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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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First received 2 December 2014; accepted in revised form 18 May 2015. Available online 4 June 2015
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
