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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)

ISSN Print (2314 – 7318) and Online (2314 – 730X) July 2015

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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[4] Minseok Joo, “Dynamic Control of Large-Scale High-Tc

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[5] Se-Kyo Chung, Hyun-Soo Kim, Chang-Gyun Kim, and Myung-

Joong Youn, “A New Instantaneous Torque Control of PM

Synchronous Motor for High-Performance Direct-Drive

Applications”, IEEE Transaction on power electronics 13 (1998)

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[6] Khalid I. Saleh, Osama A. Mohammed, and Mohammed A. Badr,

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[9] Tian-Hua Liu, Chih-Ying Lin, Jin-Shyr Yang, Wen-Yao Chang,

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[10] M. G. Say: ‘‘The performance and design of alternating current

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[11] Muhammad H. Rashid: ‘‘power electronics circuits, devices and

Application’’, 2

nd

edition, Prrentice-Hall, Englewood Cliffs, New

Jersey, June (1994).

If=0.077

If=0.154

If=0.096

If=0.096

If=0.077

If=0.154