Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
,'02
l 5D-5776
ELECTROSTATIC SHIELDING OF NON
SEQUENTIAL DISC WINDINGS IN TRANSFORMERS
This application is a divisional of Canadian
Application Serial No. 348,735, filed March 28, 1980.
The initial impulse distribution of a transformer
winding grounded at one end is given by the well known
relation V-VO sinh a (1 - x)/sinh a, where X = percent
distance along the winding from the line end, a = (Cg/Cs)
where Cg = the total capacitance between the winding
and ground and Cs= the total series capacitance of the
winding.
The initial impulse distribution along the winding
provides a voltage stress at the impulsed end of the
coil greater than the stress caused by the steady state
voltage distribution within the winding. The ratio
of the impulse voltage stress to the operating voltage
stress is equal to a . The impulse (initial) stress can
be reduced by increasing Cg causing a to decrease. The
effective series capacitance in a disc wound transformer
winding is composed of the turn-to-turn capacitance
between the electrical conductors making up the winding
and the section-to-section capacitance between the
sections along the disc winding. Various attemps have
been employed to increase the effect of both the
turn-to-turn and section-to-section capacitance of the
winding upon the effective series capacitance of a disk
winding section. One method for increasing the use of
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5D-5776
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the turn-to-turn capacitance consists in the employment of
electrostatic shields between the turn conductors.
U.S. Patent No. 3,691,494 - dated September 12, 1972 to
Okuyama and U.S. Patent No. 4,042,900 - Hinton et al
dated August 16, 1977 teach various configurations of inter
section electrostatic shields for increasing the series
capacitance in disk windings. The aforementioned U.S.
Patents teach the insertion of shields in disk winding
arrangements that are continuously connected in mechanical
and electrical series. A second method of configuring
disk winding sections makes more effective use of the
section-to-section capacitance is taught in French Patent
No. 1,147,282. This shows that an increase in series
capacitance can be achieved by connecting the sections
nonsequentially. A third method which maximizes the use
of the turn-to-turn series capacitance in the winding
is to interlace the turns so that the electrically
sequential turns are not physically adjacent.
The purpose of this invention is to provide an electro-
static shielding arrangement for nonsequential disk windings
wherein the effective series capacitance of the winding
is the highest heretofore obtained in a disk winding
configuration.
In accordance with a broad aspect of the present
invention there is provided a disc coil winding arrangement
for a transformer comprising:
a plurality of turns of insulated electrical conductors
radially disposed around a winding form in a disc winding
configuration:
a plurality of winding sections of said radially
disposed conductors linearly arranged along said winding
form;
an electrostatic ring shield adjacent one of said
winding sections and electrically connected with another
of said winding sections;
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said winding sections being electrically inter-
connected in a nonsequential arrangement wherein a first
one of said winding sections is electrically connected
with a second one of said winding sections and a third
one of said winding section is electrically connected
with a fourth one of said winding sections, said first and
said fourth winding sections being electrically connected
together, said second section being electrically connected
to the electrostatic ring shield and said third winding
section being adapted for connection to a terminal of the
transformer.
at least one electrostatic shield within said first
winding section electrically connected with at least one
electrostatic shield in said second section; and
at least one electrostatic shield in the third
winding section being electrically connected with at least
one electrostatic shield in said fourth winding section.
FIGURE 1 is a side sectional view of a shielded
nonsequential winding arrangement with shields along
the outside of the winding according to the invention;
FIGURE 2 is a side sectional view of a shielded
nonsequential coil arrangement according to the invention
with shields along the inside of the winding;
FIGURE 3 is a side sectional view of a shielded
nonsequential winding according to the invention with
shields along both the inside and outside of the winding;
FIGURE 4 is a side sectional view O:e an alternative
arrangement of the embodiment of FIGURE l;
FIGURE 5 is a side sectional view of an alternative
arrangement of the embodiment of FIGURE 4;
FIGURE 6 is a graphic representation of the
normalized effective series capacitance for various
winding configurations;
FIGURE 7 is a graphic representation of the effective
series capacitance as a function of the number of shields
for various windings configurations, and
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FIGURE 8 is a graphic representation of the per cent
voltage variable as a function of distance along the coil
for various winding configurations.
The series capacitance of a disc winding section
pair wound as a continuous disk is given by the expression
Cl = C ( n + n-2) ak)
where n = the number of turns in the section pair, C
= the capacitance from a single turn to the equal
potential plane above or below the section, ak = the ratio
of Cw to Cx where C is the capacitance between turns of
a section. The increased series capacitance of a disk
winding section pair connected as nonsequential discs is given
by the relationship
15C2 = Cx ( + ~ ~) ak )
The series capacitance of disk winding section pairs
connected as continuous disks and containing internal
shields a8 taught by the aforemention U.S. Patents is
given by the expression
20C C (n + 0 8a (n2 _ 3 n+l~
for a section pair with each section containing a single
8hield.
