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REAL-TIME MULTIOBJECTIVE OPTIMIZATION OF
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OPERATION OF WATER SUPPLY SYSTEMS
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Frederico Keizo Odan¹, Luisa Fernanda Ribeiro Reis²and Zoran Kapelan³
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Assistant Professor, Department of Science and Environmental Technology, Federal Center for Technological Education of
Minas Gerais, Av. Amazonas, 5253. CEP 30.4121-169, Belo Horizonte, Minas Gerais, Brazil. E-mail:
frederico_keizo@yahoo.com.br.
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Professor, Department of Hydraulics and Sanitary Engineering, University of São Paulo, Av. Trabalhador Sãocarlense, 400. CEP
13566-590, São Carlos, São Paulo, Brazil. E-mail: fernanda@sc.usp.br.
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Professor, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Harrison Building, North Park
Road, Exeter EX4 4QF, United Kingdom. E-mail: z.kapelan@exeter.ac.uk.
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Abstract: The need for more efficient use of energy in water distribution systems is increasing
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constantly due to increasing energy prices. A new methodology for optimized real-time operation of a water
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distribution system is developed and presented here. The methodology is based on the integration of three
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models: (1) real-time demand forecasting model, (2) hydraulic simulation model of the system and (3)
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optimization model. The optimization process is driven by the cost minimization of the energy used for
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pumping and the maximization of operational reliability. The latter is quantified using alternative measures
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into the optimization process in order to mimic the conservative attitude to pump scheduling often adopted
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by control room operators in real-life systems. Optimal pump schedules were generated by using A Multi
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ALgorithm Genetically Adaptive Method (AMALGAM), hydraulic simulations are performed by using the
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EPANET2 model and demand forecasting was performed by using the recently developed DAN2-H model.
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A number of other methodological developments are used to enable pump scheduling in real-time. The new
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methodology is tested, verified and demonstrated on the water distribution system of Araraquara, in the State
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of São Paulo, Brazil. The results obtained demonstrate that it is possible to achieve substantial energy cost
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savings (up to 13% relative to historical system operation) whilst simultaneously maintaining the level of
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supply reliability obtained by manually operating the water system.
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CE Database subject headings: Pumps, Scheduling, Optimization Model, Reliability, Water Supply.
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Author keywords: Pump scheduling, Optimization, Real-time operation, Reliability, Water Supply.
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Introduction
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Water and waste water utilities consume about 30-60% of city’s energy bill, representing one of the
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main expenditure of these companies (EPA, 2008), with pumping being responsible for up to 80% of the
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overall energy consumption (EPRI, 2002).
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The main objective of water companies is to deliver water to its customers in required quantity and
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quality, in a reliable and safe manner, at a reasonable price and in often changing demand and other
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conditions in the system and the surrounding environment. When operating their systems, water companies
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typically rely only on the experience of their operators. However, the resulting pump (and valve/source)
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schedules and the associated energy costs tend to be suboptimal as the primary goal of operators is to ensure
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reliability of supply (should something happen in the system, e.g. a pipe burst) which is often achieved by
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keeping the system tanks full of water most of the time.
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A better way of operating the system is by using some pump scheduling methodology to support
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operators in the control room. A number of such methods have been developed in the past but typically
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focused on different optimization methods used in the offline context. Initially, local search method were
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used, i.e. linear programming (Jowitt and Germanopoulos, 1992; Pasha and Lansey, 2009), nonlinear
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programming (Yu et al., 1994; Sakarya and Mays, 2000), dynamic programming (Zessler and Shamir, 1989;
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Lansey and Awumah, 1994; Nitivattananon et al., 1996; McCormick and Powell, 2003) and discrete search
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methods (Pezeshk and Helweg, 1996). Later on, global search methods became more popular, e.g. Genetic
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Algorithms (GA) (Mackle et al., 1995; Savic et al., 1997; Boulos et al., 2000; López-Ibáñez et al., 2009;
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Kang, 2013), Simulated Annealing (Goldman and Mays, 2000) and Ant Colony Optimization (López-Ibáñez
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et al., 2008). Finally, hybrid optimization methods were introduced (van Zyl et al 2004; Loganathan et al.,
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1995; Krapivka and Ostfeld, 2009; Giacomello et al. 2012) to overcome issues with local search (often
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trapped in local optima) and global search (typically computationally inefficient). In order to further increase
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the computational efficiency, alternative approaches based on black box models used to substitute the
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hydraulic model were developed (Jamieson et al., 2007; Broad et al., 2010). Besides the choice for an
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optimization method, some authors also explored the use of variable speed pumps in order to control
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pressure/flow to meet the system requirements and save energy (Lingireddy and Wood, 1998; McCormick
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and Powell, 2003; Ulanicki et al., 2007; Price and Ostfeld, 2013).
