Asymmetry in the magnetic circuit, around the air gap circumference, in a hydroelectric generator will give rise to a unbalanced magnetic pull. In this paper, a hydropower rotor system is modeled and the influence of electro-mechanical forces due to overexcitation is analyzed. The active power has been kept constant and the rotor excitation has been changed in order to vary the output of reactive power. The electromagnetic field is solved with the finite element method. Two electromagnetic models are compared: one with and one without damper winding. The mechanical model of the generator consists of a four degrees of freedom rigid disk connected to an elastic shaft supported by two bearings with linear properties. It has been found that the unbalanced magnetic pull slightly increases for reactive loads resulting in a decrease of natural frequencies and an increase of unbalance response. When the damper winding is included, the magnetic pull will decrease compared to the model without damper winding, and the pull force has two components: one radial and one tangential. The tangential component can influence the stability of the mechanical system for a range of design parameters.

1.
Behrend
,
B. A.
, 1900, “
On the Mechanical Force in Dynamos Caused by Magnetic Attraction
,”
J. Am. Inst. Electr. Eng.
0095-9804,
17
, p.
617
.
2.
Gray
,
A.
, 1926, “
Electrical Machine Design
,
McGraw–Hill
, New York, pp.
498
500
.
3.
Robinson
,
R. C.
, 1943, “
The Calculation of Unbalanced Magnetic Pull in Synchronous and Induction Motors
,”
Electron. Eng. (U.K.)
0013-4902,
62
, pp.
620
624
.
4.
Covo
,
A.
, 1954, “
Unbalanced Magnetic Pull in Induction Motors With Eccentric Rotors
,”
Trans. Am. Inst. Electr. Eng.
,
73
(
III
), pp.
1421
1425
.
5.
Ohishi
,
H.
,
Sakabe
,
S.
,
Tsumagari
,
K.
, and
Yamashita
,
K.
, 1987, “
Radial Magnetic Pull in Salient Poles Machines
,”
IEEE Trans. Energy Convers.
0885-8969,
EC-2
(
3
).
6.
Früchtenicht
,
J.
,
Jordan
,
H.
, and
Seinsch
,
H. O.
, 1982, “
Exzentrizitätsfelder als Ursache von Laufinstabilitäten bei Asynchronmaschinen. Teil I und II
,”
Arch. Elektrotech. (Berlin)
0003-9039,
65
, pp.
271
292
.
7.
Belmans
,
R.
,
Geysen
,
W.
,
Jordan
,
H.
, and
Vandenput
,
A.
, 1982, “
Unbalance Magnetic Pull and Homopolar Flux in Three Phase Induction Motors With Eccentric Rotors
,”
Proceedings, International Conference on Electrical Machines—Design and Application
, July 13–15, Budapest, pp.
916
921
.
8.
Belmans
,
R.
,
Vandenput
,
A.
, and
Geysen
,
W.
, 1987, “
Influence of Unbalanced Magnetic Pull on the Radial Stability of Flexible-shaft Induction Machines
,”
IEE Proc.: Electr. Power Appl.
,
134
(
2
), pp.
101
109
.
9.
Smith
,
A. C.
, and
Dorell
,
D. G.
, 1996, “
Calculation and Measurement of Unbalanced Magnetic Pull in Cage Induction Motors With Eccentric Rotors. Part 1: Analytical Model
,”
IEE Proc.: Electr. Power Appl.
1350-2352,
143
(
3
), pp.
202
210
.
10.
Arrkio
,
A.
,
Antila
,
M.
,
Simon
,
A.
, and
Lantto
,
E.
, 2000, “
Electromagnetic Force on a Whirling Cage Rotor
,”
IEE Proc.: Electr. Power Appl.
1350-2352,
147
(
5
), pp.
353
360
.
11.
Tenhunen
,
A.
, and
Arrkio
,
A.
, 2001, “
Modelling of Induction Machines With Skewed Rotor Slots
,”
IEE Proc.: Electr. Power Appl.
1350-2352,
148
(
1
), pp.
45
50
.
12.
Tenhunen
,
A.
,
Benedetti
,
T.
,
Holopainen
,
T. P.
, and
Arrkio
,
A.
, 2003, “
Electromagnetic Force of the Cage Rotor in Conical Whirling Motion
,”
IEE Proc.: Electr. Power Appl.
1350-2352,
150
(
5
), pp.
563
568
.
13.
Tenhunen
,
A.
