lecture note electrical machine thermal design

8/10/2019 Lecture Note Electrical Machine Thermal Design

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Thermal design

Electromagneticdesign

Specifications

P, m

Mechanicaldesign

Bearings

Thermal design

Power supply


2/32

Loss distribution in an inverter-fed motor


3/32

Loss distribution for sinusoidal supply


4/32

High-frequency flux related to the inverter supply

Figure presents the high-

frequency flux associated

with the harmonic voltagesof the inverter supply.

The machine was analysed

in inverter supply and

sinusoidal supply with the

two supply voltages having

equal fundamental

harmonics. The flux

presented in the figure is

the difference of the fluxes

of the two supply modes.


5/32

Voltage and current in the loss simulation


6/32

Insulation classes for w indings

A winding should stand for 20 000 h the temperature

defined by the insulation class (IEC 60216-1).

Montsingers rule / Arrhenius equation

A temperature rise of 10 K halves the expected live time of

an insulation system

1 0 K 0 .5 L T L T e k TL T B

Insulation class 130 155 180

Old system B F H

Maximum temperature [C] 130 155 180Average temperature rise [K] 80 105 125


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Characteristics of a permanent magnet


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= heat conductivity

= densitycp = specific heatph = power density

h( )pc T pt

q

hpTc T pt

Tq

Equations of heat conduction

Heat conduction is a solid (or static fluid)

Conservation of energy

Heat equation


9/32

Thermal conductivities of some materials

Material / Part [W/mK]

Copper 370Aluminium 240Casted iron 58Steel (0.1 % C) 52

Stainless steel 15 25Laminated core (radial direction) 18 40Laminated core (axial direction) 1 4NeFeB magnets 10Enamel coating of conductors 0.20Slot insulation 0.2 0.3

Air at 50 C 0.028Water at 20 C 0.60


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Problem: Heat transfer from solid to fluid

v

x

T

x

Tm Ta

v What is velocity distribution?

Turbulent or laminar flow?

Conduction or convection?

What is thermal distribution?=>

Semi-empirical heat transfer

coefficient c for the surface

c c m aq T T


11/32

Circumferential flow pattern in air-gap

Laminar flow Turbulent flow

r mRvR e

= density, = radial air-gap length, Rr= rotor radius, = dynamic viscosity

Re < 2000 => laminar flow; Re > 5000 => turbulent flow

Reynolds number

Rotor

r

v

Stator

Rotor

v

Stator

Rr


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Flow distribution in r,z-plane

Couette flow with Taylor vortices:

Taylor number22 3

2 m r

2

r

RT a R e

R

= density, = radial air-gap length, Rr= rotor radius,

= dynamic viscosity

Taylor vortices appear in air-gap flow, if Ta > 1700

Stator

Rotorz

Air gapr

Rr


13/32

Heat-transfer in the air-gap flow

Heat-transfer coefficient for the air-gap surfaces

From one surface to the air flow in the middle of air gap

Nu = Nusselt numberTam = Modified Taylor number (Tam Ta for air-gap flow)

Becker K.M. and Kaye J. 1962. Measurements of diabatic flow in an annulus with an

inner rotating cylinder. Transactions of the ASME, Journal of Heat Transfer, Vol. 84,

May, pp. 97105.

c ;

N um

0.3 67 4

m m

0.241 4 7

m m

2 , < 17 00

0 .128 , 17 00 1 0

0 .409 , 10 < < 1 0

N u T a

N u T a T a

N u T a T a


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Characters for air-gap flow R e

r m

R

Re < 2000 => laminar flow; Re > 5000 => turbulent flow= density, Rr= rotor radius, m angular speed, = air gap,

= dynamic viscosity

Machine A: Turbo-generator 270 MVA, 3000 1/min

Machine B: Hydro-generator 21 MVA, 125 1/min

Machine C: Cage induction motor 4.75 MW, 1500 1/min

Machine D: Cage induction motor 37 kW, 1500 1/min

Machine A Machine B Machine C Machine D

Re 660219 21678 13838 702

Ta 5.7E+10 1.6E+06 2.5E+06 3941


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Heat flow over solid-solid boundaries withan imperfect contact

An imperfect contact betweentwo solids affects heat flow rate

=>

Semi-empirical heat-transfercoefficient c for the surface

c c 1 2q T T

Contact [W/mK]

Aluminium frame Stator core 350 - 550Cast iron frame Stator core 650 - 870Rotor bar Rotor core 430 - 2600

1T 2T


16/32

Heat transfer by radiation

4 4r 1 0Q A T T

Stefan-Boltzmann law

T1 T0

Radiation: T1 = 400 K, T0 = 300 K

=> q = 992 W/m2

Natural convection: c = 14 W/m2K,

T= 100 K

=> q = 1400 W/m2

82 4

W5 .6 7 1 0

m K


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hpq

hpT

Tq

Analogy of the heat flow and electric current flow

Static fields

Heat flow

Conservation of energy

Temperature field

0 J

0

J

Electric current density

Conservation of charge

Electric scalar potential

=> The tools developed for electric circuit analysis

can be used to study heat flow


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A conductor having a constant cross-sectional area

