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Energy 47 (2012) 505e514

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Energy

journal homepage: www.elsevier .com/locate/energy

Minimizing pump energy in a wastewater processing plant

Zijun Zhang, Yaohui Zeng, Andrew Kusiak*

Department of Mechanical and Industrial Engineering, 3131 Seamans Center, The University of Iowa, Iowa City, IA 52242 e 1527, United States

a r t i c l e i n f o

Article history:Received 23 May 2012Received in revised form5 July 2012Accepted 15 August 2012Available online 18 October 2012

Keywords:Mixed-integer nonlinear programmingEnergy savingData miningPump controlParticle swarm optimizationNeural networks

* Corresponding author.E-mail address: andrew-kusiak@uiowa.edu (A. Ku

0360-5442/$ e see front matter � 2012 Elsevier Ltd.http://dx.doi.org/10.1016/j.energy.2012.08.048

a b s t r a c t

This paper discusses energy savings in wastewater processing plant pump operations and proposesa pump system scheduling model to generate operational schedules to reduce energy consumption. Aneural network algorithm is utilized to model pump energy consumption and fluid flow rate afterpumping. The scheduling model is a mixed-integer nonlinear programming problem (MINLP). As solvinga data-driven MINLP is challenging, a migrated particle swarm optimization algorithm is proposed. Themodeling and optimization results show that the performance of the pump system can be significantlyimproved based on the computed schedules.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Growing awareness of environmental issues, sustainableliving, and limited energy supply has prompted interest in energysaving research in various industrial applications, includinglighting systems [1], supply chain [2], and heating, ventilating andair conditioning [3]. In this paper, energy savings of a pumpsystem in a wastewater treatment process is investigated. In2002, Goldstein and Smith [4] reported that nearly 4% of thenation’s electricity is consumed by wastewater treatment plantsand almost 80% of the electricity in the wastewater treatmentprocess is used by pumps. Therefore, further energy studies ofpump systems are warranted.

In general, savings in pump energy can be achieved in twoways.One is by designing more efficient pumps [5,6]. Another isimproving pump performance with effective control strategies. Thelatter does not require pump replacement. Research on pumpcontrol has been reported in the literature. Raggl et al. [7] discussedan approach for sensorless control of a permanent-magnetsynchronous bearingless pump. DeWinter and Kedrosky [8] intro-duced a 3500-hp adjustable speed drive to control an oil pipelinepump. Himavathi and Umamaheswari [9] developed a fuzzy modelto control a three-phase induction motor driving a submergiblepump. As discussed in [7e9], most of the pump control research

siak).

All rights reserved.

has focused on a single pump. However, pump systems used inwastewater processing plants usually include multiple pumps. Dueto the head influence [10,11], the dynamics of the pump system isdifficult to model. Moreover, the changing system dynamics due tothe degradation of the system components has not been consid-ered. Therefore, new approaches for modeling pump systems aredesired.

The existing literature has focused on energy savings and effi-ciency improvements of pumps in buildings. Xu et al. [12] investi-gated improving energy performance of biogas heat pumps in airconditioning systems. Ge et al. [13] designed an efficient hybridheat pump system for residential air conditioning systems. Ebrahimet al. [14] proposed a neural network controller to investigateenergy savings of a three-phase induction motor driving pump.Studies of pump systems in wastewater treatment are limited. Inthis paper, scheduling a pump system in wastewater treatmentprocess to reduce energy consumption is proposed. The perfor-mance of a pump system ismodeledwith a data-driven approach. Aneural network algorithm is applied to model pump systemdynamics by using industrial data. Data mining is an emergingscience that has been applied in various domains [15e19]. The data-driven models are integrated with constraints for schedulingoperations of the pump system. The objective of the schedulingmodel is to minimize energy consumption of the pump systemwhile maintaining the performance of the hydraulic load in anexpected range. An optimal schedule determines the mostpreferred configuration of pumps and pump speed control settings.

Z. Zhang et al. / Energy 47 (2012) 505e514506

As the scheduling model involves binary variables, continuousvariables, and data-driven functions, it cannot be solved withtraditional optimization algorithms. In this research, a migratedparticle swarm optimization algorithm is designed.