The series capacitance of a section pair with each
section containing two shields is given by the expression
25C4 = C (n + ~ 8ak ~ n - lln+l ~
and the series capacitance of a sectioned pair with each
section containing three shields is given by the expression
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C5 = Cx ~ + .8 ak ~n2 _ 22n ~ 44. ~
The series capacitance of a section connected as an
interlaced disk winding is given by
C6 = Cx C 818n + ~n-4 ) ak )
It can be seen from the above expressions (C3 - C5)
that as the number of shields within each section are
increased the effective series capacitance of a continuous
disk containing shields also increases. It can also be
seen that the connection of a disk section as an inter-
laced disc winding provides a series capacitance (C6)
greater than the series capacitance connection (C5)
including as many as three shields. In order to determine
quantitative values for the various winding configurations,
examples one and two are given having the dimensions
listed in Table I.
The calculated series capacitance for the afore-
mentioned examples are given in TABLE III and it can
be seen that the interlaced winding series capacitance
(C6) is sub8tantially higher for both examples than
either the 8ection pair connected as a non~equential
diSC (C2~ or With the inclusion of internal shields
within a continuous diSk winding arrangement (C3 to C5).
The use of the interlaced winding configuration
i5 limited by the difficulties involved in winding large
cross section conductors into the interlaced configuration.
,
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TABLE I
Example 1 Example 2
R = average radius to center
av line of section 21. 34" 35. 00"
n = number of turns in
section pair 42 30
w = radial build of
conductor .115" .125~'
t = turn insulation
(both sides) . 072" .144"
h = axial height of
c conductor . 44011 . 350~
d = axial duct dimension . 225" . 22511
Rb = radial build of section 3. 92711 4 . 03511
C = turn to turn 1 10
w capacitance 5. 71X10- f 3. 73X10~ f
15 C = turn to epp -11 -10
x capacitance 9. 57X10 f 1. 89X10 f
ak CW/CX 5 . 96 1 . 97
TABLE 11
Serles
CaPacltance Example 1 Example 2
C1 7 . 14 CX 5 . 06 CX
20 C2 14 . 14 CX 10. 06 CX
C3 11 . 43 CX 6 . 44 CX
C4 15 . 33 CX 7 . 64 CX
C5 18 . 93 CX 8 . 71 CX
C6 68. 46 CX 21. 45 CX
25 C7 18.43 CX 13.04 CX
C8 31. 84 CX 15 . 83 CX
C9 40. 06 CX 18 . 42 CX
Increased series capacitance, attained by including a plurality
of electrostatic shields within transformer disk windlngs arranged
in a nonsequential connection and containinq a single shield as shown
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in FIGURE l, follows the expression:
C7 = C ~ ( 2 ) )
The series capacitance of a section pair connected in a
nonsequential arrangement and containing two shields
per section is given by the expression:
C8 = Cx ~ + .8 k ~ 2 ~ J
Quantitative values for the aforementioned nonsequential
winding sections containing three shields in one of the
sections is given by the expression:
9 Cx Cn3 + 8 ak ~ n ~ 22n + 44~5 ~
Quantitative values for the aforementioned nonsequential
winding section8 containing from one to three shields
for the examples I and II of TABLE I are given in TABLE
II. It can be ~een by comparision that the combination
of eleCtrostatiC shield8 within nonsequential di8c winding
8ections provides a serie9 capacitance in excess of 8eries
connected disk winding section having an equivalent
number of electrostatic shields.
The nonsequential winding arrangement of the invention
with one pair of electrostatic shields is shown in FIGURE
1 wherein the winding 10 consisting of a plurality of
turns of a conductor 11 containing an insulating coating
12 is radially arranged around a winding form 13 in at
least a first section 14 second section 15, third 16 and a
fourth section 17. Alt~ough four sections are shown in
the disk winding configuration depicted in FIGURE 1 this
is for purposes of example only since any number of
sections can be employed depending upon the transformer
design. The sections are interconnected in nonsequntial
winding arrangement wherein an electrostatic ring shield 18
t 1 6 ~ ~ 0 2
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is electrically connected by means of conductor l9 to
the second section and the first section is connected to the
fourth section by means of electrical conductor 20. To
complete the nonsequential arrangement the first section
is electrically connected to the second section by means
of conductor 22 and the third section is electrically
connected to the fourth section by connector conductor 23.
An electrostatic shield 24 in the first section is
electrically connected to a corresponding electrostatic
shield 24 in the second section by means of conductor 25.