,
Holopainen
,
T. P.
, and
Arrkio
,
A.
, 2003, “
Impulse Method to Calculate the Frequency Response of the Electromagnetic Forces on Whirling Cage Rotors
,”
IEE Proc.: Electr. Power Appl.
1350-2352,
150
(
6
), pp.
752
756
.
14.
Tenhunen
,
A.
,
Holopainen
,
T. P.
, and
Arrkio
,
A.
, 2004, “
Effects of Saturation on the Forces of Induction Motors With Whirling Cage Rotor
,”
IEEE Trans. Magn.
0018-9464,
40
(
2
), pp.
766
769
.
15.
Gustavsson
,
R. K.
, and
Aidanpää
,
J.-O.
, 2004, “
The Influence of Magnetic Pull on the Stability of Generator Rotors
,”
Proceedings 10th of International Symposium on Transport Phenomena and Dynamics of Rotating Machinery
, Honolulu, HI, March 7–17.
16.
Gustavsson
,
R. K.
, and
Aidanpää
,
J.-O.
, 2006, “
The Influence of Non-linear Magnetic Pull on Hydropower Generator Rotors
,”
J. Sound Vib.
0022-460X,
297
(
3–5
), pp.
551
562
.
17.
Karlsson
,
M.
, and
Aidanpää
,
J.-O.
, 2005, “
Dynamic Behavior in a Hydropower Rotor System Due to the Influence of Generator Shape and Fuid Dynamics
,”
Proceeding of PWR2005
, ASME Power, Chicago, IL, April 5–7, pp.
905
913
.
18.
Lundström
,
N.
, and
Aidanpää
,
J.-O.
, 2007, “
Dynamic Consequences of Electromagnetic Pull due to Deviations in the Generator Shape
,”
J. Sound Vib.
0022-460X,
301
(
1–2
), pp.
207
225
.
19.
Lundström
,
L.
,
Gustavsson
,
R.
,
Aidanpää
,
J.-O.
,
Dahlbäck
,
N.
, and
Leijon
,
M.
, 2007, “
Influence on the Stability of Generator Rotors due to Radial and Tangential Magnetic Pull Force
,”
IET Electric Power Applications
,
1
(
1
), pp.
1
8
.
20.
Burakov
,
A.
, and
Arkkio
,
A.
, 2006, “
Low-Order Parametric Force Model for a Salient-pole Synchronous Machine With Eccentric Rotor
,”
Electr. Eng.
0948-7921,
89
(
2
), pp.
127
136
.
21.
Burakov
,
A.
, and
Arkkio
,
A.
, 2006, “
Low-Order Parametric Force Model for a Eccentric-Rotor Electrical Machine With Parallel Connections in Stator Winding
,”
IEE Proc.: Electr. Power Appl.
1350-2352,
153
(
4
), pp.
592
600
.
22.
Tampion
,
A. A.
,
Stoll
,
R. L.
, and
Sykulski
,
J. K.
, 1991, “
Variation of Turbogenerator Stator Core Vibration With Load
,”
IEE Proc.-Commun.
,
138
(
5
), pp.
389
400
.
23.
Karlsson
,
M.
,
Perers
,
R.
,
Gustavsson
,
R.
,
Aidanpää
,
J.-O.
,
Karlsson
,
T.
, and
Leijon
,
M.
, 2006, “
Rotor Dynamical Analysis of a Hydropower Generator for Active Power
,”
Proceedings of International Symposium on Water Resources and Renewable Energy Development in Asia
, November 30–December 1, Bangkok.
24.
Arkkio
,
A.
, 1987, “
Analysis of Induction Motors Based on the Numerical Solution of the Magnetic Feld and Circuit Equations
,”
Acta Polytech. Scand.
,
59
, pp.
1
97
.
25.
Coulomb
,
J. L.
, 1989, “
Methodology for the Determination of Global Electromechanical Quantities From a Fnite Element Analysis and its Application to the Evaluation of Magnetic Forces, Tourques and Stiffness
,”
IEEE Trans. Magn.
0018-9464,
19
(
6
), pp.
2514
2519
.
26.
Tenhunen
,
A.
,
Holopainen
,
T. P.
, and
Arkkio
,
A.
, 2003, “
Effects of Equalizing Currents on Electromagnetic Forces of Whirling Cage Rotor
,”
Proceedings of IEMDC 03
, Vol.
1
, Madison, WI, June 1–4, pp.
257
263
.
You do not currently have access to this content.