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A visual tool to calculate optimal control strategy for

non-identical pumps working in parallel, taking motor and

VSD efﬁciencies into account

Markus I. Sunela and Raido Puust

ABSTRACT

A simple graphical tool was developed, that ﬁnds the optimal combination of pumps and their

rotational speeds for all possible working points for a pump battery. The tool was integrated into

EPANET as well as EPA SWMM simulation packages. The tool allows us to analyse and optimize

operation non-identical parallel pumps with different minimum and maximum frequencies for all

possible working points. Pump characteristics and efﬁciency curves can be given in tabular format or

as analytical functions of ﬂow. Degradation of pump efﬁciency at lower rotational speed is taken into

account, as well as motor and variable speed drive efﬁciencies at partial loads. The optimal solution

provided by the tool was compared to measurements in two case studies. Our case studies showed

6.1–8.5% reduction in energy usage using the optimal parallel pumping control strategy compared to

the currently used strategy, where all running pumps have the same frequency.

Markus I. Sunela (corresponding author)

Raido Puust

FCG Design and Engineering Ltd,

Tampere 33200,

Finland

and

Tallinn University of Technology,

Tallinn 19086,

Estonia

E-mail: markus.sunela@fcg.ﬁ

Key words |case study, EPANET, EPA SWMM, optimization, parallel pumping, variable speed drive

INTRODUCTION

Pumping presents up to 80% of the energy demand of water

supply systems (Brandt et al. ). Good design can save

30% of this energy demand. It’s not enough, however, to

consider just the pump’sefﬁciency, but the pumping

system must be considered as a whole. The optimal design

should also account for the speciﬁcs of the system, such as

variable ﬂow and head. (Kaya et al. ).

Tools for optimizing the pump station design and oper-

ation have been lacking, especially when differently sized

pumps are to be used. While recently some work in this

ﬁeld has been done: the research by Costa Bortoni et al.

(),Yang & Borsting (),Wu et al. ()and Koor

et al. (). The methods for optimization were genetic

algorithm, non-linear programming, mixed integer non-

linear programming and dynamic programming, respect-

ively. The earlier research has focused on identical pumps

or characteristic curves which can be presented in second

order polynomial formulation, and only a little attention is

paid to degradation of pump hydraulic efﬁciency at lower

rotational speed, or motor and variable-speed drive (VSD)

efﬁciencies at reduced loads.

In this research paper, a tool was developed to solve the

aforementioned limitations. The tool was applied in two

case studies showing its feasibility for both identical and

non-identical pumps. The efﬁciency model and the tool

were implemented also in EPANET (Rossman ) and

EPA SWMM (Rossman ).

METHODS

Background

The pump battery is described as a set of pumps. Each pump

is given a characteristic curve, an efﬁciency curve, minimum

and maximum allowed frequency, nominal motor power

1115 © IWA Publishing 2015 Water Science & Technology: Water Supply |15.5 |2015

doi: 10.2166/ws.2015.069

P

NOM

, and either IE efﬁciency class and number of poles,

for standard motor efﬁciency values based on IEC-

(), motor efﬁciency values at both 100% and 75%

load, η

M,100

and η

M,75

, respectively, or tabular motor

efﬁciency curve as a function of load.

The pump characteristic curve can be expressed either

in tabular format as (Q,H) pairs, which is then linearly

interpolated, or in analytical power curve format as in

EPANET (Rossman )

H(Q)¼ω2Hmax ω2στQσ, (1)

where ω¼(f2=f1)¼(N2=N1) is the relative rotational speed,

and σand τare ﬂow exponent and ﬂow coefﬁcient, obtained

by curve ﬁtting. A separate pump speciﬁc parameter Q

max

determining the maximum ﬂow at the nominal speed can

be speciﬁed.