2. Modeling pump system performance

2.1. Pump system in wastewater pre-treatment

The pre-treatment process in a wastewater processing plant is tocollect wastewater from sewers, filter large solids contained in thewastewater (e.g., paper and sticks), and deliver filteredwastewater totheprimaryprocess.Apumpsystemwhich is composedof six55MGDclass variable speed pumps is installed to accomplish the delivery ofwastewater in the pre-treatment process. The maximum energyconsumption of a single pump is 700 kWh per 15-min (2800 kWh).Accordingtothevariousflowratesof influent, sixpumpsindexed from1 to 6 are determined to work alone or in parallel associations. Themaximum number of operating pumps is limited to 5 while theremainingpump is considered as abackup system. Fig.1 illustrates thewastewater pre-treatment process and shows the location of thepumpsystem.AsshowninFig.1, thewastewater fromdifferent sewersflows into the rawwastewater junction chamber after filtering by thebar screen. The pump system is located between the rawwastewaterjunction chamber and the primary process to lift the filtered waste-water from junction chamber to the primary process.

In the pre-treatment process, five rules are utilized to determinethe number of operated pumps based on the level of raw waste-water junction chamber. An example of the rule is presented next(Rule 1).

Rule 1. Assume the number of operating pumps at time t is one.The number of operating pumps changes to two if L is higher than5 ft at t þ T.

Where L is the level of raw wastewater junction chamber, tpresents the current time and T describes the time interval. Rulesare used to control the number of operating pumps to maintain thelevel of the raw wastewater junction chamber in a specified range.In addition, the selection of operating pumps according to the fiverules is based on balancing the runtime of the six pumps. The fiverules focus on maintaining hydraulic performance of the pumpsystem; however, the energy efficiency aspect of the pumps isoverlooked. This paper investigates development of a newmodel tooperate the pump system improving energy efficiency and main-taining its hydraulic performance.

Fig. 1. Pre-treatment process and the pump system.

2.2. Pump system configurations

The six pumps considered in the study were produced by thesame manufacturer. However, due to upgrades and repairs overyears, the dynamics of the pumps has changed. Moreover, due tothe head influence, the dynamics of the pump system is notequivalent to the linear combination of the dynamics of each pump.Therefore, the pump system exhibits different dynamics due to theconfigurations of the pump system which are defined in Definition2.1.

Definition 2.1. The configuration of a selected pump system isa parallel working association. For example, Pump 1 and Pump 2form a configuration if only these two pumps deliver wastewater tothe primary process simultaneously.

Since the pump system includes six pumps, the total number ofpossible configurations is expressed in (1).�16

�þ�26

�þ�36

�þ�46

�þ�56

�¼ 62 (1)

In this study, each configuration is described as a set of pumpindexes, for example, {1}, {1, 2}, {1, 3}.

2.3. Data-driven modeling approach

The analytical model for estimating the pumping power ispresented in (2).

P ¼ DPQh

(2)

where P is the power,DP is the change in the total pressure betweeninlet and outlet,Q is the fluid flow rate, and h is the pump efficiency.

Power consumed by a pump based on Eq. (2) is not accuratebecause the pump efficiency, h, is not constant. The pump efficiencyis highly nonlinear and depends upon various factors such aspumps’ configuration, rotational speed, fluid density, and viscosity.To describe pump efficiency, a pump curve usually obtained eitherfrom fluid dynamics simulation or testing is utilized. However, dueto the upgrades andmaintenance, the dynamics of a pump changesand the accuracy of pump curve gradually degrades. In addition,due to the head influence [10,11], higher nonlinearity is introducedin a pump system including more than two pumps working inparallel. Therefore, a novel approach to model the pump systemconsisting of multiple pumps needs to be investigated.

In this section, a data-driven approach is introduced to modelthe pump system performance based on configurations describedin Section 2.2. Two parameters, the energy consumption of pumpconfigurations and the wastewater flow rate downstream of thepump outlets, are considered to evaluate the pump systemperformance from two aspects, energy consumption and hydraulicwork performance. The data-driven models are developed andvalidated based on the industrial data discussed in Section 2.3.1. Aneural network algorithm [20e22] is utilized to develop themodelsof energy consumption and wastewater flow rate in Sections 2.3.2and 2.3.3. In the implementation of neural network algorithm,the number of the hidden layer is set to 1 and the number of hiddenunits is set to a random number between the number of inputparameters and six times the number of input parameters. Fouractivation functions, exponential, hyper-tangent, identity, andlogistic, are randomly considered in building the neural networkmodel. The back propagation algorithm [23] is utilized to learn theoptimal neural network structure by minimizing the sum of squareerror.