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Having said this, the quest to both effective and computationally efficient pump scheduling method
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continues. This paper explores the application of an alternative optimization method, AMALGAM (Vrugt
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and Robinson, 2007), which is unique in a sense that it uses simultaneously several other search methods
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with the aim to identify optimal solutions in a computationally efficient manner - exactly what is needed in
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pump scheduling. In addition, the above pump scheduling approaches are driven by the single objective, the
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minimization of pumping energy costs thus not giving any (explicit) considerations to the
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reliability/resilience of water supply which is of obvious concern to the system operators in real-life
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conditions.
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Most of the existing pump scheduling approaches cited above formulate and solve the pump
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scheduling as an offline problem. Once optimized offline, the resulting pump schedules are used to develop
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simple control rules which are then used by the operators. However, in real-life conditions, the system is
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often subjected to irregular demands changes, which cannot be adequately addressed by offline optimization.
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This can be overcome by introducing real-time (i.e. online) pump scheduling ( (e.g. Coulbeck et al.,1988,
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Jowitt and Germanopoulos, 1992, Rao and Salomons, 2007; Martinez et al., 2007; Shamir and Salomons,
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2008). These approaches typically combine specific hydraulic, demand forecasting and optimization models
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into a single real-time scheduling system. However, none of the very few real-time approaches developed so
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far seems to offer a way of dealing with the number of pump switches which needs to be minimized in real-
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time, in order to limit/minimize the maintenance costs associated with the wear and tear of pumps.
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This paper presents a new real-time pump scheduling methodology based on the integration of two
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unique models, a specific water demand forecasting model and a specific optimization model (neither used
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before in the real-time pump scheduling context) with the conventional hydraulic simulation model into a
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single framework. The framework also makes use of the new algorithm for handling the number of pump
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switches in real-time and the generation of pump schedules is driven by the novel, two objective
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optimization approach where the maximization of reliability/resilience of water supply is considered
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explicitly in addition to the minimization of pumping energy costs. This way the complex tradeoff between
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these two objectives is explored thus supporting the operators in making relevant, more realistic choices.
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Finally, unlike in many past approaches, the methodology proposed here is tested and verified on a large
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system case study.
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Real-time Pump Scheduling Framework
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The real-time pump scheduling framework is shown in Figure 1. As it can be seen from this figure,
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real-time pump schedules are generated by using the pump scheduling system (i.e., software tool based on
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the methodology described in this paper) which is run every hour. The real-time pump scheduling procedure
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is as follows:
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1. Receive latest data from the Data Acquisition part of the SCADA (Supervisory Control and
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Data Acquisition) system. These data comprise tanks levels, pump and valve statuses and
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flows in/out of the system that are used to estimate the current water consumption in the
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system.
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2. Forecast water demands for the next 24 hours by using current and past water consumption
data;
3. Update the Hydraulic Simulation Model (or Simulator) of the analyzed WDS by using data
obtained in steps 1 and 2;
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4. Run the Optimization Model to identify the optimized system operation, i.e., best pump
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schedule for the next 24 hours. During the optimization process use the Hydraulic Simulator
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to evaluate alternative pump schedules generated by the optimizer in terms of optimization
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objectives and to check the feasibility of the generated pump schedule (with respect to
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constraints);
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5. Implement the optimal pump schedule identified in the previous step for the next hour only.
This is done via the Supervisory Control part of the SCADA system (see Figure 1).