Flow and head at different rotational speeds are calcu-

lated using afﬁnity laws (Volk )

Q2

Q1

¼N2

N1

¼ω(2)

and

H2

H1

¼N2

N1

2

¼ω2:(3)

The pump efﬁciency curve can be given either in tabular

format, which is then linearly interpolated, or as a func-

tional, second order polynomial curve with either one or

two points. For one point, the best efﬁciency point, BEP,

(Q

BEP

,η

BEP

) the efﬁciency curve is

η(Q)¼aQ2þbQ, (4)

where

aQ2

BEP þbQBEP ηBEP ¼0

2aQBEP þb¼0

(5)

and for two points (Q

BEP

,η

BEP

) and (Q

2

,η

2

), Q

2

>Q

BEP

the

curve is

ηQðÞ¼ aQ2þbQ,Q<QBEP

a2Q2þb2Qþc2,QQBEP

(6)

where aand bare solved as described in Equation (5) and

a2Q2

BEP þb2QBEP þc2ηBEP ¼0

2a2QBEP þb2¼0

a2Q2

2þb2Q2þc2η2¼0

8

<

:

(7)

Pump hydraulic efﬁciency at different rotational speed

(Sârbu & Borza )

ηP¼ηP,2 ¼1(1 ηP,1)N1

N2

0:1

¼1(1 ηP,1)1

ω

0:1

:(8)

While there are more general, friction factor (Strub et al.

) or Reynolds number (Wiesner ) based methods,

Equation (8) is accurate for medium sized pumps and

reasonable variation of rotational speed (Simpson &

Marchi ).

Hydraulic power

PH¼ρgQH, (9)

and pump shaft power (Volk ):

PS¼PH

ηP

:(10)

Motor load (US Department of Energy ):

L¼PS

(PNOM=ηM,100 ), (11)

where η

M,100

is the motor efﬁciency at rated load.

IEC- ()standard provides an equation to

calculate an approximation of motor efﬁciency at any partial

load based on the motor’s rated and 3/4 load efﬁciencies

η

M,100

and η

M,75

):

vL¼

1

ηM,100

1

0:75 1

ηM,75

1

0:4375

v0¼1

ηM,100

1

vL

ηM¼1

1þ(v0=L)þvLL(12)

1116 M. I. Sunela & R. Puust |A visual tool to calculate optimal control strategy for non-identical pumps Water Science & Technology: Water Supply |15.5 |2015

Wallbom-Carlson ()proposes usage of an idealized

VSD efﬁciency factor that would include losses from the

VSD itself and losses generated in the motor by the VSD.

However, experiments presented in Burt et al. (), and

Brandt et al. ()support that the motor’sefﬁciency does

not change much if a VSD is used. This work assumes

that modern VSDs can mostly compensate generated

losses in motors. The VSD efﬁciency is taken from a

lookup table based on load calculated as in Equation (11),

rotational speed and VSD’s nominal power as per

IEC- ().

Motor power becomes

PM¼PS

ηM

, (13)

pump train electrical power

PE¼PM

ηVSD

, (14)

and the total pump train efﬁciency (Bernier & Bourret

):

ηTOT ¼PH

PE

¼ηPηMηVSD:(15)

Table 1 shows an example, how load and different efﬁ-

ciency components change; when the pump’s rotational

speed is reduced in a zero static head system. The motor

presented in the table is a 55 kW motor, with 4/4 load efﬁ-

ciency of 85.0% and 3/4 efﬁciency of 85.5%. The VSD is

also 55 kW. The pump’s BEP is 80% at nominal rotational

speed at 50 Hz. While the pump’s BEP decreases from

80.0 to 78.6% when the rotational speed is reduced from

50 to 25 Hz, motor’sefﬁciency reduces from 85.0 to 65.6%

and VSD efﬁciency from 97.9 to 95.7%. This results in a

total efﬁciency of 66.6% at 50 Hz and only 49.3% at 25 Hz.

Algorithm development

The optimization is done for every working point the pump

battery can produce, using user speciﬁed resolution Q

step

×

H

step

. The step size depends on the wanted accuracy, and

it affects the computational time and amount of memory

required.

The optimization problem for each working point

(Qi,Hj) becomes

min

fi,j∈Xi,j

PEQi,Hj,

fi,j

, (16)

where

fi,jis a vector of each pump’s frequency, and the

search space Xi,jincludes all allowed combinations that

result in total ﬂow and head of (Qi,Hj). The optimization

is done using direct search, thus all possible solutions are

compared, and a global optimum for each working point

is guaranteed. (Hooke & Jeeves ).

The algorithm and user interface were developed using

Java programming language 1.8 and Swing toolkit,

JFreeChart 1.0.19 charting library and Apache POI 3.10.1

library for Excel ﬁle access. The programming language

was chosen for rapid development cycle, good industry

acceptance and penetration, and good multi-thread pro-

gramming features. The calculation is parallel and utilizes

all available threads at the computer.

