Variable Speed Induction Starting Synchronous Motor Driving Centrifugal Pump

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International Journal on Power Engineering and Energy (IJPEE) Vol. (6) – No. (3)
ISSN Print (2314 – 7318) and Online (2314 – 730X) July 2015
Operation Performance of Variable Speed
Induction Synchronous Motor
Mohamed. I. Abd-Elwanis Ragab A. El-Sehiemy
Department of electrical Engineering
University of Kafrelsheikh
Kafrelsheikh, Egypt
{ mohamed.soliman4&elsehiemy }@eng.kfs.edu.eg
Abstract-This paper presents the steady state performance of
the variable speed centrifugal pump driven by an induction-
synchronous motor. The steady state performance aims at
studying the variation of the armature voltage, armature
current, input apparent power, air gap power, mechanical
torque with respect to the varied motor speed. At certain
motor speed within the operating range, the motor output
mechanical power is equated to the input mechanical power
of the centrifugal pump. A steady-state mathematical model
is derived and solved analytically to predict the steady-state
performance of the system for efficient describing the system
behavior under different loading conditions. Comparison
studies are employed to show the full agreement between the
computed results and laboratory simulation for the system.
Keywords-Synchronous motor (SM), space vector PWM,
variable speed centrifugal pump.
NOMENCLATURE
n
f
:
Base frequency f:
v
ariable frequency
sn
X
:
synchronous reactance at base frequency
sb
n
:
synchronous speed at base frequency fn
ρ
w
: the fluid density (kg/m3) P
ip
: the input power
required
H : the energy Head added to the flow (m)
N : Pump speed, Q = Flow
(GPM)
R
a
:
A
rmature
r
esistance
s
n
:
the variable synchronous speed and
g : the gravitational constant (9.81 m/s2)
P : Pressure (Feet), HP = Horsepower
Ηp : is the efficiency of the pump plant as a decimal
Qw : the flow rate (m3/s),

:
Current angle
Van : Rated voltage

:
Power angle
I. I
NTRODUCTION
Variable-speed synchronous motors (VSSM) have been
widely used in very large capacity pumping and centrifuge
type applications (up to MW) [1]. It usually supplied by
naturally commutated current-source thyristors converters.
At low-power loads, the current-source space vector pulse
width modulation (SVPWM) inverter-feed SM has become
very popular in recent years. The features of three-phase
SM that have allowed them, especially the lower capacity
motors, to be controlled with high dynamic performance
using cheaper control hardware than is required for the
induction motor of similar capacity. Since the average
speed of the SM is precisely related to the supply
frequency, which can be precisely controlled, multi-motor
drives with a fixed speed ratio among them are also good
candidates for SM drives.
Reference [2] presented the performance of the variable-
speed salient-pole SM drive using the steady-state
equivalent circuit followed by dynamics of the vector-
controlled SM drive. Self excited synchronous induction
motor is presented in [3]. Control strategy and dynamic
simulation of the large-scale high-superconducting
synchronous motor fed by an auto-sequentially
commutated inverter is presented in [4]. Torque-control
strategy is presented for high-performance control of a
permanent magnet (PM) synchronous motor. In order to
deal with the torque pulsating problem of a PM
synchronous motor in a low-speed region, new torque
estimation and control techniques was presented [5].
Reference [6] presented a method to control a synchronous
motor in such a way to resemble the characteristics of a dc
motor. The method suggests including a second field
winding to the rotor of a voltage-source-inverter-fed
synchronous motor. Reference [7] presented a practical
optimal current control method for a newly emerging class
of synchronous motors with hybrid rotor fields by both
permanent magnet and winding. Reference [8] presented a
Modeling of a wound rotor salient pole synchronous
machine and its converter in the constant power zone.
Reference [9] presented a study of the dynamic behavior
of a static frequency converter driving a synchronous
generator which is used in a pumped storage power plant.
In the constant power zone, the maximum voltage, due to
the embedded accumulators, is applied. Generally, the
supplied voltage tends from a sinusoidal to a rectangular
waveform. This technique allows the use of the maximum
value of the DC bus.

