On the layout of low temperature bushings for high ac voltage

Bushings for high ac voltages may cause a noteworthy heat inleak into cryostats due to dielectric losses and heat conduction and rising at least with the square o f the voltage. The overall heat inleak from the bushing insulator and other parts can be minimized for given radial dimensions by using the optimum length. Then the heat exchange with the outside at the warm flange region vanishes. To ensure a low heat input insulators with low product values of the dielectric loss factor and the heat conductivity and with a high dielectric strength should be used. A t least the prospects for Ioweririg the heat inleak by precooling with cold gas are hinted.

On the layout of low temperature bushings for high ac voltage J. G e r h o l d

Nomenclature

A

heat conducting cross section, m 2

Amin

minimum cross section of insulators, m 2

AN

NQx

sum heat flow in axial direction of N coupled heat conductors, W

individual cross section of one of N coupled heat conductors, m 2

NQA

sum heat input or output at the flange region of N coupled heat conductors, W

D

cryostat diameter, m

r

radius, m

E

electrical field strength, V m -1 (rms)

ra

outer radius of an insulator, m

f

frequency, s-1

ri

inner radius of an insulator, m

K

factor of integration

T

temperature, K

l

length of an insulator between ground flange and cold end, m

Tk To

temperature of the cold dip, K

/opt N

optimum length of an insulator, m

TN

number of coupled heat conductors

individual temperature of one of N coupled heat conductors, K

P

dielectric losses, W

TA

insulator temperature at the flange, K

P

pressure, Pa

TAN

individual temperature of one of N coupled heat conductors at the flange region, K

0

heat power, W

N Tzx

heat input into a cold dip of temperature Tk, W

mean temperature over N coupled heat conductors at the flange region, K

U

voltage, V (rms)

minimum heat input into a cold dip of temperature Tk, W

V x

volume, m

individual heat input into a cold dip from one of N coupled heat conductors, W

eo

km=

ax

QAN NQk

axial distance from the flange, m dielectric loss angle dielectric constant (8.85 x 10 -12 A s

V-X m-l)

heat flow in axial direction, W heat input or output of an insulator at the flange, W

ambient temperature (293 K)

er

permittivity

(ertg~)

dielectric loss factor heat conductivity, W m -1 K -1

individual heat input or output at the flange region of one of N coupled heat conductors, W

~N

sum heat input into a cold dip from N coupled heat conductors, W

individual heat conductivity of one of N coupled heat conductors, W m -1 K -1

Oad

admissible tensile strength, N m -2

To lead high ac voltages from ambient temperature into

cryogenic apparatus needs special bushings. In the case of cold gases or liquids to be used as basic insulating agents,

The author is from Anstalt for Tieftemperaturforschung A-8010 Graz, Steyrergasse 19, Austria. Paper received 17 December 1980.

these should not be stressed at higher temperatures by high

elecitrical fields due to the lowered dielectric strength, z

0011-2275/81/007428-05 $02.00 © 1981 IPC Business Press Ltd 426

CRYOGENICS . JULY 1981

Otherwise excessive radial dimensions of the cryostat must be envisaged. The use of a long insulating body with potential screens seems to be adequate to hold off dielectric stresses from warm gas regions. Fig. 1 shows such an arrangement. The bushing consists essentially of the insulating body inserted into the grounded flange which seals off the top of the cryostat. The warm end of the insulator may be surrounded by air for instance; no spark-over must occur between the central conductor and the flange. The cold end of the insulator may be embedded within a cryogenic liquid or cold gas; again no spark-over must occur at this end. Suitable shaped electrodes ha've been used successfully for this purpose ;2 on the other hand capacitive stress grading known from conventional high voltage bushings seems to be very suitable too. Bushings with capacitative stress grading have been used successfully for field tests of a superconducting cable. 3 The interconnecting link of the insulator shown in Fig. 1 which is surrounded by the cryogenic gas will be considered in particular. Potential screens joined to the conductor and the ground prevent the electrical stress from the gas, as may be seen from the electrical flux lines indicated in the figure. Unfortunately, all solid insulators exhibit dielectric losses which are small at cryogenic temperatures in general but

Conductor

Air

I

Inc. atinbody Insul g

El cal~_~ fluexlctri ines

noteworthy at higher temperatures. The equivalent heat flows in axial direction x to the ends of the insulator. At the cold end the heat must be taken off by the cold gas or liquid dip thereby charging the refrigerator. Sufficient heat transfer seems to be very important to prevent any boundary layer of low dielectric strength on the stressed insulator surface; otherwise flashover could occur. An additional heat input has to be taken into account due to the heat flow within the screens and the wall of the cryostar. The overall heat input caused by the insulator, the screens and the wall can be minimized by using a matching optimum length/opt as will be shown in the following section.