First each pump’s working regime is optimized. Mini-

mum and maximum allowed head, and maximum allowed

ﬂow are calculated based on the pump characteristic curve

and the allowed frequency range. The code loops over

allowed frequencies using a step size of 0.01 Hz. Each result-

ing pump frequency combination is pushed to a queue, from

which one of the processor threads picks it up and calcu-

lates all possible ﬂow and head combinations for the given

Table 1 |Different efﬁciency components at various loads and rotational speeds

Hz Load (%)

Efﬁciency

Motor (%) VSD (%) Pump (%) Total (%)

50.0 100.0 85.0 97.9 80.0 66.6

45.4 75.0 85.5 97.9 79.8 66.8

39.7 50.0 84.5 97.3 79.5 65.4

31.5 25.0 77.9 96.5 79.1 59.4

25.0 12.5 65.6 95.7 78.6 49.3

18.4 5.0 43.8 95.0 77.9 32.4

14.6 2.5 28.1 94.7 77.4 20.6

10.8 1.0 13.5 94.3 76.7 9.8

1117 M. I. Sunela & R. Puust |A visual tool to calculate optimal control strategy for non-identical pumps Water Science & Technology: Water Supply |15.5 |2015

frequency. If multiple frequencies result in overlapping

working points in the Q

step

×H

step

resolution, the frequency

that produces the highest total efﬁciency is chosen for that

particular working point.

The results of the working regime calculation are stored

in the two pump speciﬁc lookup arrays shown in Equation

(17). The ﬁrst, F, contains the optimal frequency and the

other, H, contains the total pump train efﬁciencies for all

working points. Array elements that present invalid working

points are set to 0.

F¼

fQ1,H1fQ2,H1...

fQ1,H2fQ2,H2

.

.

..

.

...

.

fQm,H1

fQm,H2

.

.

.

fQ1,HnfQ2,Hn... fQm,Hn

2

6

6

6

6

4

3

7

7

7

7

5

,

H¼

ηQ1;H1ηQ2;H1...

ηQ1;H2ηQ2;H2

.

.

..

.

...

.

ηQm;H1

ηQm;H2

.

.

.

ηQ1;HnηQ2;Hn... ηQm;Hn

2

6

6

6

6

4

3

7

7

7

7

5

(17)

Next, all the possible non-identical pump combinations

are considered. The combinations are presented as a binary

string, S, where 1 signiﬁes the pump is on and 0 the pump is

off. Minimum and maximum head is calculated for each

combination so that each pump running in the combination

can work within the limits:

Hmin ¼max Hmin;1;Hmin;2;...;Hmin;n

Hmax ¼min Hmax;1;Hmax;2;...;Hmax;n

;(18)

where nis the number of pumps running in the

combination.

For each combination the algorithm iterates over the

allowed heads in the range [H

min

,H

max

] using the head

step size. Head H

i

and combination string S, are added to

a queue, where one of the processor threads picks it up

for calculation.

A processor thread calculates all possible combinations

of ﬂows for the pumps running in Sthat result in a head of

H

i

. Each pump’s total efﬁciency is looked up from the

pump’s working regime array H. The total efﬁciency for

the total ﬂow Q

i

is calculated. If it’s less than the previous

best value for the same working point (Q

i

,H

i

), the combi-

nation and efﬁciency are stored in the result arrays Cand R.

The end result is two arrays that cover the full possible

working regime of the whole pump battery. Each element

represents an area deﬁned by Q

step

and H

step

. Results array

Ccontains the numerical presentation of the optimal combi-

nation binary string and Rcontains the optimal total pump

train efﬁciencies:

C¼

cQ1,H1cQ2,H1...

cQ1,H2cQ2,H2

.

.

..

.

...

.

cQm,H1

cQm,H2

.

.

.

cQ1,HncQ2,Hn... cQm,Hn

2

6

6

6

6

4

3

7

7

7

7

5

,

R¼

ηQ1,H1ηQ2,H1...

ηQ1,H2ηQ2,H2

.

.

..

.

...

.

ηQm,H1

ηQm,H2

.

.

.