International Journal on Power Engineering and Energy (IJPEE) Vol. (6) – No. (3)
ISSN Print (2314 – 7318) and Online (2314 – 730X) July 2015
Reference Number: W14-P-0019 561
This paper presents the steady state performance of the
variable speed self starting synchronous motor drives
centrifugal pump. The steady state performance aims at
studying the variation of the armature voltage, armature
current, input apparent power, air gap power, mechanical
torque with respect to the varied motor speed. The
proposed mathematical model of the combined system
comprises a variable speed drive connected to synchronous
motor to drive variable speed centrifugal pumps.
II. MATHEMATICAL MODEL OF VARIABLE SPEED
SYNCHRONOUS MOTOR
The steady state equivalent circuit of the round rotor
synchronous motor is shown in Fig. 1 as in [10]. To
deduce the steady state performance, the mathematical
model is derived from the equivalent circuit which
constitutes a variable voltage source which refers to the
armature voltage (V
a
), armature impedance (R
a
+j X
s
) and
internal generated voltage (E
f
).
Fig. 1. steady state equivalent circuit of wounded rotor synchronous
motor
The armature voltage changes linearly with the inverter
frequency. Then, V
a
is computed as:
f
n
f
an
V
a
V=
(1)
And variable synchronous reactance (X
s
) is computed as:
f
n
f
sn
X
s
X=
( 2)
And variable per unit synchronous speed n is:
50
f
sb
n
s
n
n==
(3)
From the Equivalent circuit, the internal generated voltage
(E
f
) is computed as:
)0
(
saaf
jXRVE
a
I
+−
∠
=−
∠

(4)
Where,
a
I
refers to the armature current.
Equation (4) can be rewritten as:
[ ]
22
)()sin(cos
s
X
a
R
s
jX
a
Rj
f
E
a
V
s
jX
a
R
f
E
a
V
a
I
+
−−−
=
+
−
=


(5)
The armature current can be written in the rectangular
form as:
)sin(cos


j
a
I
a
I−=
;
Then, the real part of equation (5) is:
22
sin)cos(
cos
sa
XR
s
X
f
E
f
E
a
V
a
R
a
I
+
−−
=



(6)
The input power is:

cos3
a
I
a
V
i
P=
[ ]
22
sin)cos(3
sa
XR
s
X
f
E
f
E
a
V
a
R
a
V
+
−−
=


(7)
The air gap power is:
cu
P
i
PP
g
−=
(8)
The copper loss is:
a
R
a
I
cu
P2
3=
(9)
Substituting from Eq. 7 and Eq. 9 in to Eq. 8
a
R
a
I
a
I
a
VP
g
2
3cos3 −=

(10)
Performing this and by algebraic manipulation the
following non-linear equation for the power angle

is
obtained:
( )
s
X
a
R
f
E
a
V
g
Pf ,,,,=

(11)
The power angle

is functions of the field current,
applied voltage and other parameters. For a given
mechanical power Eq.11 is solved numerically using the
iterative method such as Newton-Raphson method to
obtain

.
Then, other variables as power, torque, efficiency and
power factor can be easily computed. The input apparent
power can be calculated as:
a
I
a
V
i
S3=
(12)
And active/reactive powers are computed from (13) and
(14), respectively as:

cos
i
S
i
P=
(13)

sin
i
S
i
Q=
(14)
The synchronous motor armature copper loss is
determined from:
a
R
a
I
cu
P2
3=
(15)
The gape power is:
cu
P
i
P
g
P−=
(16)
The field power is:
2
f
IRf
f
P×=
(17)
a
V
a
I
a
R
s
X
f
E