Principle of the minimizing procedure To demonstrate the minimizing procedure, a simple bushing arrangement will be discussed initially; a more realistic case will be considered later on. For the simple arrangement the following assumptions and conditions are prearranged. The screened part of the insulator with the length I will be treated as adiabatic with no radial heat transfer to outside. In accordance with this, the conductor must be assumed to be uncoupled from the insulator. An uncoupling by means of a thermal insulation seems to be useful in practice, since sudden temperature changes due to, eg, short circuits, will not affect insulators, thus protecting them from uncontrolled mechanical stresses. The heat flow within potential screens and within the wall of the cryostat will be neglected. The insulator cross section will be taken as a constant. Dielectric losses rising at the cold end of the insulator embedded into the dip will be neglected. Within any element of volume of the insulator, dielectric losses arise. dP

dV

~'~f°

.

Flange

-1

_ 2~feo(ertgS)E2

(1)

The loss factor (ertgS) depends on the material, the frequency and the temperature but not on the electrical field strength E given by geometrical conditions and by the voltage. The integration of (1) over the insulator cross section results in

ii

Cryostot

II

Gas I

> Screens

,i

dP = K27rfeo ( e r t g S ) U 2 dx

(2)

where K matches the integration procedure. For insulators with a hyperbolic radial field distribution E(r) -

U r 1 n(ra/r.~

(3)

a value of 2rr/ln (r~/r.~ entails for K. The heat flow within the insulator is given by Qx = - L4 dT ~--

Liquid -

-

(4)

where the heat conductivity X depends also on the temperature.

-

~_ ~

Electrodes

The heat balance on an element of the insulator shown in Fig. 2 results in

/

dP 0x + d0x = Qx + ~ - dx

Fig,1 Highvoltagebushingwithscreenedinsulator C R Y O G E N I C S . J U L Y 1981

(5)

From (4) and (5) follows the differential equation for the axial temperature distribution

427

x

used. But there are physical limits to this. The electrical stress within solids cannot be increased indefinitely. For any admissible field strength Eed, the matching radial dimensions of the insulator have to be evaluated, for instance from (3). For fields described by (3) the minimum cross section

r(x)

llllllll I

A rain = z'(ra2 - ri2)

r(x,dx)

x+dx

Fig. 2

Element of insulator with dielectric heat

~- b l - -

occurs with a ratio ra/ri of 2.2.4 Even smaller cross sections may be realized with condenser bushings. The field strength values admissible within solid insulators are below 10 7 V m -1 in general with regard to overvoltages. Small voids may lower this limit further since partial discharges should be avoided in long term service.

source

(6)

+~=0

To f'md out the minimum of the total heat input into the cold bath it seems to be useful to write the heat balance (S) as dOx

dP dT

-

dx dT dx

=

-xa

dP

A vanishing temperature gradient dT/dx at the flange needed for minimum total heat input can be guaranteed only by a matching optimum length/opt to be evaluated for the given cross section of the insulator. Theoretically, this optimum length may be found easily by integrating (6) at a first step to

xA

-÷

de=C

02)

(7) with zero for the integration constant. Further investigation may be effected by inserting a loss factor (ertg6) averaged over the length I which is :known only very roughly a priori.

Using this with (4) leads to

0xd0x

(11)

(8)

dr

The optimum length for a minimum total heat input into the dip

to be integrated by replacing dP/dx from (2). Then

lopt = ( K l r f e o ~ U 2

TA

Q~ - 0.~ = K 47rfeoU~ A fTk

X(ertg~ ) dT

(9)

which implies the assumption that the insulator takes the cold end temperature Tk at the distance l from the flange, which is not possible due mainly to the limited heat transfer into the dip. It may be seen from (9) immediately that the heat input into the dip, Qk, takes its minimum value for a vanishing heat exchange at the warm flange, Q,x.4 From this, dT/dx should be zero at that point. Exactly the same minimum condition is known for adiabatic current leads. The temperature of the insulator at the flange region Ta may be somewhat above the ambient temperature since noteworthy dielectric losses arise and effective cooling may be difficult to bring about. Since the losses diminish above the flange region due to the lowering field strength within the insulator, see Fig. 1, T~ may represent the highest temperature of the insulator.