Z. Zhang et al. / Energy 47 (2012) 505e514 507

2.3.1. Data descriptionThe data used in this study was collected at a municipal

wastewater processing facility from July 20, 2010 to Jan 31, 2012.Data of more than 1400 parameters in the wastewater treatmentprocess was recorded and stored on an SQL server. Data pre-processing was utilized to select parameter data related to thepump system in the pre-treatment process with a 15-min samplinginterval. The parameters related to the pump system in the pre-treatment process were the pump speeds of six pumps, energyconsumed by the pump system, level of the raw wastewaterjunction chamber and the wastewater flow rate downstream of thepump outlets.

The selected dataset was then separated into various subsetsaccording to the pump configurations discussed in Section 2.2.Although the time length of the data considered in this research isabout 1.5 years, only a portion of the pump configurations areobserved from the data. Since, in the data-driven analysis, anappropriate amount of data points is required, only observed pumpconfigurations that included more than 300 data points werefinally selected in the development of the pump models. The set ofdata points belonging to each pump configuration was then splitinto two parts, a training dataset and a test dataset, by 3/4 and 1/4.The training dataset was utilized to learn the dynamic character-istic functions of the corresponding pump configuration via datamining algorithms. To validate the learned model, a test datasetwas employed. Table 1 describes the data sets used in this research.

The first column in Table 1 represents pump configurationsselected for modeling. The second and third columns provide thenumber of available and used data points. For the first six pumpsystem configurations, a portion (800 points) of available datapoints was used for development of accurate models. Besides theindustrial data, influent flow rate data was derived and incorpo-rated in this study. In thewastewater processing plant, the flow rateof wastewater influent is not measured due to several reasons. First,there are many sewers connected to the wastewater processingfacility while only some major sewers are equipped with sensors.Another reason is that the distance between the location of thesensors and the facility is not exactly measured. The value of the

Table 1Data sets associated with pump configurations.

Pump systemconfiguration

Configurationsets

Availabledatapoints

Used datapoints

Trainingdatapoints

Testdatapoints

C1 {1} 6649 First 800 600 200C2 {2} 2514 First 800 600 200C3 {3} 3368 First 800 600 200C4 {4} 7720 First 800 600 200C5 {5} 4740 First 800 600 200C6 {6} 3500 First 800 600 200C7 {1, 3} 786 786 590 196C8 {1, 4} 695 695 522 173C9 {1, 5} 620 620 465 155C10 {1, 6} 478 478 359 119C11 {2, 4} 447 447 336 111C12 {2, 6} 1080 1080 810 270C13 {3, 6} 872 872 654 218C14 {4, 6} 3451 3451 2589 862C15 {5, 6} 1602 1602 1202 400C16 {1, 4, 5} 407 407 306 101C17 {2, 4, 5} 354 354 267 87C18 {2, 4, 6} 584 584 438 146C19 {2, 5, 6} 1078 1078 809 269C20 {3, 4, 5} 485 485 364 121C21 {3, 4, 6} 347 347 261 86C22 {3, 5, 6} 479 479 360 119C23 {1, 3, 4, 5} 329 329 247 82C24 {2, 3, 4, 5, 6} 729 729 547 182

influent flow rate is critical to the planning of pump system oper-ations. Although there is no measured influent flow rate data, it canbe derived based on the mass balance equation in (3).

Qin ¼ QoutT þ AðLtþT � LtÞT

(3)

where Qin is the influent flow rate, Qout depicts the fluid flow ratedownstream of the pump outlets, t is the time, T is the samplingtime interval (15-min), L is the level of raw wastewater junctionchamber, and A is the bottom area of the junction chamber, which isassumed to be 10,000 ft2.

Since the two parameters, Qout and L, are recorded in the data-base, the influent flow rate, Qin, can be estimated with an assumedA.

2.3.2. Energy consumption modelsThe energy consumption model of pump systems can be

described as a multi-inputs single output (MISO) model. Based on(2), pump speeds and the level of the raw wastewater junctionchamber are used as inputs to predict the output, the energyconsumption of the pump system configuration. The predictionmodel is learned by a neural network algorithm based on thedataset of Section 2.3.1. The model is expressed in (4).

Pi;t ¼ fi�ui;tLt

�; i˛fC1;C2;.;C24g (4)

where i is the index denoting a pump system configuration, P is theenergy consumed by the pump system configuration i at time t, u isa dynamic vector of pump speeds for configuration i at time t, and f(�) represents the developed neural network model for predictingenergy consumed by pump system configurations. The remainingnotation is the same as (3).