6. Repeat steps 1 to 5 continuously, i.e., until scheduling is completed.
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The demand forecasting was implanted here by using the Hybrid Dynamic Neural Network (DAN2-
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H) developed by Odan and Reis (2012). It is a self-constructing neural network based methodology which
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models the previous water consumption and the forecasted demand produced by a Fourier Series. The
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demand forecasting model estimates demands 24 hours ahead at each scheduling time step (i.e. every hour
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here). These values are then used to optimize the operation of a water network for the next 24 hours. More
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details about the demand forecasting model can be found in the aforementioned reference.
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The hydraulic model used here is the well known EPANET2 simulation model (Rossman, 2000),
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which implements the Gradient Method proposed by Todini and Pilati (1987). This model performs
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extended period simulation of the pressurized water distribution system and is used here to estimate the
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energy (and hence cost) consumed by the system pumps for given forecasted demands and assumed pump
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operations over the 24 hour scheduling horizon.
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The following section present the optimization model in more detail.
Optimization Model
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Optimization model is used to determine optimal pump schedules for the next 24 hours given
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forecasted demands for the same period. The pump scheduling problem is formulated and solved as an
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optimization problem with specific objectives, constraints and decision variables.
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The two objectives used in the approach adopted here are the minimization of pumping cost and the
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maximization of operational reliability. The pumping cost is defined as the cost of energy consumed by the
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motor pump set, without considering the demand cost of the electricity. The operational reliability is
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estimated by using four alternative measures: (1) entropy measure, (2) modified resilience index, (3) the
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minimum reservoir level and (4) the surplus head available, as described below.
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The entropy reliability proposed by Tanyimboh and Templeman (1993) interprets the flows from the
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probabilistic point of view. The probability of the water to be conducted by a certain path depends on the
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pipes of that path. For a network with known flow and its directions, the entropy is defined as follows:
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Nn
S  S 0   FQi S i
(1)
i 1
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where S is the entropy of the water supply system; S0 is the entropy of the water sources; Si is the entropy of
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the node i; FQi=FTi/Tot is the fraction of the total flow of the network that reaches node i; FTi is the total
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flow that reach the node i and Tot is the sum of the demand at the Nn nodes of the system. The source
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entropy is given as follows:
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S 0  
iI
Q0i  Q0i 
ln 

Tot  Tot 
(2)
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where Q0i is the inflow at the source i; I represent the water source set. In an analogous manner, the node
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entropy is expressed as follows:
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Si  
Q
Q 
Qi  Qi 
   ij ln  ij  i  1,..., N n
ln 
FTi  FTi  ijNDi FTi  FTi 
(3)
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where Qi is the demand at node i;Qij is the flow at the pipe connecting nodes i and j; and NDi is the pipe set
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connected to node i. For any water supply system, the entropy depends only on the pipe flow, as the node
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demand is predefined, which is specific for a certain demand pattern. In other words, the entropy measures
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the flow uniformity of the water network.
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The modified resilience index is based on Todini (2000) and modified by Jayaram and Srinivasan
(2008) to consider multiple water sources:
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 Q H
Nn
MI r 
j 1
i
j
 H min, j 
 100
Nn
Q H
j 1
i
(4)
min, j
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where Qj is the demand at node j; Hj is the head at node j; Hmin,j is the minimum necessary pressure to supply
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node j.
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The minimum reservoir level is the minimum sum of all reservoir level at a given time, to guarantee
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existence of minimum water volume at the reservoirs to be used in emergency situations. It is expressed as
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follows:
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 Nr 
L min  min  Lr 
 r 1 
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(5)
where Lr is the level of reservoir r and Nr is the number of reservoirs of the considered system.
