XVIII International Conference on Electrical Machines ���ICEM 2008

New Theoretical Approach to the Synchronous Reluctance Machine (SynRM) Behavior and Performance

Conclusions� A new operating diagram for the SynRM is introduced

based on the machine vector model in the rotor reference frame.

�The main machine performance can be explainedand evaluated by this diagram that demonstrates the machine flux, current, torque, and power factor for all possible machine operating points below and above base speeds.

�The saturation effect on torque, IPF, current and flux is discussed with this diagram by FEM calculations.

� An online parameter estimator based on the machine terminal values and power factor is presented.

Main Performance (Ideal & Saturation Effect)

SynRM Operating DiagramA new operating diagram for the SynRM demonstrates the machine flux,

current, torque, and power factor for all possible machine operating points in just one diagram, by combining the torque vs. current angle

graphs at constant current, constant flux and power factor.

Parameter Estimator

Reza R. Moghaddam ‡†, Freddy Magnussen †, Chandur Sadarangani ‡†, Heinz Lendenmann †

‡ Royal institute of Technology, KTH, School of Electrical Engineering, Department of Electrical Machines and Power Electronics , Stockholm, Sweden. † ABB Corporate Research, Västerås, Sweden.

0

5

10

15

20

25

30

0 10 20 30 40 50 60 70 80 90Current Angle (elec. Deg.)

Sal

ienc

y R

atio

(Zea

ta)

IPF=0,9IPF=0,85IPF=0,8IPF=0,7IPF=0,6IPF=0,5

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 10 20 30 40 50 60 70 80 90Current Angle (elec. deg.)

IPF

zetha=200zetha=12zetha=8zetha=4

θ

T

ctefEEEE

=>>> 4321

4f

cteEffff

=<<< 4321

4I

1tan =θξδ /1tan =ξθ =tan

1tan =δ

4321 IIII >>>

4λ

4321 λλλλ >>>

3λ2λ

1λ

3f

2f

1f

4E

3E

2E

1E

T

θ

3I

2I

1I

( ) ( )θ2sin22

3 2ILLp

T qdag ⋅−=

���

����

����

����

�⋅���

����

�⋅��

�

�

��

�

�−= −

ξθ

ωtan

tan2sin11

223 1

2E

LLp

Tdq

ag

( )( ) .sincottancos 1 θθξθ <⋅+−= −IPF

( )( )IPF1costantan −+⋅−= θθξ

0121

1 TTB

���

����

� +=

ξξ

A

B

C

D

G

1tan =θξδ /1tan =

ξθ =tanξδ /1tan =

ξθ =tan1tan =δ

θ

IPFT

., cteIIT C ==

., cteIIT A ==

., cteT A == λλ

., cteT G == λλ

., cteT B == λλ

.,

cteT

D

C

====

λλλ

IPF11

, +−=

ξξ

GDIPF

���

����

� +

���

����

�−

=

=

ξξ

ξξ

121

121

,,,, EBCFAIPF

0

0

121

112

T

TTD

���

����

�+

=

=+

=

ξξ

ξξ

0TTTT GCA === IPF

IPF

1

., cteIIT G ==

900

., cteIIT C ==

0.20.20.2

0.40.4

0.4 0.6

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1

1

1

1

1

1.2

1.2

1.2

1.2

1.2

1.4

1.4

1.4

1.4

1.4

1.4

1.6

1.6

1.6

1.8

2

Current angle ϑ [d]

Tor

que

T ag [

pu]

10 20 30 40 50 60 70 80

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0.20.40.40.4

0.60.60.6

0.80.80.80.8

11

11

1.2

1.2

1.2

1.2

1.4

1.4

1.4

1.4

1.4

1.6

1.61.6

1.6

1.6

1.8

1.8

1.8

1.8

1.8

2

2

2

2.2

Current angle ϑ [d]

Tor

que

T ag [

pu]

10 20 30 40 50 60 70 80

1

2

3

4

5

6

7

8

0.4

0.4

0.6

0.6

0.6

0.8

0.8

0.8

0.8

1

1

1

1

1.2

1.2

1.2

1.4

1.4

1.6

1.6

1.8

Current angle ϑ [d]

IPF

[*]

20 30 40 50 60 70 80

0.2

0.3

0.4

0.5

0.6

0.7

0 0.5 1 1.50

0.5

1

1.5

Time [s]

| i s

|

[pu]

| i s |

0 0.5 1 1.50

2

4

6

8

10

Time [s]