Since the data sampling frequency is 15-min, model (4) predictsthe average energy consumed by the pump system configurationfor each 15-min interval, which represents the energy consumed bythe pumps.

A neural network algorithm was applied to develop model (4)for every pump system configuration. To evaluate the accuracy ofthe neural network models based on the test sets in Table 1, fourmetrics were utilized: mean absolute error (MAE), standard devi-ation of absolute error (SD of AE), mean absolute percentage error(MAPE), and standard deviation of absolute percentage error (SD ofAPE) in (5)e(8).

MAE ¼ 1n

Xni¼1

����byi � yi

���� (5)

SD of AE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n

Xni¼1

����byi � yi

����� 1n

Xni¼1

����byi � yi

����!2

vuut (6)

MAPE ¼ 1n

Xni¼1

0@������byi � yiyi

������1A� 100% (7)

SD of APE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n

Xni¼1

0@������byi � yiyi

������� 1n

Xni¼1

������byi � yiyi

������1A2

vuuut � 100% (8)

where y is the measured value, by is the value predicted by theneural network model, and i is the index of the data point.

The test results of the energy consumption models are illus-trated in Table 2. As shown in Table 2, the error of models in the

Table 2Test results of neural network energy consumption models.

Pump systemconfiguration

MAE SD of AE MAPE SD of APE

C1 8.14 6.87 0.02 0.01C2 6.31 5.33 0.01 0.01C3 8.56 10.66 0.02 0.02C4 21.75 14.44 0.05 0.04C5 5.15 5.95 0.01 0.01C6 9.15 6.78 0.02 0.02C7 11.75 24.16 0.02 0.03C8 5.50 4.72 0.01 0.01C9 12.51 16.68 0.02 0.02C10 14.30 13.31 0.03 0.03C11 30.24 23.63 0.05 0.05C12 19.41 40.02 0.03 0.06C13 14.95 11.64 0.03 0.02C14 15.25 12.24 0.02 0.02C15 15.39 13.61 0.03 0.03C16 14.19 13.90 0.01 0.01C17 8.15 6.00 0.01 0.01C18 12.04 10.13 0.01 0.01C19 14.41 11.95 0.02 0.01C20 30.54 109.71 0.03 0.07C21 16.92 10.85 0.02 0.01C22 16.55 14.62 0.02 0.01C23 8.69 5.97 0.01 0.00C24 34.72 36.72 0.02 0.02

Fig. 3. Predicted and observed energy consumption for C8.

Z. Zhang et al. / Energy 47 (2012) 505e514508

prediction of pump system configuration consumed energy iswithin 3%.

Three models, C1, C8, and C18, were selected to visualize theprediction in Figs. 2e4. In Figs. 2e4, the predicted and observedvalues of the first 100 data points in the test dataset aredemonstrated.

2.3.3. Wastewater flow rate modelsSimilar to the energy consumption models discussed in Section

2.3.2, the wastewater flow rate of a pump system configuration ispredicted by the same inputs, the pump speeds and the level of rawwastewater junction chamber. A neural network algorithm wasutilized to develop the prediction model formulated in (9).

Qi;t ¼ f1�ui;t ; Lt

�; i˛fC1;C2;.;C24g (9)

where Q is the wastewater flow rate at time t after the pumps inconfiguration i. The remaining notation is the same as (4).

The test results of wastewater flow rate model are shown inTable 3. As shown in Table 3, the accuracy of models predictingwastewater flow rate is generally higher than 95%.

Fig. 2. Predicted and observed energy consumption for C1.

Similar to Section 2.3.2, models of configurations, C1, C8, and C18,were selected to visualize prediction accuracy. Figs. 5e7 display thefirst 100 test results for each of the three models.

3. Formulation of the pump system scheduling model

In the current pre-treatment process, the pump system isoperated to achieve a single objective, pumping the wastewater tokeep the level of junction chamber within a safe range. In thissection, a scheduling model was developed to account for energyconsumption of the pump system while maintaining a similarhydraulic load. Two types of information, the selected pump systemconfiguration and the settings of the pump speeds of the operatedpumps, are provided by the computed schedule.

3.1. Variables

Two variables, xi and u, are considered in scheduling the pumpsystem. The variable, xi, is a binary decision variable that deter-mines on and off of the available pump system configuration, xi ¼ 1if the pump system configuration i is turned on, 0 otherwise, wherei˛fC1;C2;.;C24g. The variable, u, is a vector of pump speedsettings for the selected pump system configuration. The size of thevector ranges from 1 to 5.