International Journal on Power Engineering and Energy (IJPEE) Vol. (6) – No. (3)
ISSN Print (2314 – 7318) and Online (2314 – 730X) July 2015
Reference Number: W14-P-0019 562
Then the motor efficiency can be computed from:
f
P
Pi
Pg
η+
=
(18)
And, the electromagnetic torque is:
f
p
g
P
T

4
= (19)
III. SPACE VECTOR PWM METHOD
The space vector PWM (SVPWM) method is an
advanced, computation-intensive PWM method and is
possibly the best among all the PWM techniques for
variable frequency drive applications. Because of its
superior performance characteristics, it has been finding
widespread application. This is typical of a centrifugal
pump and a fan [5]. The PWM methods have only
considered implementation on a half-bridge of a three-
phase bridge inverter. If the load neutral is connected to
the center tap of the dc supply, all three half-bridges
operate independently, giving satisfactory PWM
performance. With a machine load, the load neutral is
normally isolated. The SVM method considers this
interaction of the phases and optimizes the harmonic
content of the three-phase isolated neutral load.
A. Output voltages of three-phase inverter
The circuit model of a typical three-phase voltage source
PWM inverter is shown in Fig.2. S1 to S6 are the six
power switches that shape the output, which are controlled
by the switching variables a, a′, b, b′, c and c′. When an
upper transistor is switched on, i.e., when a, b or c is 1, the
corresponding lower transistor is switched off, i.e., the
corresponding a′, b′ or c′ is 0. Therefore, the on and off
states of the upper transistors S1, S3 and S5 can be used to
determine the output voltage.
B. Basic Switching Vectors and Sectors
To implement the space vector PWM, the voltage
equations in the abc reference frame can be transformed
into the stationary dq reference frame that consists of the
horizontal (d) and vertical (q) axes.
As a result, six non-zero vectors and two zero vectors
are possible. Six nonzero vectors (V1-V6) shape the axes
of a hexagonal as depicted in Fig. 3, and feed electric
power to the load. The same transformation can be applied
to the desired output voltage to get the desired reference
voltage vector V
ref
in the d-q plane. The objective of space
vector PWM technique is to approximate the reference
voltage vector V
ref
using the eight switching patterns. One
simple method of approximation is to generate the average
output of the inverter in a small period, T to be the same as
that of V
ref
in the same period.
Fig. 2. SVPWM inverter connection diagram
Fig. 3. Basic switching vectors and sectors
Fig. 4. Voltage Space Vector and its components in (d, q).
Fig. 5. Reference vector as a combination of adjacent vectors
at sector 1.
C. Realization of Space Vector PWM
Space vector PWM can be implemented by the
following steps:
Step 1: Determine Vd, Vq, Vref, and angle (

)
From Fig. 4, the V
d
,V
q
,V
ref
, and angle (α) can be
determined as follows:
Coordinate transformation: abc to dq
cn
V
2
1
bn
V
2
1
an
V
d
V−−=
(20)
Diode
rectifier
Synch.
Motor
Speed
Controller
SV
M
a
I
a
V,
PWM
inverter
Speed
Comma
S
1
a
S
4
a`
S
3
b
S
6
b`
S
2
c`
S
5
c
n
v
a
v
b
v
c
C
A
B
f
I

International Journal on Power Engineering and Energy (IJPEE) Vol. (6) – No. (3)
ISSN Print (2314 – 7318) and Online (2314 – 730X) July 2015
Reference Number: W14-P-0019 563
cn
V
2
3
bn
V
2
3
an
V
q
V−+=
(21)
2
q
V
2
d
V
ref
V+=
(22)
t
s
f2 πt
s
ω)
d
V
q
V
(
1
tanα ==
−
=
(23)
Step 2: Determine time duration T1, T2, T0
From Fig. 5, the switching time duration can be
calculated as follows:
Switching time duration at any Sector
⎟
⎠
⎞
⎜
⎝
⎛
−
⋅⋅
=