ηQ1,HnηQ2,Hn... ηQm,Hn

2

6

6

6

6

4

3

7

7

7

7

5

(19)

Two naive algorithms were implemented too, to facili-

tate easier comparison of various control strategies. Naive

1 algorithm drives all running pumps with equal frequency,

and naive 2 algorithm adjusts only the lastly added pump’s

frequency while the other pumps run at their respective

maximum frequencies. The naive algorithms store the

results the same way as the optimizator, so the algorithms

can be used interchangeably.

The program contains a graphical user interface, for

inputting the pump battery information, and for presenting

the results graphically, shown in Figure 1. Colour scheme

is selected by the user: speciﬁc energy, total efﬁciency,

number of pumps running, or pump combination number

(i.e. decimal representation of the combination binary

string). All the other parameters are shown in a tool-tip,

and in a separate panel, if the user clicks on the chart.

The user can optionally import a set of working points

and their relative probabilities to the program. Working

points can be imported from an Excel ﬁle, comma or tab

separated ﬁles, or from EPANET or EPA SWMM results.

If the ﬁle contains no probability information, the points

are considered to be equally probable. The program then

shows the working points on the chart, and calculates

total annual energy consumption for the set of points.

The result array and the working points including their

total efﬁciencies, if available, can be saved to an Excel ﬁle

for further processing and analysis. The saved ﬁle can be

1118 M. I. Sunela & R. Puust |A visual tool to calculate optimal control strategy for non-identical pumps Water Science & Technology: Water Supply |15.5 |2015

reopened in the program saving the need to recompute the

results.

The efﬁciency model was integrated into EPANET

(Rossmann ) and EPA SWMM (Rossmann ) simi-

larly to Simpson & Marchi ()to enable better energy

analysis and pump battery control strategy optimization in

hydraulic models. A new pump battery element

was developed for both simulators, which uses the tool to

calculate pump and frequency combinations and

efﬁciencies.

RESULTS

The tool was used for evaluating the current performance

and optimizing the control strategy of network pumping

from the freshwater tank of two different ground water

sources of two different, major Finnish water utilities. The

ﬁrst case has three identical pumps and the second case

has four pumps of two different types. The pump character-

istic curves for the new pumps were used in both cases.

In both cases, the pump battery was modelled in the

pump battery analysis tool, and the optimal combinations

for all possible working points were calculated. The aver-

aged ﬂow and head combinations calculated from

Supervisory Control and Data Acquisition (SCADA) were

imported into the tool as working points, and later exported

back to Excel with the optimal efﬁciency and power values.

The computed optimal efﬁciency and power values were

compared with the values collected from the VSDs by the

SCADA.

The SCADA systems collect VSD power and frequency,

and pump ﬂow and head. Data from the year 2013 were pro-

cessed and the hourly averages were used in the ﬁrst case

and ﬁve minute averages in the second case.

The case optimizations were performed on an Intel Core

i7-4800MQ @ 2.70 GHz laptop, with 32 Gb of RAM,

Windows 7 operating system and Java runtime version

1.8.0_31. Calculation times are reported as average for ﬁve runs.

Case study 1 –identical pumps

The pump battery has three identical pumps of which at

most two can run in parallel. About 1.5 million m³ is

pumped from the source into the network annually. The

median ﬂow is about 200 m³/h, and the median total head

is about 62 m of water.

Figure 1 |The user interface showing optimization results (the full colour version of this ﬁgure is available in the online version of this paper, at http://www.iwaponline.com/ws/toc.htm).

1119 M. I. Sunela & R. Puust |A visual tool to calculate optimal control strategy for non-identical pumps Water Science & Technology: Water Supply |15.5 |2015

The pumps are Pleuger 50 kW QN83-7a submersible

pumps with Pleuger 55 kW M8-480-2 motors. Each pump

has its own 55 kW VSD. The pumps have a BEP of 80%,

and the motors’4/4 load efﬁciency is 85.0% and 3/4 load

efﬁciency is 85.5%.

The optimal annual energy consumption with the cur-

rent pump conﬁguration is 421,227 kWh/year, which is

8.5% lower compared to the measured energy consumption

460,302 kWh/year. Figure 2 shows how the optimized total

efﬁciency compares to the measured efﬁciencies as a func-

tion of ﬂow. Optimization took 2.7 s to complete.