3.2. Objective function

The objective of scheduling model is to minimize the energyconsumed by the pump system (see (10)).

Fig. 4. Predicted and observed energy consumption for C18.

Table 3Test results of neural network wastewater flow rate models.

Pump systemconfigurations

MAE SD of AE MAPE SD of APE

C1 0.78 0.59 0.02 0.01C2 0.77 0.49 0.02 0.01C3 1.00 2.89 0.02 0.08C4 4.06 4.41 0.08 0.10C5 0.74 0.67 0.02 0.01C6 1.10 0.80 0.02 0.02C7 2.05 4.84 0.03 0.07C8 1.25 0.92 0.02 0.01C9 2.03 3.34 0.02 0.05C10 1.86 4.67 0.03 0.07C11 4.77 3.80 0.07 0.07C12 2.31 2.67 0.04 0.06C13 4.45 7.13 0.07 0.13C14 3.17 6.40 0.04 0.10C15 3.22 4.39 0.05 0.08C16 15.58 28.02 0.09 0.16C17 1.16 0.93 0.01 0.01C18 2.83 2.37 0.03 0.02C19 1.97 1.65 0.02 0.01C20 4.56 3.69 0.04 0.04C21 2.13 1.37 0.02 0.01C22 3.70 2.45 0.03 0.02C23 2.40 1.66 0.01 0.001C24 24.07 37.13 0.10 0.16

Fig. 6. Predicted and observed wastewater flow rate downstream of the pump outletsfor C8.

Z. Zhang et al. / Energy 47 (2012) 505e514 509

minXC24

i¼C1

xi;tPi;t (10)

where x is the decision variable defined in Section 3.1 and P is theenergy consumed by the pump system configuration discussed inSection 2.3.2.

3.3. Constraints

Four important constraints need to be considered in schedulingthe pump system. The first constraint states that only one pumpsystem configuration can be selected at a time (see (11)).

XC24

i¼C1

xi;t ¼ 1 (11)

The second constraint reflects that the hydraulic performance ofthe pump system is restricted by the change of junction chamberlevel in a small range as shown in (12).

Fig. 5. Predicted and observed wastewater flow rate downstream of the pump outletsfor C1.

jLt � Lt�T j � x (12)

where x is the upper bound of the change of the junction chamberlevel.

In addition, the junction chamber level cannot be higher thanthe height of the junction chamber as expressed in (13).

Lt � h (13)

where h is the height of the junction chamber.The last constraint is the pump speed constraint. In the waste-

water processing facility, the collected pump speed data have beenstandardized to a range (0%, 100%). When a pump is operated, thepump speed can only vary between 80% and 100%. Therefore, in thisresearch, the pump speed is bounded according to (14).

u˛½0:8;1� (14)

where u is the vector of pump speed settings of the operatedpumps.

3.4. Formulation of the scheduling model

By integrating the energy consumption model in Section 2.3.2,the wastewater flow rate model in Section 2.3.3, variables inSection 3.1, objective function in Section 3.2, and constraints inSection 3.3, a model for scheduling the pump system operationscan be formulated as (15).

Fig. 7. Predicted and observed wastewater flow rate downstream of the pump outletsfor C18.

Z. Zhang et al. / Energy 47 (2012) 505e514510

minx;u

PC24

xi;tPi;t

i¼C1

s:t:PC24

i¼C1

xi;t ¼ 1

Pi;t ¼ f1�ui;t ; Lt

�; i˛fC1;C2;.;C24g

Qi;t ¼ fi�ui;t ; Lt

�; i˛fC1;C2;.;C24g

Lt ¼�Qin;t � Qi;t

�T

Aþ Lt�T

jLt � Lt�T j � x

Lt � h

ui;t˛½0:8;1�; i˛fC1;C2;.;C24gxi;t˛f0;1g; i˛fC1;C2;.;C24g

(15)

Themodel (15) can be rewritten as (16) bymoving two inequalityconstraints, jLt � Lt�T j � x and Lt � h, to the objective function.

minx;u

PC24

i¼C1

xi;tPi;t þM1maxf0; jLt � Lt�T j � xg þM2maxf0; Lt � hg

s:t:

PC24

i¼C1

xi;t ¼ 1

Pi;t ¼ fi�ui;t ; Lt

�; i˛fC1;C2;.;C24g

Qi;t ¼ fi�ui;t ; Lt

�; i˛fC1;C2;.;C24g

Lt ¼�Qin;t � Qi;t

�T

Aþ Lt�T

ui;t˛½0:8;1�; i˛fC1;C2;.;C24gxi;t˛f0;1g; i˛fC1;C2;.;C24g

ð16Þ

where M1 and M2 are large numbers to ensure that the twoinequality constraints are satisfied in the minimization.