An electrostatic shield 24 in the third section is
electrically connected by means of conductor 26 to a
corresponding electrostatic shield 24 located in the
fourth section. The arrangement of electrostatic shields
24 in the winding 10 of FIGURE 1 is such that the shields
are located between the outermost conductors of the section,
that is, at the end of the section furthest from the
winding form 13. Electrical connection with the winding is
made by means of electrical conductor 21. The series
capacitance value for this single shield configuration
is given by the mathematical expression for C7 given
earlier for the examples listed in Table I and has the
calculated capacitance values listed in Table II.
~ further embodiment of a nonsequential disk winding
containing electrostatic shields is shown in FIGURE 2
wherein the sections 14, 15, 16 and 17 are radially
arranged around winding form 13 in the same manner as
described for the embodiment of FIGURE 1 so that like
reference numerals will employed to designate similar
elements. In the embodiment now depicted, an electrostatic
shield 24 is located in the first section between the two
most inner turns or strands, that is, the end of the
section closest to the winding form. The shield in the
first section is electrically connected to the electrostatic
ring shield 18 by means of electrical conductor 27. A
pair of shields is inserted within the inner end of the
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5D-5776
_ g _
second and third sections and are electrically interconnected
by means of electrical conductor 28. The effective series
capacitance of the configuration depicted in FIGURE 2,
where the electrostatic shields are located at the inner
end of the winding sections is given also by the expression
for C7. The values for the parameters of examples l and 2
in Table I result in the calculated capacitances given in
Table II.
FIGURE 3 contains an embodiment of the nonsequential
winding arrangement 10 wherein a pair of electrostatic
shields 24 are employed in each winding section and
wherein one shield is situated in the outer end of the
8ection and one shield is situated in the inner end of
the 8ection. The embodiment of FIGURE 3 is similar to
the earlier embodiments of FIGURES 1 and 2 and similar
reference numbers will be used to depict similar elements.
The 8erie8 capacitance of the two 8hield relationship is
81ightly larger than that given by the expression for C8.
A 8implified non8equential winding arrangement
according to the invention employing a single pair of
8hields i8 8hown in FIGURE 4 wherein the non8equential
winding lO contains a shield 24 in the second section
and a 8hield 24 in the third 8ection electrically
connected together by mean8 of conductor 30. The effective
8erie8 capacitance value for this arrangement is given
by the following expreSsion:
n ~ 3 k C n ~)
Although embodiments containing nonsequential windings
whiCh include either a single shield or a pair of 8hields
within each 8ection are disclosed, it is within the
teachings of this invention to include as many shields
as required to achieve the particula~ value of series
capacitance desired for a particular transformer design.
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The relationship between the effective series capacitance
for various winding configurations as a function of the
number of winding turns per section is given in FIGURE 6.
A nonsequential disk winding arrangement similar to
FIGURE 5 containing four shields on the outside of each
winding section is shown at A. The series capacitance
for an interlaced winding arrangement is shown at B for
comparison purposes. It is to be noted that the normalized
effective series capacitance for nonsequential disk winding
arrangement A is very large for coils having a relatively
few number of turns per section. The effective series
capacitance for a nonsequential winding arrangement
similar to FIGURE 5 containing a single shield at the
outside of each winding section is shown at C. A non-
sequential winding arrangement having a single shield inthe outer end as shown in FIGURE 1 wherein one shield in
the first section is electrically connected to one shield
in the 8econd section, and one shield in the third section
is connected to a single shield in the fourth section,
is shown at D. The normalized series capacitance for a
nonsequential winding arrangement not containing any
electro~tatic shield is shown at E. The normalized
effective series capacitance of a continuous winding
arrangement containing one shield per section is shown at
F for comparision purposes.
The variation in the effective series capacitance as
a function of the number of shields employed per winding
section i~ shown in FIGURE 7. Curve A i8 the effective
8eries capacitance for a given section geometry as the
number of shields per section is increased from zero
(i.e. a plane continuous disk) to some integer value.
Curve B is the effective series capacitance for a given
section geometry wound as a nonsequential disk as the
number of shields per section is increa~ed from zero to
some integer value. The nonsequential configuration used
for obtaining the data in Table II is the embodiment shown
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in FIGURE 5.
The initial voltage distribution after an impulse
voltage is applied is shown for various winding configurations
in FIGURE 8. The greatest variation in per cent voltage
along the winding occurs at G which represents a continuous
winding with one shield per section. The next greatest
variation occurs at E which represents a nonsequential
winding arrangement without electrostatic shields. The
voltage variation for an interlaced winding arrangement is
shown at B to be less distorted than either a continuous
winding arrangement with a shield or a nonsequential
winding without electrostatic shields. A more nearly linear
distribution along the coil occurs at A for a nonsequential
winding arrangement containing internal shields in
accordance with the teachings of this invention.
Electrostatic shields within nonsequential disk
windings are disclosed for power transformer operation.
Thi8 i~ for purposes of example only since the inclusion
of electrostatic shields within nonsequential winding
arrangements finds application in any inductive device
where hlgh effective series capacitance i~ de~ired.