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The surplus head is similar to the Modified Resilience index. This measure is only weighted by the
node demand, as shown by Equation (6):
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 Q H
Nn
Pexc 
j 1
i
j
Nn
Q
j 1
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 H min, j 
 100
(6)
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The pump scheduling optimization is subject to the following constraints:
 Pressure at any network node must not be below a pre-specified minimum threshold. A
threshold of 10 m is used here, based on Brazilian standards;
 Final water tank levels must not be lower than the level at the beginning of the simulation, to
ensure sustainable long-term system operation;
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 Number of pump switches must be lower than a pre-specified threshold. Excessive pump
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switching ON and OFF causes premature wear and tear and leads to increased maintenance
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costs. A threshold of 4 pump switches is used here, based on Lansey and Awumah (1994).
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 Occurrence of errors during hydraulic simulation, caused by pipes been disconnected or
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occurrence of negative pressures is not allowed and the corresponding infeasible pump
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schedules are discarded.
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Each pump schedule is represented using the binary form where 0 represents pump OFF and 1
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represents pump ON status. Therefore, for a period of 24 hours, the search space size for each pump being
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scheduled is 224 possible combinations. In order to reduce the search space, the representation proposed by
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López-Ibañez (2009) and used by López-Ibáñez et al. (2011), called the relative time-controlled trigger, is
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used here. This representation schedules the pumping by combining the duration of the operating and idle
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intervals and explicitly limit the number of pump switches. The control is represented by successive pairs of
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decision variable ti and t'i, representing the period the pump should be OFF and ON, respectively. In this
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paper three (3) pairs were used, which means the pump switch was limited to three (3), considering the
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production of the decisions of the next 24 hours.
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The AMALGAM optimization method (Vrugt and Robinson, 2007) is used here to solve the above
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optimal pump scheduling problem. AMALGAM simultaneously uses four different metaheuristics which
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learn from each other by sharing data from a common population of points. The search process starts by
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creating a random initial population P0 of possible solutions (of dimension N) by using the Latin Hypercube
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Sampling method (Iman and Conover 1982) with uniform distribution. The elements of P0 are then sorted by
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using the Fast non-dominated sorting algorithm (Deb et al., 2002). The next population Q0 (of the same size
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N) is created by using the multi-method search, combining k individual metaheuristics, to generate the
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population Q0  Q01 ,..., Q0k . Each algorithm creates a specific number of solutions, N  N t1 ,..., N tk , from
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P0. The solutions are combined to produce R0  P0  Q0 of size 2N, which are sorted using the fast non-
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dominated sorting algorithm. The elitism is guaranteed by including the non-dominated solutions in R0.
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Finally the next solutions are chosen to compose population P1, based on their rank and on their diversity
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(see crowded comparison operator from Deb et al, 2002). Then a new population is generated from
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population P1, repeating the previous steps until convergence is achieved. Each algorithm generates
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offspring solutions N tk proportional to their success in the previous generations of solutions. The main idea
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of the method is to combine the strengths of different metaheuristics to have a more efficient and effective
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optimization process. The four metaheuristics used here are the same as in Vrugt and Robinson (2007): (1)
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the NSGA-II (Non-dominated Sorting Genetic Algorithm II), (2) the PSO (Particle Swarm Optimization),
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(3) the Adaptive Metropolis Search (AMS) and (4) the Differential Evolution (DE).
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


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The AMALGAM metaheuristics produce real value solutions hence the use of relative time-
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controlled trigger representation makes necessary to convert these solutions into integer values, in order to
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reduce the available search space, otherwise, the search space would be unlimited. Each time a new
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population of solutions is generated, a routine is used to fix the solutions. First, the decisions variables are
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rounded. If the sum of the decision variables of a solution exceeds the period T (e.g., 24 hours), the fixing
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operator keeps reducing their values proportionally to their initial values, until the sum is equal to the period
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T.
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The optimization constraints were handled by using an alternative method proposed by Deb and
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Agrawal (1999) and modified by Prasad and Park (2004). At each generation, one solution is replaced at
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random by a schedule that turns ON the pump for the next 24h. In addition, a random solution is replaced at
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each generation by a solution so that all pumps are switched ON. The above random replacements are done
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to ensure the existence of at least one feasible solution in the population during the optimization run.