Sal

ienc

y R

atio

ζ

Actual ζEstimated ζ

0 0.5 1 1.50

10

20

30

40

50

Time [s]

L d [mH

]

Actual L dEstimated L d

0 0.5 1 1.50

2

4

6

8

10

Time [s]

L q [m

H]

Actual L qEstimated L q

( ) ( )( )( )IPF

ii iqd

1costantan

tantan,−+⋅−=

=+⋅−=

θθ

ϕθθξ

( )

( )

( )( )θ

θω

θϕθ

ω

θδ

ωθδλλ

sincoscos

sincos

sinsin

sinsin

,

1 IPFIE

IE

IE

iiiiL

i

q

qqdq

−+−⋅=

=+−⋅=

=⋅=⋅==

Torque at Constant Stator CurrentThe maximum torque per ampere (MTPA) is when

for certain current the torque is maximized

Under Saturation FEM

Ideal

Torque at Constant Stator Flux The maximum torque per volt (MTPV) is

when for certain flux the torque is maximized

IdealUnder Saturation FEM

Internal Power Factor (IPF) at Constant Stator Current

The maximum torque per kilo volt-ampere (MTPkVA) is when for certain current the power factor is maximized

IdealUnder Saturation FEM

Saliency Ratio at Constant Internal Power Factor (IPF)

Stator Current (p.u.) as parameter

Stator Current (p.u.) as parameterStator Flux (p.u.) as parameter

Machine Model

J. K. Kostko rotor 1923

d

λ

i

e

vqv

dvdλ

qλ

di

qi

si

q

ssiR

�

�

�

i�

�

( )( )

�e�cosIPF

�cosPF

RR

i

s-cr-c

⊥=

=

→

∆

∆ci

MOGHADDAMRREZA .

β

d

q

( ) θξλ

λδ

ϕθtan

1tan

tan1 ====+

−

dd

qq

d

q

i iL

iL

100

100

100

100

200

200

200

200

300

300

300

300

400

400

400

400

500

500

500

500

600

600

600

600

700

700

700

70050

50

50

50

100

100

100

150

150

150

200

200

200

250

250

250

250

300

300

300

300

350

350

350

350

400

400

400

400

dq-axis Current idm & iqm [A Peak]

dq-a

xis

flux

λ d & λ

q [Vs

Pea

k]

λd & λq [Vs Peak] as function of d- and q-axis current

50 100 150 200 250 300 350 400

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

d-axis flux

(iq Parameter)

q-axis flux

(id Parameter)

Ldt

d�

�j�

cR

si isR

v e

ci

MOGHADDAMRREZA .

Saliency Ratio Estimator based on Power Factor

Inductances Estimator based on Terminal Values

SynRM

Internal Power Factor (IPF) at Constant

Saliency Ratio

angleload

angletorque

anglecurrent

::

:

δβ

δβθ +=The SynRM used for FEM and calculations

Simulated Machine Performance at Start Up and Nominal Load in Matlab-Simulink Including Saturation

IMSynRM

SynRM = Reluctance Concept + Rotating Sinusoidal Magneto Motive Force – the same as in IMIn this paper a simpler method to describe the SynRM behavior is discussed.

SynRM Capabilities vs. IMo Higher Efficiency;Eff1,+0.5-4%-unit.o Higher Torque density at same dT-rise; ~+25%.o Higher Overload Capacity. o Easier Production; no Cage.o Adaptability:

o Same Production Line.o Same enclosure.o ~ Same Inverter.

o Lower maintenance. o Higher Reliability.o ~ Same Field-Weakening.o Easier Sensor-less Control.o Braking at Standstill.

Constant torque

hyperbolae

Constant current circles

Constant voltage ellipses

di

qi

A

B

� Possible operating points of SynRM: points “A – G”. � Different control strategies: dashed vertical lines:

� MTPA (�=45°), MTPkVA (tan�=��) and MTPV (tan�=�)

� Delivering T0 with different control strategies:� Points “A”, “G” and “C” represent MTPA, MTPkVA and

MTPV respectively. Running the machine in all these conditions produces same torque T0.

� Field-weakening: If MTPA is followed for below base speed operation, point “A”, then in one strategy the machine current trajectory above base speed and in constant power region starts from “A” and moves to “D”, and for another method it passes point “D” and moves to “B”.

� Traditional Circle Diagram for machine operation demonstration