Modelling and Analysisof MultiphysicalInteractions inHydropower RotorSystems

Martin Karlssonkarmar@ltu.se

Polhem LaboratoryDivision of Computer Aided DesignLulea University of Technology971 87 LuleaSweden

OutlineBackground and Introduction

Electromechanical Models

Fluid-Rotor Interactions

Identification of Excitations and Eigenfrequencies

Conclusions

Outlook

Hydropower Generation

The Research ProblemHow should multiphysical interactions in a hydropower

rotor system be modelled, simulated and evaluated, in

order to predict the dynamical behaviour?

M−→x + (C + ΩG)−→x + K−→x =−→

F (1)

Appended Papers

Paper A

Paper B

Paper C

Paper E

Paper D

Paper F

Identification

Fluid-rotor

Electromechanical

Electromechanical Interactionsy

x

e

Fr = kM,re (2)

M−→x + (ΩG + C)−→x + (K − KM )−→x =−→

F (3)

Effects of Damper Windings

y

x

e

Fr = kM,re, Ft = kM,te (4)

Whirling Dependent Forces

−0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

Relative eccenticity in x−direction [−]

Rel

ativ

e ec

cent

icity

in y

−di

rect

ion

[−]

20% 1*Ω and 10% 3*Ω

Fr = kM,re + cM,re, Ft = kM,te + cM,te (6)

M−→x + (ΩG + C − CM,r − CM,t)−→x + (K − KM,r − KM,t)

−→x =−→

F , (7)

Results

−2 −1 0 1 2 3−100

−50

0

50

100

150

200

250

Relative Whirling [−]

Fo

rce

[kN

]Electromagnetic Forces

Results

−2 −1 0 1 2

3.7

3.75

3.8

3.85

3.9

3.95

4

4.05

4.1

4.15

Relative Whirling [−]

Re

lativve

Eig

en

Fre

qu

en

cy [−

]

First Forward Mode

−2 −1 0 1 2 3−0.01

0

0.01

0.02

0.03

0.04

0.05

Relative Whirling [−]

Da

mp

ing

Ra

tio

[−

]

First Forward Mode

Results

−2 −1 0 1 2

−3.75

−3.7

−3.65

−3.6

−3.55

−3.5

−3.45

−3.4

Relative Whirling [−]

Re

lativve

Eig

en

Fre

qu

en

cy [−

]

First Backward Mode

−2 −1 0 1 2 3−0.01

−0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Relative Whirling [−]

Da

mp

ing

Ra

tio

[−

]

First Backward Mode

Fluid-Rotor Interactions

Measurements by Gustavsson R., et al.

Computational Fluid Dynamics

YX,Z

Section Ia

Section Ib

Effect of Boundary Conditions

YX,Z

Section Ia

Section Ib

θ [rad]

y’ [m

]

0 1 2 3 4 5 60.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

−2.2

−2

−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

θ [rad]

y’ [m

]

0 1 2 3 4 5 60.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

−2.2

−2

−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

θ [rad]

y’ [m

]

0 1 2 3 4 5 60.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

−2.2

−2

−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

Results

−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2−0.5

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

Relative Force in x−direction [−]

Rela

tive F

orc

e i

n z

−dir

ecti

on

[−

]

Axi-symmetric inlet

Wicket gate inlet

Spiral casing inlet

Added Coefficients

K

θ(t)

Jp

YX,Z

Section Ia

Section Ib

Jpθ + Cθ + Kθ = M(t), (8)

(JP + JP,F luid)θ + (C + CFluid)θ + (K + KFluid)θ = M(t), (9)

Identification

500 1000 1500 2000 25000

0.05

0.1

0.15

0.2

Perturbation Frequency [rad/s]

Pol

ar In

ertia

[Nm

s2 ]

52 rad/s62 rad/s72 rad/s

500 1000 1500 2000 25000

50

100

150

200

250

300

350

400

450

Perturbation Frequency [rad/s]

Dam

ping

[Nm

s]

52 rad/s62 rad/s72 rad/s

Results

500 1000 1500 2000 2500

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Perturbation Frequency [rad/s]

Red

uctio

n of

Eig

enfr

eque

ncy

[−]

52 rad/s (undamped)62 rad/s (undamped)72 rad/s (undamped)52 rad/s62 rad/s72 rad/s

500 1000 1500 2000 25000.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Perturbation Frequency [rad/s]

Dam

ping

Rat

io [−

]

52 rad/s62 rad/s72 rad/s

Identification of Eigenfrequencies and

Excitations

Measurements by Gustavsson R., et al.

Airgap Shape

Fx(j) =n∑

i=1

∆gap(i, j)cos((i − 1)1

n2π)

km,r

n, (10)

Fluid Excitations

YX,Z

Section Ia

Section Ib

Results

Identification of Eigenfrequency

Results

Results

5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Relative Frequency [−]

Re

lative

Fo

rce

[−

]

Hydraulic Forces at 30% Load

ConclusionsThe electrical and hydraulic system shows large influence on systemcharacteristics and excitations

Damper windings seems to damp the excitation of an unstable mode

Electric forces has the same characteristics as earlier presented forasynchronous machines

Boundary conditions for a CFD-model has a large influence oncorresponding forces and moments

Operational analysis of a hydropower rotor system requires goodunderstanding of the physics in the different components

Outlook

Paper A

Paper B

Paper C

Paper E

Paper D

Paper F

Shape deviations

and pole configurations

Characteristics due to

different inlet and operating

conditions

Parallel stator windings

Transient operations of components and whole system

Modelling and simulationExperimental characterisation Optimization

AcknowledgementElektra (Elforsk AB and Swedish Energy Agency)

Kempe Foundations, Knut and Alice Wallenberg Foundation,Swedish Hydropower Center

The Swedish Research Council (SNIC)

Urban Lundin, Håkan Nilsson, Richard Perers

Rolf Gustavsson and Mattias Nässelqvist

Jan-Olov Aidanpää and Thommy Karlsson

Thank you, for

your attention!