The numerical values calculated from (13) using an estimated mean loss factor can be taken only for an order of magnitude. More exact values have to be calculated by an iterative method adapting the temperature distribution using the temperature dependent loss factors and heat conductivities.

r

z..,

,-,|

IK 4~feoU2A fT~ X(ertg6) dTJ 1/2

lira l

l

U '- Insulating T body Flange

(10)

It should be pointed out that this represents only a relative minimum proportional to x/A. This is due to the known fact that in normal electrotechniques the dielectric losses do not depend on the cross section of an insulator and therefore no equivalent exists to the Wiedemann-Franz-law which is valid for conductors. To maintain the total heat input from insulators as low as possible, small cross sections should be

428

"l I

TA =

(13)

turns out to be proportional to the radial dimensions of the insulator. Fig. 3 may illustrate an optimum temperature distribution of a bushing to ensure minimum total heat input.

From vanishing Qt, the minimum total heat input into the dip is found from

(2kmin

~ZXXdT} '/2 Tk

/®t

Fig. 3

x

0

Optimum axial temperature distribution

CRYOGENICS, JULY 1981

Minimum overall heat input from screened bushings and walls High voltage bushings inserted into a cryostat are more complicated. The potential screens shown in Fig. 1 for instance are in close thermal contact with the insulator. Transient voltages are relevant for their layout. Carbon black paper used in large amounts for common bushings at ambient temperature may not always match the requirements at low temperatures due to its high resistivity. Metallic screens have to be used in part, the ohmic resistance of which is connected with the thermal conductivity by the Wiedemann-Franz-law. Such screens can be optimized with regard to their thickness which turns out to be very small.4 In addition heat flows within the inner wall of the cryostat. This wall may also be in thermal contact with the bushing, brought about by the cryogenic gas filling up the gap between the insulator and the wall, see Fig. 1. Excessive heat input due to free convection phenomena should be hindered by means of barriers or by using very small gaps.4 The thickness of the inner wall depends on the diameter D and the gas pressure. The cross section can be roughly derived from 7r

Aw = ~ D:POaO

(14)

with Oad for the admissible mechanical strength. 4 Despite the complex heat flow phenomena occurring within such bushing arrangements, the minimum for the overall heat input caused by the insulator, the screens and the wall may be found with a few simplifications only. Since the thermal coupling between these elements cannot be perfect, various temperature distributions dTN/dX have to be expected. It will be assumed that the temperature variations over the radius do not exceed the limit for using averaged values of the loss factor and the heat conductivity of the insulator over the cross section. Furthermore, no heat exchange of the whole arrangement with the outside should take place over the length l with exception of the ends. At the cold end all of the N single elements have the temperature Tk giving up an overall heat

N0k =

X0kN

(15)

N

At the flange (x = 0) a mean temperature NTa wilt be assumed. In reality the flange connected with the,cryostat may hold the ambient temperature, whereas the insulator will exhibit a higher temperature due to the dielectric losses. A net radial heat flow will result from the insulator into the flange superimposed on any axial heat flow. The exact calculation of the heat flows at the flange region may be very complicated, s With these simplifications the axial heat flow equation (4) takes the extended form s

dTN

N(~× = - ZAN~-N N dx

(16)

The heat balance (5) can be taken over without modifications. Using the procedure as shown with (8) an extended equation

NO.Zx - NO.ZA = K 2nfeo Ua Z4N

XN(ertgS) dTN

N

Tk

CRYOGENICS. JULY 1981

(17)

results by which (9) has to be replaced. Thereby

N0a = X LN

(18)

N

represents the net heat flow of all coupled elements at the flange including axial as well as radial heat flow. For exact calculations of (17) the mean flange temperature U Ta has to be replaced by the N different temperatures, TaN. The overall heat input into the cold dip caused by the N elements again has a minimum value for a vanishing i(~aBut since now finite values for the single elements have to be taken into account, the single temperature gradients dTN/dX cannot be taken with zero at the flange. Consequently the evaluation of the matching optimum length seems to be much more difficult compared to the simple insulator discussed before.