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Post-processing of optimized pump schedules
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The pump scheduling optimization is performed every hour for the forthcoming 24 hours. However,
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only the optimized schedule for the first hour is actually implemented in a real-life system, as shown by
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shaded squares in Figure 2. Having said this, Implementing the first hour schedule may lead to exceeding the
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maximum number of pump switches allowed for 24 hours. The reason for this is that the currently
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implemented pump schedule does not consider the schedules already implemented in the past hours of the
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day.
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To overcome this issue, the previously implemented pump schedule is evaluated here jointly with the
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currently optimized pump schedule, as shown in Figure 3. This combined pump schedule is denoted as the
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Combined Optimized Schedule (COS). In the example shown in Figure 3, the COS consists of two
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implemented decisions (i.e. actual pump schedules for the past two hours) and the first 22 decisions of the
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next 24 hours optimized pump schedule.
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To check if the COS containing the latest optimized pump schedule is feasible, three techniques are
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used and applied sequentially for each COS. These techniques are: (1) selection of the combined optimized
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schedule to evaluate, (2) minimization of pump switches in the COS and (3) minimization of pumping
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during peak energy cost hours (6-9 pm in the case study analyzed here). When these techniques are applied,
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the binary pump schedule representation is used instead of the relative time-controlled trigger representation
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(López-Ibañez, 2009) used during the optimization process. This was done as using the binary representation
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makes combining pump schedules easier.
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The selection of a single COS evaluates the Pareto front, i.e., the non-dominated points (i.e., pump
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schedules) until a feasible solution is found. Instead of using any specific method to select a single solution,
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the selection follows the order of solution produced by AMALGAM heuristc in order to save computational
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processing. If there are no feasible COS solutions on the non-dominated Pareto front, then solutions from the
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first next dominated front are considered as potential candidates (and so on, until a feasible solutions in the
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population is found). If no feasible solution exists in the population then the first evaluated solution (of this
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selection process) from the non-dominated Pareto set is selected. This technique is used to save
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computational time by avoiding the evaluation of all solutions. In addition, it is simple to handle and
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implement (e.g. there are no additional parameters to tune etc.).
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The selected COS is further processed with the aim to minimize the number of pump switches. The
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following procedure is used for each pump and only for the decisions prior to the peak hours (high energy
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cost hours, 6-9 pm in the case study analyzed here):
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1. Store selected COS in schedule1;
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2. If decision nh (Figure 4), in rounded square (in the case, OFF – 0) is different from decision
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nh+1, in the shaded square (on the case, ON – 1), then the decision nh+1 is stored in
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variable status. Afterwards, the decision nh+1 is modified to the same value of decision nh,
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i.e., it turns 1 to 0, or 0 to 1 if decision nh is ON (1). The new COS is stored in schedule2;
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3. Evaluate schedule2. If it is not feasible, proceed to next step, otherwise, proceed to step 5;
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4. Search the next decision of schedule2 equal to the value stored in variable status. In example
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from Figure 5, it is in position nh+3. The decision immediately preceding it and different of
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the value stored in status (decision nh+2) is modified to the value stored in status (0->1).
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The new solution is stored in schedule2;
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5. Compare schedule e1 and schedule2 using the fast non-dominated sorting and crowding
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distance algorithms (Deb et al. 2002) and select the best, i.e. non-dominating schedule If both
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schedules are non-dominated then select schedule2.
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The COS resulting from the above processing is further modified here by using the procedure that
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minimizes the pumping during peak hours. This technique is applied if pumps are being used during peak
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hours, i.e., if the next 24 hours part of the COS uses pump during peak hours, and only for the optimized
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schedules of the next 24 hours, because the already implemented decisions cannot be changed. The
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procedure is as follow:
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1. Store original COS in schedule1. Obtain number of decisions of schedule1 with status ON
during peak hours. This number will be denoted as npeak;
2. Repeat below sub-steps npeak times, for each decision with the status ON during peak hours:
2.1. Turn OFF the decision nh+i (1 ->0) and store modified schedule in vector schedule2, where
i represents the difference between nh and the peak hour considered (Figure 6);
2.2. Evaluate schedule2. If it is infeasible, proceed to step 3.3, otherwise proceed to step 4;
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2.3. a) If the decision to be implemented is prior to the peak hours, turn ON the decisions prior to
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the peak hours, until the schedule becomes feasible (Figure 7);
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b) If the decision to be implemented is during peak hours, turn ON the decision posterior to
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the peak hour until it becomes feasible, initiating from the last decision (Figure 8);
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3. If the decision was successfully modified, classify schedule1 and schedule2 using fast non-
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dominated sorting and crowding distance algorithms and then select the non-dominating
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schedule between the two. If both are non-dominated then select schedule2.
