model assumes conservative water quality parameters. Changes in water quality within the network are achieved by changing the removal ratio of reverse osmosis in desalination treatment plans and by control of mixing (dilution) at junction nodes. The decision variables in the model are the operation of treatment plants, pumps and control valves. The model minimises the sum of the costs of water at sources, treatment, energy and loss of agricultural yield due to irrigation with low quality water. Three case studies are presented: (1) a network without treatment plants and water salinity as the only water quality parameter; (2) as for (1), but with treatment plants included; and (3), as for (2), but with the addition of magnesium and sulphur quality parameters. The results demonstrate the ability of the model to handle a regional water supply system having water quality problems, with optimal solutions being found in cases where there is a conflict between hydraulic and water quality requirements.

Hierarchical control of multi-quality water distribution systems

Abstract More poor-quality water will have to be utilized in order to satisfy the increasing demand for irrigation water. This can be done if it is sufficiently diluted with fresh water. The dilution process takes place within the water distribution networks, which therefore become multi-quality networks, with simultaneous control of water quantity and quality. This brings up numerous new problems which can be solved by a special hierarchical control method with two control levels. The upper level transfers the consumer demands into setpoints for water flow and quality in the network. An optimization alogrithm was developed for this upper level, which computes these setpoints so as to minimize total operational costs. The lower level attempts to achieve these setpoints using digital and analog feedback controllers. A digital simulation model of a typical case study offers the possibility to check the control algorithm very accurately. Some simulation results are presented, and recommendations for designing such multi-quality networks are made.

A model for optimal real-time computer control of pumping stations in irrigation systems

Abstract A model for computerized optimal real-time control of pumping stations in irrigation systems is proposed. This model minimizes energy consumption of the system searching through the possible operating points of the irrigation network and the pumping station (with several possible combinations of pump arrangements) until the optimal operating point is achieved. Discharges and pressure heads required at the irrigation control heads for the individual irrigation plots comprise the constraints of the model. The optimization procedure is carried out by a microcomputer attached to a commercial electronic controller. The performance of the suggested optimal control algorithm is demonstrated for a large irrigation system with 135 pipe sections, 115 irrigation control heads, and a pumping station of five pumping units. Theoretical analysis reveals approximately 10% savings in pumping cost, comparing the proposed method with conventional computer controller that is in use today.

Machinery for installation of small diameter pipes at shallow depths

Abstract A method of installing 20–35 mm diameter drain tube using low-cost machinery is described. Extensive soil loosening above and beside the drain is achieved using wing attachments and shallower leading tines. Top soil placement above the drain is incorporated in the same pass as the pipe is installed, to eliminate cavities, enable firm pipe bedding, and good grade control.