The current control strategy seems to use always two

pumps in parallel regardless of the ﬂow and the head.

Even the naive 1 algorithm, which resembles the currently

used control algorithm very closely, results in 7.8% savings

compared to the current strategy, mainly because it uses

only one pump when the requested ﬂow is small.

Case study 2 –non-identical pumps

The pump battery has two pairs of pumps: the older pumps,

number 3 and 4, are Grundfos’80 kW NK100-200/219 with

110 kW ABB HXR 280MC 2 B3W motors with full load efﬁ-

ciency of 95.1% and 3/4 load efﬁciency of 95.0%, and the

new pumps, number 1 and 2, are Flygt’s 80 kW L150-

400U3SN-7504 pumps with 75 kW FFD SEE 280 S4

motors with full load efﬁciency of 95.2% and 3/4 load efﬁ-

ciency of 94.9%. The Grundfos pumps have BEP of 84.3%

and the Flygt pumps –86.4%. Each pump has its own VSD.

About 3.8 million m

3

is pumped from the source

annually. The median ﬂow is about 425 m

3

/h, and the

median head about 35.5 m of water.

The optimal annual energy consumption with the cur-

rent pump conﬁguration is 515,561 kWh/year which is

6.1% lower compared to the measured energy consumption

of 548,486 kWh/year. Figure 3 shows how the optimized

total efﬁciency compares to the measured efﬁciencies as

a function of ﬂow. Optimization took 40 seconds to

complete.

From Figure 3 it is apparent, that the current control

algorithm results in one pump pumping only with too high

ﬂows and two pumps pumping with too low ﬂows. The opti-

mal ﬂow to switch from one to two pumps and vice versa, is

about 130 l/s, depending on the exact head required.

CONCLUSIONS

The developed tool provides interesting insight into pump

battery working behaviour, such as the available working

regime, speciﬁc energy usage and efﬁciency. The calculated

optimal pump combinations and their frequencies for differ-

ent ﬂow and head regimes provide a good basis for

developing more optimal pump control strategies and com-

paring different sets of pumps for the case at hand.

The developed tool can handle non-identical pumps that

can also be described by non-analytical methods. Both fea-

tures are quite common in practical engineering work, but

Figure 2 |Comparison between the measured (diamonds) and optimized (rectangles) efﬁciencies as a function of ﬂow (the full colour version of this ﬁgure is available in the online version

of this paper, at http://www.iwaponline.com/ws/toc.htm).

1120 M. I. Sunela & R. Puust |A visual tool to calculate optimal control strategy for non-identical pumps Water Science & Technology: Water Supply |15.5 |2015

so far, little research has been done on the optimization of

the pump battery with non-identical pumps.

The problem with the tool is that doing an exhaustive

search on a large number of pumps, results in exponential

growth in computational time as the number of concurrently

running pumps increases. The algorithm implementation

optimizes calculation for identical pumps and combi-

nations, and up to four or ﬁve concurrently running non-

identical pumps can easily be calculated in a short time on

modern workstation computers, but a larger number of con-

current pumps can quickly result in a long calculation time.

However, the search method is guaranteed to ﬁnd a global

optimum, thus the presented method can be used as a refer-

ence benchmark for computationally more efﬁcient

optimization methods.

The case studies show that the tool gives efﬁciency that

is comparable to the values measured from VSDs, but opti-

mizing the pump battery control can still lead to savings in

the range of 5–10%. The savings depend largely on the cur-

rent control strategy, pump speciﬁcs and working points. In

some cases it may be beneﬁcial to install differently sized

pumps as this leaves more room for optimization.

However, implementing the optimal strategy into the

control system can be troublesome. One possibility is to

use the optimization results as a lookup table, but as the

pumps degrade there must be a compensation for the lost

capacity. An easier way is to use the tool to calculate the

optimal pump combinations for different regions in the

working regime, and implement an algorithm that chooses

the combination based on predeﬁned ﬂow and head

threshold.

ACKNOWLEDGEMENT

This work was supported by the institutional research

funding IUT (IUT19-17) of the Estonian Ministry of

Education and Research.

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1122 M. I. Sunela & R. Puust |A visual tool to calculate optimal control strategy for non-identical pumps Water Science & Technology: Water Supply |15.5 |2015