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Case Study
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The water supply network studied here is operated by the Autonomous Department of Water and
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Sewage (DAAE), from the city of Araraquara, state of São Paulo, Brazil. The studied DMA has two zones:
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High Zone and Low Zone, with average water consumptions 144 and 122 m³/h, respectively. The water is
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largely consumed by residential user but also industrial facilities. The DMA has 125 km of pipes, with
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diameters varying from 50 to 400 mm. The pipes are made of cast iron, PVC and asbestos cement.
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The hydraulic model (see network layout in Figure 9) has 1236 nodes and 1491 pipes. The boundary
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between the two zones is represented by thick dashed line. The Water Supply Facility (WSF) is comprised
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by the reservoir, the pumping station and the well, located in the thick ellipse (southwest). The Aldo Lupo
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Well pumps water to the reservoir R25 and is located southeast, highlighted by a thick ellipse (southeast).
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The WSF, highlighted by another blue ellipse is detailed in Figure 10. The Iguatemi Well usually pumps
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water to R25, but if necessary can supply water to the reservoir Upper R11 as well. The Upper R11 is
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usually supplied by the pump located between it and the reservoir Lower R11, which is linked to the R25.
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The Low Zone is supplied by the R25, while the Upper R11 supplies the High Zone. The detailed
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information of the reservoirs is in Table 1. The pumps of the wells have 142 kW and supplies 235 and 180
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m³/h, while the pump that supplies the Upper R11 has 46 hp and provides 240 m³/h.
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The electricity has two different prices for the peak and off-peak hours, R$ 5.41 and R$ 0.76,
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respectively. The peak hour refers to the three consecutive hours between 18:00 to 21:00 pm. In order to
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allow comparison between optimized operation and the operation currently practiced by the water company,
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it was necessary to identify a period of time without faulty data which was done on a monthly basis. At the
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end, one month of data was chosen for each District Metering Area (DMA) to optimize its operation, from
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August 12 to September 12 of 2010. Cost was calculated in Real (R$), where US$1.00 was equivalent to
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R$2.28, according to the currency exchange on 9th September of 2013.
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The DMA hydraulic model was previously calibrated. The water is supplied from the underground
wells. Although their level varies with time, an average value was used for the selected month of analysis.
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The studied problem has 3 pumps, each one can have two possible status (ON/OFF) for each hour
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during the period of 24 hours, resulting in a search space of 224x3 = 272 = 4.7 1021 possible combinations. The
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latter certainly justifies the need for applying an optimization method. Each optimization run was limited to
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2,500 objective function evaluations with a population size of 100, meaning that each optimization run was
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run for 25 generations. The aforementioned parameter values where chosen after a limited number of initial
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optimization trials.
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Results and Discussion
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The multi-objective optimization framework shown here was applied to the analyzed DMA. The
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pump scheduling optimization is performed for Tuesday, August 17, a typical day of the week. The
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optimization run took 16.5 minutes, on a Desktop Intel Core i7-3770 3.40 GHz, 8 GB RAM, Windows 64
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bits, to generate optimal pump schedules for the next 24 hours.
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Table 2 shows the results obtained by performing five multiobjective optimization runs, using a
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different combination of objective function(s). The optimized system operation is shown in the second
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column and the actual (historical) operation by the DAAE is shown in last row. Once the optimization has
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finished, a solution from the Pareto front, i.e., the first nondominated solution from the list produced by the
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AMALGAM heuristic was selected in each run. The values of cost, entropy, resilience, minimum level and
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surplus head were evaluated performing another simulation run. This additional run also evaluated the
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energy use during the period of 24 hours and during the peak hours (i.e., high energy price) of the evaluated
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day (see columns 3-7). All these values were evaluated for the historical operation as well.