sin
3
coscos
3
sin
3
1
nn
dc
V
refV
z
T
T
(24)
⎟
⎠
⎞
⎜
⎝
⎛
−
+
−
−
⋅⋅
=




3
1
cos.sin
3
1
sin.cos
3
2
nn
dc
V
refV
z
T
T
(25)
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
°≤≤
==
−−=∴
60α0
6)toSector1is,(that6through1n,
s
f
1
z
Twhere,
,
210 TT
z
TT
(26)
IV. VARIABLE SPEED CENTRIFUGAL PUMP
A centrifugal pump works by the conversion of the
rotational kinetic energy, typically from an electric motor
or turbine, to an increased static fluid pressure. This action
is described by Bernoulli's principle. The rotation of the
pump impeller imparts kinetic energy to the fluid as it is
drawn in from the impeller eye (centre) and is forced
outward through the impeller vanes to the periphery. As
the fluid exits the impeller, the fluid kinetic energy
(velocity) is then converted to (static) pressure due to the
change in area the fluid experiences in the volute section.
Typically the volute shape of the pump casing (increasing
in volume), or the diffuser vanes (which serve to slow the
fluid, converting to kinetic energy in to flow work) are
responsible for the energy conversion. The energy
conversion results in an increased pressure on the
downstream side of the pump, causing flow. The energy
usage in a pumping installation is determined by the flow
required, the height lifted and the length and
characteristics of the pipeline. The power required to drive
a pump
(
ip
P
),
is a defined simply using SI unit by:
g H Q
ww
Pi p
p


=
(27)
The head added by the pump (H) is a sum of the static
lift, the head loss due to friction and any losses due to
valves or pipe bends all expressed in meters of water. The
value for the pump efficiency η may be stated for the
pump itself or as a combined efficiency of the pump and
motor system. A set of formulas that are used to predict the
operation of a centrifugal pump at any operating point
based on the original pump characteristics is known as the
affinity laws.
1
2
1
2
N
N
Q
Q=
,
2
1
2
2
1
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
=
N
N
P
P
,
3
2
1
1
2
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
=
N
N
HP
HP
(28)
Using the pump example as the throttling system, we can
calculate the power requirements for the system when the
pump speed is shown in Table 1.
Table 1
Pump speed verses HP, flow rate and GPM
GPM 250 200 150 100
Flow% 100 80 60 40
Rpm 1750 1400 1050 700
Break HP 25 12.5 5.4 1.6
Using fitting curve of Fig.6 to find the mechanical input
power to the centrifugal pump:
21
3
.0
4
10677.9
26
1029.1 +
−
×−
−
×= nn
mp
P
(29)
The synchronous motor with the mathematical model
presented in II is connected to centrifugal pump through a
variable speed drive. At any given motor speed within the
operating range, the motor output mechanical power is
determined by solving the electrical system which is
equated with the centrifugal pump input mechanical
power
mp
P
.
0.2 0.4 0.6 0.8 1 1.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
p.u. speed
Pump power
Fig. 6. Input power-speed characteristics in centrifugal pump
V. APPLICATIONS
The paper results are based on a squirrel-cage
induction motor (4-pole, 220V, Y, 50Hz, 1.98 kVA) which
is designed at 27-military production factory. Simulation
of proto-type synchronous machine is carried out to by
modifying the cylindrical rotor of squirrel-cage induction
motor to a 4-pole wounded rotor in order to the rotor of a
4-pole synchronous machine. The modified SM starts as
an IM and the continuous operation will be synchronous.