4. Migrated particle swarm algorithm

Traditional solution approaches, such as Outer Approximation(OA) methods [24], Branch-and-Bound [25], Cutting Plane algo-rithm [26], and Generalized Bender’s Decomposition [27], guar-antee global optimality only when convexity is observed. Inaddition, traditional solution approaches [24e27] do not performwell for large-scale MINLPs. Lastly, an explicit formulation of theMINLP (mixed-integer nonlinear programming problem) isrequired by traditional solution approaches. None of theserequirements are met by model (16) and therefore a migratedparticle swarm optimization algorithm (MPSO) was developed.

The MPSO algorithm is inspired by the concepts of particleswarm optimization (PSO) [28,29] and heuristic search algorithmsfor discrete optimization, such as variable neighborhood search[30,31] and genetic algorithms (GA) [32]. Fig. 8 shows the structureof the migrated particle swarm optimization algorithm.

As shown in Fig. 8, the MPSO is a two-echelon hierarchicalsearch procedure. The first echelon is the migration procedurewhere a discrete optimization search algorithm optimizes thebinary variable, x, in (16). Based on the searched value of binaryvariable, a flight procedure is implemented. In the flight procedure(second echelon), the particle swarm optimization algorithm isutilized to optimize the real value variable, u.

Since the total number of pump system configurations is 24,Pseudo Code I is used in the migration procedure.

In Pseudo Code I, function run.PSO() represents the flightprocedure of Pseudo Code II, cal.fitness() is a function to calculatethe value of objective function ofmodel (16) based on variables, andMIN() is a function to obtain the minimum of the computedobjective value.

The flight procedure is the canonical PSO [28,29] which isillustrated by Pseudo Code II.

In Pseudo Code II, the function, GetDimensions() provides thesize of variable u, InitializeParticles() is a function to initialize theparticle position and particle velocity of m particles, cal.fitness() isthe same as in Pseudo Code I, and G is the stopping criterion of theflight procedure.

Two functions, UpdateVelocity() and UpdatePosition(), areapplied to update particle velocity and position at every iterationaccording to (17) and (18).

vgk ¼ dvgk þ c1r

g1

�bpgk � pgk

�þ c2r

g2

�bgk � pgk

; k ¼ 1;.;n (17)

pgk ¼ pgk þ vgk; k ¼ 1;.;n (18)

where v is the particle velocity, p is the particle position, bp is thelocal best, b is the global best, d is the inertia, c is the constant tocontrol the velocity, r is a random number generated from a U[0,1],g is the generation index, and k describes the dimensions ofparameters.

Fig. 9. Convergence of flight procedure for u ¼ 3.

Fig. 8. Migrated particle swarm optimization algorithm.

Z. Zhang et al. / Energy 47 (2012) 505e514 511

The local best and global best of the particle swarm are updatedby (19) and (20), representing the UpdateLocalBest() and theUpdateGlobalBest(). The local best is the minimal value of theobjective function searched by a particle. The global best is theminimal value of the objective function searched by the swarm.The local best and global best are compared with the fitness ofeach particle (objective value searched by the particle) at eachsearch step. If the local and global best are worse than the fitnessvalue of a particle, the local and global best will be updated as (19)and (20).

bpgk ¼ pgk if cal:fitness

�xi; p

gk

� cal:fitness

�xi; bpg

k

�(19)

bgk ¼ pgk if cal:fitness�xi; p

gk

� cal:fitness

�xi; b

gk

(20)

where the notation is similar to (17).

5. Optimization results

5.1. Convergence evaluation

To implement the MPSO algorithm, the settings of parameters,including d, c, and G, need to be investigated. According to [28,29],the value of d is usually set to 0.5 and the value of c is usually set to2. G is the number of algorithm implementation iterations thatdescribes the stopping criterion of the flight procedure in MPSO. Insome research, the algorithm is terminated by evaluating thechange of fitness value over a certain number of iterations.However, setting a maximal number of implementation iterationsis preferred by more research since the running time of the algo-rithm is better controlled. In this study, a computational experi-ment was conducted to determine a suitable stopping criterion G ofMPSO.

Table 4Convergence of the flight procedure.