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As it can be seen from Table 2, by using real-time pump scheduling it is possible to reduce the cost of
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energy used by as much as 13.2% (see schedule 4) when compared to the historical DAEE operation, yet
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maintaining a reasonable minimum reservoir level. As it can be seen from Table 2, pump schedules 1, 2 and
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4, which have the lowest cost, used pumps for shorter periods during the peak hours, as it was done
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historically by the DAEE operation. The optimization of cost along with reliability measures resulted in
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higher minimum reservoir levels than the ones obtained when optimizing for cost only as can be observed in
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schedules 2, 3, 4 and 5. As expected, DAAE operation maintained high minimum reservoir level due to the
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conservative operation, resulting in the second highest level.
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The optimized pumping schedules are shown in Figure 11, where Pumps 1, 2 and 3 correspond to
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pumps of the Aldo Lupo Well, Iguatemi Well and the pump between Lower and Upper R11 reservoirs,
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respectively. . The schedule 2, that was generated by optimizing the Cost and Entropy based operational
332
reliability, achieved the highest entropy value, which is probably due to highest quantity of energy used. Due
333
to the small variation of the Resilience and Surplus Head function values, it was not possible to draw a
334
conclusion about their benefits, except that they resulted in the highest energy cost (see schedules 3 and 5).
335
Analyzing further the results in Table 2 and Figure 11, it is possible to notice that: 1) The 13.2%
336
reduction on cost of energy (see cost of schedule 4) when compared to the historical DAEE operation was
337
possible because DAEE operation is done in a rather conservative manner with reservoirs kept full most of
338
the time, as demonstrated in Figure 11 and by the fact that the second highest minimum reservoir level is in
339
the case of historical DAEE operation; 2) Optimizing for cost and some measure of operational reliability
340
simultaneously typically results in higher energy costs (see schedules 2, 3 and 5) than when optimizing for
341
costs only (schedule 1). This is the price to pay for increased operational reliability, as demonstrated by the
342
higher entropy based reliability values, higher resilience values, higher minimum reservoir level values and
343
typically higher surplus head values obtained when optimizing for both cost and reliability (relative to cost
344
optimization only); 3) Optimizing for cost and some measure of operational reliability simultaneously may
345
result in lower costs (see schedules 2 and 4) but, at the same time, not that dissimilar operational reliability
346
values when compared to the historical DAEE operation. This further demonstrates the benefits of using
347
optimization. Having said this, based on Figure 11 results, it seems that the price to pay for the reduced cost
348
in optimized solutions (schedules 1-5) when compared to the historical DAEE operation is that the former
349
seems to have slightly larger number of pump switches than the latter (in most cases).
350
The variation of level at reservoirs Upper R11 and R25 can be examined in Figures 12 and 13,
351
respectively. During the peak hours (marked by a red shade in these two figures), a drop in the reservoir
352
levels is usually observed as pumps are typically turned off, to save energy during the peak hours, as shown
13
353
by the optimized strategies and the historical DAAE operation (see Figure 11). This is most obvious from
354
schedule 1 that was obtained by minimizing costs only which resulted in utilizing the full reservoir capacity
355
(see Figure 12 and 13), but at the price of reduced reliability (as demonstrated in Table 2). Note that,
356
opposite of schedule 1, schedules 2 and 4 (see Table 2) are simultaneously addressing the pumping cost and
357
supply reliability costs and are, as a consequence, able to raise reliability whilst still keeping the costs cost
358
low.
359
Figure 14 presents the final Pareto front obtained from a two objective optimization run (cost and
360
minimum reservoir level). As it can be seen, this front has 6 non-dominated points of which the lowest cost
361
schedule leads to savings of 13% when compared to the historical system operation. The graph shows the
362
tradeoff between the two objective functions, where solution A has the slowest cost and minimum level (R$
363
678,47 and 4,29 m), while solution B has the highest minimum level cost (R$ 1011,43 and 14,76 m).