International Journal on Power Engineering and Energy (IJPEE) Vol. (6) – No. (3)
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Reference Number: W14-P-0019 564
Figures 7-9 show the comparison between the calculated
values and the experimental readings, (armature current-
field current, input power-field current, power factor-field
current, reactive power-field current and apparent power-
field current) at torque of 0.4 Nm.
It's obvious that, the armature current decreases when the
field current rises at constant speed. The increasing of field
current leads to increase the lagging power factor until the
maximum power factor (unity) which occurs at 0.12 of the
rated field current. This is lead to a constant in
synchronous motor air gap power. The apparent power and
reactive are decrease with the field current increase. The
armature voltage attains its rated value the exciter control
to make the motor operate at variable excitation.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.055 0.075 0.095 0.115 0.135 0.155
If pu
Ia p u
Fig. 7. armature current against field current simulation ▲experimental
0
0.2
0.4
0.6
0.8
1
1.2
0.07 0.09 0.11 0.13 0.15 0.17
If pu
p f
Fig. 8. power factor against field current simulation ▲experimental
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.07 0.09 0.11 0.13 0.15 0.17
If p u
S p u
Fig. 9. Input power, input reactive and apparent power against field
current
Figure 7 shows the armature current verses field current.
The experimental results are compared with simulation
results. It is obvious that the minimum armature occurred
at 0.115 pu. At this point the power factor is maximized at
shown in Fig. 8. When the field current is below 0.115 of
its rated value the power factor is lagging while with
increased field current over 0.115 p.u. the power factor
goes to lead p.f. region. Over the range of field current, the
input power is remain constant as shown in Fig. 9. Figure
9 shows the variation of reactive power versus the field
current. The SM is a source of reactive when the field
current increased than 0.115 P.U. this mean the SM can be
used for power factor correction application that
customized from the easily controlled of reactive power at
constant active power. In terms of the input apparent
power the minimum input S is occurred at the point of
maximum pf as shown in Fig. 9.
Figures 10-13 show the performance of synchronous
motor under variable speed condition for three different
values of field current. Figures 10-13 show that the
increase of the synchronous motor speed leads to increase
the armature current, input power and power factor,
respectively. At this load the reactive power is load and
fed reactive power to network at the value of field current
is 0.154 pu.
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
0.21
0.22
0.6 0.7 0.8 0.9 1
n pu
Ia pu
Fig. 10. armature current -SM speed simulation and ■ experimental
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.6 0.7 0.8 0.9 1
n pu
Pi pu
Fig. 11. input power -SM speed simulation and ■ experimental
If=0.154
If=0.077
If=0.096
o input power
Δ apparent power
□ input reactive power

International Journal on Power Engineering and Energy (IJPEE) Vol. (6) – No. (3)
ISSN Print (2314 – 7318) and Online (2314 – 730X) July 2015
Reference Number: W14-P-0019 565
0.52
0.57
0.62
0.67
0.72
0.77
0.82
0.87
0.92
0.97
1.02
0.6 0.7 0.8 0.9 1
n p u
pf
Fig. 12. power factor -SM speed simulation and ■ experimental
-0.12
-0.07
-0.02
0.03
0.08
0.13
0.18
0.6 0.7 0.8 0.9 1
n pu
Q pu
Fig. 13. reactive power -SM speed simulation and ■
experimental
VI. CONCLUSIONS
This paper presents the steady state analysis of the
variable speed centrifugal pump driven by synchronous
motor starting as an induction motor. At the same speed
the obtained motor output power is equated with input
mechanical power of the centrifugal pump during the
centrifugal pump operate at constant head.
An analytical technique to determine the steady-state
performance of the variable speed centrifugal pump driven
by synchronous motor has been presented. The armature
current rises as the speed rise this is lead to an increasing
in both synchronous motor active power and reactive
power. The proposed technique is based on the
synchronous machine steady-state equivalent circuit. The
major advantages of the proposed method are:
i- The ability of efficient analysis of the steady-state
performance of the variable speed centrifugal pump
driven by synchronous motor with fewer efforts to
model the compound system.
ii- Possibility to improve system power factor, input
power and system efficiency.
iii- There is a good agreement between computed and
measured results.
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If=0.077
If=0.154
If=0.096
If=0.096
If=0.077
If=0.154