Size of u No. of iterations

1 92 143 8394 4005 62

Since the size of u varies from 1 to 5, five computational caseswere developed to evaluate the implementation iterations requiredby the flight procedure to converge. Pump system configurations,C1, C7, C16, C23 and C24, were selected to evaluate convergence speedof the flight procedure for u ¼ 1, 2, 3, 4 and 5. Table 4 presents theconvergence assessment results. The maximum number of itera-tions of the flight procedure was set to 1500. Based on the resultsillustrated in Table 4, G is set to 850 by considering theworst case incomputation.

Figs. 9 and 10 demonstrate the convergence of flight procedurewhen size of u equals to 3 and 4. The vertical axis if Figs. 9 and 10presents the standardized fitness computed according to (21).

Standardized fitness ¼ fitnessg

maxffitnessgg (21)

5.2. Computational instances

Three computational instances (CI1, CI2 and CI3) representingthree influent flow rate scenarios (low, medium and high) wereselected. Each computational instance involves 20 data points. Thefirst computational instance (CI1) included 20 data points from 11/10/2010, 11:06:06 PM to 11/11/2010, 3:51:06 AM. The influent flowrate during this period is low, which is between 40MGDe 55MGD.The second computational instance (CI2) included 20 data pointsfrom 7/22/2010, 12:23:38 PM to 7/22/2010, 5:08:38 PM. In thisperiod, the range of influent flow rate is between 115 MGD e

120 MGD. The 20 data points included in the third computationalinstance (CI3) started from 7/23/2010, 11:23:38 PM to 7/24/2010,4:08:38 AM. The influent flow rated in this instance varies from160 MGD e 175 MGD.

Fig. 10. Convergence of flight procedure with size for u ¼ 4.

Table 5Computed schedules for CI1, CI2 and CI3.

Schedulingtime windows

Computed schedule for CI1 Computed schedule for CI2 Computed schedule for CI3

Pump systemconfigurations

Pump speedsettings

Pump systemconfigurations

Pump speed settings Pump systemconfigurations

Pump speed settings

1 C1 {81.23} C21 {81.11, 92.81, 85.54} C18 {98.13, 84.26, 80.77}2 C2 {85.35} C14 {80.58, 91.42} C15 {100, 90.55, 100}3 C2 {86.18} C21 {82.50, 92.91, 85.01} C15 {100, 90.55, 100}4 C3 {88.39} C14 {80.58, 91.42} C15 {100, 90.55, 100}5 C3 {85.05} C21 {81.20, 93.81, 86.19} C15 {96.47, 100, 100}6 C3 {87.10} C21 {81.20, 93.81, 86.19} C22 {91.80, 89.61, 98.83, 86.22}7 C14 {80, 80} C21 {81.20, 93.81, 86.19} C22 {93.94, 88.98, 100, 86.62}8 C14 {80, 80} C21 {81.30, 92.59, 87.68} C22 {96.40, 83.40, 97.07, 98.30}9 C14 {80, 80} C19 {81.81, 83.95, 82.29} C22 {95.83, 82.06, 97.11, 98.96}10 C14 {80, 80} C19 {81.81, 83.95, 82.29} C22 {95.79, 82.69, 96.53, 98.}11 C14 {80, 80} C14 {80, 92.53} C22 {89.65, 84.26, 100, 94.14}12 C14 {80, 80} C19 {83.21, 85.36, 83.95} C15 {100, 85.75, 100}13 C3 {86.68} C16 {86.71, 84.46, 89.30} C15 {97.77, 88.02, 97.47}14 C3 {85.14} C19 {80, 80, 80} C20 {80, 80, 80}15 C5 {90.20} C21 {81.54, 95.86, 84.56} C18 {93.29, 80, 80.42}16 C3 {85.25} C12 {96.90, 92.75} C20 {81.48, 80, 86.44}17 C1 {88.38} C21 {80, 96.66, 87.30} C20 {80, 80.83, 86.36}18 C1 {87.64} C21 {80, 96.66, 87.30} C20 {85.64, 81.59, 88.35}19 C1 {86.91} C21 {80, 97.55, 87.55} C20 {80.12, 84.09, 88.96}20 C1 {86.68} C19 {80.56, 80, 83.64} C18 {91.46, 80.98, 82.12}