364
365
366
Of the operational supply reliability measures proposed and analyzed in this paper, the measures
367
based on minimum reservoir level and surplus head seem most suitable for real-time pump scheduling
368
because their measurement units can be easily understood by the operator and the minimum reservoir level
369
showed higher sensitivity to the different pump schedules. Opposite of this, the two measures based on the
14
370
entropy and the modified resilience do not seem suitable as they showed low sensitivity to different pumping
371
strategies. The reason for this is that these measures come from the field of WDS design and the system
372
configuration does not change during the operational optimization. Having said this, these reliability
373
measures could possibly be of use in more complex distribution systems.
374
375
Conclusion
376
This work developed new methodology for real-time pump scheduling by combining two promising
377
techniques for real-time demand forecasting (DAN2-H method) and optimization (the AMALGAM
378
optimization method). Unlike in the existing approaches, the pump scheduling is driven by two optimization
379
objectives, the maximization of operational water supply reliability (several different measures explored) in
380
addition to the more traditionally used minimization of pumping costs. The methodology proposed here also
381
benefitted from the new algorithm for handing the number of pump switches constraint in real-time. Finally,
382
the methodology developed was tested and demonstrated on a real-life water distribution system of
383
Araraquara city in State of São Paulo, Brazil.
384
Based on the case study results obtained, the following observations can be made:
385
1. The proposed real-time pump scheduling methodology can deliver substantial cost savings for the similar
386
level of supply reliability obtained by manually operating the water system. This is achieved by
387
constantly adapting, in an optimized way, pump schedules to the changing demand conditions in a
388
distribution system. In the real-life case study shown here, the pumping energy costs savings obtained
389
were approximately 13% when compared to the historical system operation (for the similar level of
390
operational reliability).
391
2. Using the two objective optimization approach suggested here it is possible to produce an optimized
392
pump schedule that follows more the natural intuition of the water company system operator to 'play
393
safe' by keeping the water level in the reservoir above the minimum allowed for most of the time which,
394
in turn, provides the ability to respond to unplanned events such as e.g. pipe bursts and hence prevent the
395
resulting supply interruptions. Even more, the explicit optimization of operational supply reliability in
396
addition to pumping costs enables identification of the whole tradeoff between the two, which, in turn,
397
enables the system operators to make an informed decision about pump schedules based on their attitude
15
398
toward risk. Note that although the operational reliability can be potentially imposed indirectly (by e.g.
399
tightening the constraints on reservoir levels in optimization driven by cost minimization only), this
400
would prevent directly evaluating the actual operational reliability and defining the corresponding targets
401
hence is not desirable from the practical point of view.
402
3. The AMALGAM optimization method seems to be a reliable and potentially useful method for real-time
403
pump scheduling, at least based on the case study analysis conducted here and the corresponding results
404
obtained.
405
The work presented in this paper is by no means fully conclusive on the topic of optimized real-time
406
pump scheduling. Further work is required to test, validate and demonstrate the methodology shown here on
407
more complex case studies with larger and more complex water distribution networks with additional tanks,
408
booster pumps, variable speed pumps, etc. The developed methodology could be used to cope with the real-
409
time upscaling/implementation issues in more complex water distribution when combined with suitable
410
metamodels (as in e.g. Rao and Salomons 2007, Martinez et al., 2007) and parallelized computing.
411
Further investigation into the tradeoff between pumping costs and operational reliability is required
412
too, perhaps by considering additional reliability measures. Other means of selecting the Combined
413
Optimized Strategy (COS) can be considered too. Finally, additional work is also required to develop new
414
optimization methods that are perhaps better suited to real-time pump scheduling.
415
Acknowledgements
416
The authors acknowledge the support from the São Paulo Research Foundation (FAPESP), from the
417
Coordination for the Improvement of Higher Education (CAPES) and from the Brazilian Scientific and
418
Technological Development Council (CNPq) for providing the PhD's scholarship and Grant to the second
419
author, and also from the Araraquara’s Autonomous Department of Water and Sewage (DAAE-Araraquara,
420
SP, Brazil) for providing data and assistance through the agreement between the company and the University
421
of São Paulo.
422
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