Example To illustrate the expediency of minimzing the heat input caused by high ac voltage bushings the following example may be considered: Nominal voltage phase-ground 123 kV, frequency 50 s-t . temperature 5 - 300 K, insulating material pertinax 100 ® (registered trademark of Felten and Guilleaume Dielektra) with capacitative stress grading suitable for low temperature applications, inner screen radius 0.1055 m, outer screen radius 0.137 m, heat conducting cross section 0.033 m 2. Bushings of similar radial dimensions have been used successfully for a field test of a superconducting ac cable within a 60 kV power grid. 6 From the radial dimensions the factor K can be calculated resulting in dielectric losses per unit length of the insulator of 1010 (ertgS) Ua W m -1 . Using the temperature dependent loss factor 7 and the heat conductivity of pertinax 100 ® the integral X(ertg8) over T has been evaluated with 5.8 W m -1 . This results in a total minimum heat input into the 5 K region of 20 W. The matching optimum length may be taken from (13). Assuming a mean loss factor of 0.02, an order of 0.75 m is obtained for/opt. This length seems to be surprisingly short. Together with several carbon black paper screens embedded within the insulator of the bushing, an additional grounded screen made out of aluminium for instance may be suitable to control impulse voltages. The total heat input wilt be enlarged only slightly by such an aluminium screen of a few micron thickness, despite the fact that it may exhibit a considerable amount of heat flow at no load or low voltage operation where the dielectric losses are small, s However a noteworthy additional heat input may be caused by the cryostat wall. Assuming a pressure of 10 bar (10 6 N m -2) a cross section of 0.002 m 2 has to be envisaged for a stainless steel wall. For an optimum layout (NQa = 0) an overall heat input due to the bushing with screens and the wall of around 30 W results. The corresponding optimum length will be slightly enlarged as may be seen in a qualitative manner from (13).

Precooling by cold gas There exists an effective means to reduce the overall heat input. It is well known from current leads that the heat input can be lowered drastically by precooling them with cold gas. In a similar manner the wall o f a cryostat may be precooled with, for instance, gas taken off from the cold

429

dip and leaving the cryostat at the ground flange at nearly ambient temperature. By treating the wall as uncoupled from the insulator, a theoretical reduction of the heat input of the wall down to 30% of the heat input without precooling has been calculated. Thereby the expenditure for recooling the gas by an ideal refrigerator has been accounted,a For the insulator such a precooling provision seems to be not very effective. Since no cooling channels may be inserted into an insulator stressed by high electrical field strengths and the radial heat conductivity perpendicular to the plane of lamination must be taken to be low in general, a poor heat exchange between a precooling gas and an insulator charged with dielectric losses must be envisaged.

Conclusions Bushings for high ac voltages cause a noteworthy heat input into the cold region of the cryostat. A minimum heat input can be guaranteed by using an optimum length for which the net heat input into the cryostat at the warm flange

430

vanishes. Insulator materials used for low temperature bushings should exhibit a low dielectric loss factor and heat conductivity. Their dielectric strength should be high to ensure small cross sections. Potential screens needed to prevent dielectric stress from warm gas regions seem to be insignificant with regard to the heat input at high voltages. Precooling may be very effective to limit additional heat input from the cryostat wall, but seems to be less effective for the insulator due to poor heat exchange.

References 1 2 3

4

Gerhold, J. Cryogenics 19 (1979) 571 Mauser,S.F., Burghart,R.R., Fenger, M.L., Dakin, T.W., Meyerhoff, R.W.IEEE Trans PAS-95 (1976) 909 Klaudy,P. Oze 33(1980) 217 Gerhold, J. Elektrische Kryoeinf~lhrungen,Anstalt f ~ Tieftemperaturforschung,Graz, Austria (1980)

5

Sehauer,F. Cryogenics20(1980)472

6

Klaudy,P., Gerhold, J., Beck, A., Rohner, P. $eheffler, E., Ziemeck,G. First field trials of a superconductingpower cable within the power grid of a public utility, Applied Superconductivity Conference,Santa Fe, New Mexico (1980) Paper CA-12 Privatecommunicationfrom BrookhavenNational LaboratoryPower Transmission Project (1980)

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CRYOGENICS. JULY 1981