P

IA

l U

P = Power,

Temperature

difference

R

A

l

AdTAdqPAA

eR

UA

l

UAdAdJI

A A

Equations for the heat flow and electric current (ph = 0)

Thermal resistance

lR

A

el

RA


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Ax

212hh

2

2

2 cxcx

pxT

p

dx

Td

= constant;ph = constant

1D thermal network

hpT

ph

T1 T2

1

2

0T T

T l T=>

21h

2T

l

xT

l

xlxlx

pxT


20/32

A

l

Thermal network for 1D heat flow

ph

T1 T2

A thermal network for the bar with 1D heat flow

AlR

A

lRR

6

2

3

21

T1

T2

Ta

P

R1

R2

R3

Ta is the average temperature of the bar


21/32

Matrix of round wires

Equivalent thermal conductivity for round conductors ina stator slot

d

d

i

)

'

( i

i

ir

d

d


22/32


23/32

Thermal network for the stator

Yoke

Tooth Winding End ring

Boundary layerfrom yoke to air

Boundary layer fromteeth to air gap

Boundarylayers to

and fromend caps

The two end-regions combined

Air in air gap

Air outside

Airoutside

End-winding air

Heat source

Thermal resistor


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Thermal network for the PM rotor

core

Boundary layer fromcore to air gap

Boundary layerfrom PM to core

Air-gap air


25/32

The original

cage inductionmotor

The stator of thePM machine wasborrowed from this

machine.


26/32

Thermal network for a cage rotor

Boundary layer fromteeth to air gap

Tooth Bar End ring

End-windingair

The two end-regionscombined

Air-gap air


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Results from the thermal networks

Temperature rise; Pshaft = 37 kW

PM machine Induction machine

T [K]

Yoke 56Stator winding

- core region 84

- end winding 89

Air gap 102

Rotor cage 136

End-winding air 86

T [K]

Yoke 32Stator winding

- core region 48

- end winding 51

Air gap 47

Permanent magnet 54

End-winding air 21


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Results from the thermal networks II

Maximum power from the PM machine if the temperature of

the stator winding is allowed to rise by 90 K isP = 55 kW

T [K]

Yoke 51

Stator winding- core region 82

- end winding 89

Air gap 69

Permanent magnet 76

End-winding air 37

Note: The temperature rise of the permanent magnets is close to amaximum that can be allowed for NdFeB magnets. If a higher temperaturerise is expected, SmCo magnets could be used.


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Validation Cage induction machine

IM DCG~

~

Frequencyconverter

CurrentVoltagePower

Temperaturesensors

Grid

Torque


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Temperature-rise test

0

20

40

60

80

100

120

140

0 2 4 6 8

Time [h]

Te

mperaturerise[K]

Thermocouples in end-windings

Steady state when the temperature rise per half anhour is less than 1 K.


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Cooling-down curve at the end of test

Reference resistance 0.1235 at 22 C

Ambient temperature 29 C

Temperature rise about 87 C

0.161

0.162

0.163

0.164

0.165

0.166

0.167

0.168

0.169

0 20 40 60 80 100

Time [s]

Resistance[C]

100

102

104

106

108

110

112

114

116

118

120

0 20 40 60 80 100

Time [s ]

Temperature[C]

o

o0 0

235 C

235 C

R T

R T

Stator resistance is measured after the switch-off of the supply.Switch-off at time instant t= 0.


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Literature on thermal analysis of electrical machines

Lumped parameter thermal models

Hak J., Lsung eines Wrmequellen-Netzes mit Bercksichtigung der Khlstrme.Archiv fur Elecktrotechnik, Vol. 42, No. 3, pp. 138-154, 1956.

Mellor P.H.; Roberts D.; Turner D.R., Lumped parameter thermal model for electrical

machines of TEFC design, Proc. Inst. Elect. Eng., pt. B, vol.138, pp.205218, 1991.

Numerical thermal field analysis Armor A.F.; Chari M.V.K., Heat flow in the stator core of large turbine generators by

the method of three-dimensional finite elements, Part I: Analysis by scalar potential

formulation; Part II: Temperature distribution in the stator coreIEEE Trans. Power

App. Syst., vol. PAS-95, pp.16481656, 16571668, Sept./Oct. 1976.

Driesen J., Coupled electromagnetic-thermal problems in electrical energy

transducers. PhD Thesis, Faculty of Applied Sciences, K. U. Leuven, 2000.

Kolondzovski Z., Thermal and mechanical analyses of high-speed permanent-

magnet electrical machines, PhD Thesis, Aalto University, 2010, available at:

http://lib.tkk.fi/Diss/2010/isbn9789526032801/

lecture note electrical machine thermal design

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