Z. Zhang et al. / Energy 47 (2012) 505e514512

5.3. Analysis of the computational results

The computed schedules of operating the pump system basedon three computational instances are summarized in Table 5. In theobserved data, only pump system configuration C1 is selected in CI1,pump system configuration C19 is operating in CI2, and two pumpsystem configurations, C19 and pump systemwith configuration {2,3, 5, 6}, are used in CI3. The performance of the selected pumpsystem configurations is illustrated in Table 6. In Table 6, thecomputed and observed value of energy consumption and waste-water flow rate downstream of the pump outlets are compared forthe three computational instances. Based on the gain computed by(22), it is observed that the energy consumed by the pump systemis reduced at the cost of the hydraulic performance of the pumpsystem. In CI1, the influent flow rate is low and single pumpconfigurations are utilized most of the time. Since the dynamics ofa single pump is relatively simple, the current control system iscapable of controlling pump efficiency and the room for energysaving is small. However, in CI2 and CI3, since the dynamics ofa pump system configuration that includesmore than two pumps ismore complex, the integration of the control system and the fiverules of Section 2.1 does not offer the best performance of the pumpsystem. Based on Table 6, the potential to reduce energyconsumption of the pump system is significant while the perfor-mance of the hydraulic load can almost be maintained at the samelevel. The results in Tables 5 and 6 indicate that the proposedmodelreduces the energy consumed by the pumps while maintaining thehydraulic load.

Table 6Computed and observed pump system performance.

Objectives Computedvalue

Observedvalue

Gain

Energy consumption for CI1 (kW) 378.34 409.28 �7.56%Wastewater flow rate for CI1 (MGD) 49.66 51.63 �3.82%Energy consumption for CI2 (kW) 748.64 976.84 �23.36%Wastewater flow rate for CI2 (MGD) 117.99 118.28 �0.25%Energy consumption for CI3 (kW) 1159.79 1531.08 �24.25%Wastewater flow rate for CI3 (MGD) 176.83 178.41 �0.89%

Gain ¼ Computed value� Observed valueObserved value

(22)

Figs.11 and 12 demonstrate the computed and observed value ofthe energy consumption of the pump system based on CI2 and CI3.Figs. 13 and 14 illustrates the computed and observed value of thewastewater flow rate downstream of the pump outlets in CI2 andCI3.

The proposed approach will be implemented in industryaccording to the following steps. Step 1: The operational data of thepump system will be collected and the neural network model willbe initially trained and then updated as neededwith the latest data.Step 2: Compute a schedule of settings of the pump system every15 min. Step 3: Implement the computed settings in the pumpsystem schedules.

The runtime balance constraint is not considered in the sched-ules. It is mainly because of the short scheduling time window (15-min). The runtime balance constraint applies to longer termscheduling of the pump system (for example, when a schedulingtime window is longer than 6 h). Applying it to the 15-minwindowwould lead to frequent switching of the pumps and may adverselyimpact health of the pumps. In the actual implementation,

Fig. 11. Computed and observed pump system energy consumption for CI2.

Fig. 12. Computed and observed pump system energy consumption for CI3.

Fig. 13. Computed and observed wastewater flow rate downstream of the pumpoutlets based on CI2.

Fig. 14. Computed and observed wastewater flow rate downstream of the pumpoutlets for CI3.

Z. Zhang et al. / Energy 47 (2012) 505e514 513

balancing the runtime of the pumps can be accomplished bya control system.

6. Conclusion

A model for scheduling the operations of a pump system ina wastewater processing plant was studied in this paper. Theperformance of the pump system was measured by two parame-ters, the energy consumption of the pump system and the waste-water flow rate downstream of the pump outlets. A neural networkalgorithm was utilized to develop the data-driven models for pre-dicting energy consumption and wastewater flow rate. Variousconfigurations of the pumps were analyzed. A pump system

scheduling model was established by integrating the energyconsumption model and the wastewater flow rate model with theconstraints of the pre-treatment process. Two types of variables,binary and continuous, were involved in the scheduling model. Amigrated particle swarm optimization algorithm was developed tosolve the scheduling model.

The optimization results indicated that better performance ofthe pump system can be achieved based on the schedules providedby the proposed model. Moreover, the energy consumption ofpump system configurations with multiple pumps could be moresignificantly reduced while the same amount of wastewater couldbe delivered.

The proposed scheduling model was able to generate a one-stepoperational schedule recursively for the pump system. In futureresearch, the proposed scheduling model could be extended toprovide schedules over a longer scheduling time horizon (Forexample, generating 30-min schedule per computation). In addi-tion, the hydraulic load constraints and machine runtime balanceconstraints of the pump system need to be extended throughoutthe wastewater treatment process.

Acknowledgement

This research was supported by funding from Iowa EnergyCenter Grant No. 10-1.

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