Обмотки з полюсами, що перемикаються, для однофазних двошвидкісних конденсаторних асинхронних двигунів: Автореф. дис… канд. техн. наук / Діатілу Пед

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IAOe?IIAEUeIA AEAAeAI?ss IAOE OE?A?IE

?INOEOOO AEAEO?IAeEIAI?EE

Ia i?aaao ?oeiieno

IAAe?O EOIA Ae?AO?EO

(AIAIEA)

OAeE. 621.3.045.5:621.313.333

IAIIOEE C IIETHNAIE, UI IA?AIEEATHOUeNss, AeEss IAeIIOACIEO
AeAIOAEAeE?NIEO EIIAeAINAOI?IEO ANEIO?IIIEO AeAEAOI?A

Niaoe?aeuei?noue: 05.09.01 — aeaeo?e/i? iaoeie ? aia?aoe

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa oaoi?/ieo iaoe

Ee?a – 1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia a Iaeanueeiio aea?aeaaiiio iie?oaoi?/iiio oi?aa?neoao?,

Iiiinoa?noai inaioe Oe?a?ie.

Iaoeiaee ea??aiee: aeieoi? oaoi?/ieo iaoe, i?ioani?

Caoa?ia Ieoaeei Einoyioeiiae/,

Iaeanueeee aea?aeaaiee
iie?oaoi?/iee oi?aa?neoao,

i?ioani? eaoaae?e aeaeo?e/ieo
iaoei.

Io?oe?ei? iiiiaioe — aeieoi? oaoi?/ieo iaoe, i?ioani?

Aieoao Ieaenaiae? A?naiiae/,

Iaoeiiiaeueia aeaaeaiiy iaoe
Oe?a?ie, Iinoeooo

aeaeo?iaeeiai?ee, i?ia?aeiee
iaoeiaee ni?a?ia?oiee

a?aeae?eo aeaeo?iiaoai?/ieo
nenoai;

— eaiaeeaeao oaoii/ieo iaoe,

I?eia/aiei Aeieo?i Aieiaeeie?iae/

Oe?a?inueeee iaoeiai-aeine?aeiee ?inoeooo

aeaeo?iiiaooiaeo iaoei “AANOA”,

ia/aeueiee a?aeae?eo aeaeo?ii?eaiaeo.

I?iaiaeia onoaiiaa — Iaoe?iiaeueiee oaoi?/iee oi?aa?neoao Oe?a?ie

“Ee?anueeee iie?oaoi?/iee
?inoeooo”

Iiiinoa?noaa inaioe Oe?a?ie,
eaoaae?a aeaeo?iiaoai?ee

Caoeno a?aeaoaeaoueny “29” ethoiai 2000 ?. i 14 aiae. 00 oa.

ia can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae 26.187.03 a ?inoeoooi
aeaeo?i-aeeiaiiee Iaoeiiiaeueii? aeaaeaii? iaoe Oe?a?ie, ca aae?anith:
252680,

i. Ee?a-57, i?ini. Ia?aiiae, 56, oae. 446-91-15.

C aeena?oaoe??th iiaeia iciaeiieoenue o a?ae?ioaoe? Iinoeoooo
aeaeo?iaeeiaiiee Iaoeiiiaeueii? aeaaeaii? iaoe Oe?a?ie (252680,
Ee?a-57, i?ini. Ia?aiiae, 56).

Aaoi?aoa?ao ?ic?neaiee “21” n?/iy 2000 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee
Oeoei I. I.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. Iiaea?i?caoe?y aaaaoioaeaee?nieo
(aeaioaeaee?nieo) iaeii- ? aeaioacieo aneio?iiieo aeaeo?iaeaeaoi?a,
?icoe?aiiy ?o iiiaieeaoo?e c oei, uia i?aeaeueoe
eiieo?aioiini?iiiaei?noue aeaieo iaoei ia iniia? iie?ioaiiy niiaeea/eo
yeinoae, ? caaaeaiiyi iaiaeiicia/iei. Eiai iiaeia ae??ooaaoe o?eueee c
aeei?enoaiiyi iiaiai iieie?iiy AII, ui iathoue aenieo oaeaeeiae?th ?
cia/iee ianya iia?aoeaii? iai’yo?. Oea aeicaiey? cae?enithaaoe nenoaiiee
i?aeo?ae aei aaoiiaoecaoe?? i?iaeooaaiiy oaeeo iaoei, ui aeeth/a?
noai?aiiy neeaaeieo i?ia?aiii-oaoi?/ieo cania?a, ye? aeicaieythoue
cae?enithaaoe ae??oaiiy caaaeaiue aea/aiiy o?ce/ieo i?ioean?a, ui
?niothoue i?e ?iaio? aneio?iiieo eiiaeainaoi?ieo aeaeaoi?a (AEAe). Oea
aeicaiey? ioe?ithaaoe aeanoeaino? oa oa?aeoa?enoeee iaoeie a
aoaeue-yeiio ?aaeei? ?iaioe c aeinoaoiueith oi/i?noth.

Ia iniia? o?ceei-iaoaiaoe/ii? iiaeae? AAe ia eaoaae?? aeaeo?e/ieo
iaoei IAeIO (i. Iaeana) ?ic?iaeaia i?ia?aia “ IEAAe ” ia?aa??i/iiai
?ic?aooieo, ia iniia? yei? noai?ai? nenoaia oa iioei?caoe?y iaiioeiaeo
aeaieo ye iaeiioaeaee?nieo, oae ? aeaioaeaee?nieo eiiaeainaoi?ieo
aeaeo?iaeaeaoi?a.

Aei oeueiai /ano aeei?enoiaoaaeany ?ic?aooieiaa i?ia?aia aeey
iaeiioaeaee?nieo aeaeo?iaeaeaoi?a. Ia a?aei?io a?ae ia?, a i?ia?ai?,
i?aaenoaaeai?e a oe?e ?iaio?, ?ic?aoiaothoueny ? aeine?aeaeothoueny
aeaioaeaee?ni? AEAe. I?e oeueiio a?aoiao?oueny, ui ooo neeaae aa?iii?e
I?N ? ia iaia?aae caaeaiei, a aecia/a?oueny ca ?acoeueoaoaie
aa?iii?/iiai aiae?co I?N iaiioee.

?iaioa c? noai?aiiy iaoiaeeee aeai?eoi?a i?ia?aie aiae?co aeanoeainoae
aeaioaeaee?nieo aeaioacieo iaiioie AAe ? aeooaeueiith caaea/ath.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie.

Oaia aeena?oaoe?eii? ?iaioe “Iaiioee c iiethnaie, ui ia?aieeathoueny,
aeey iaeiioacieo aeaioaeaee?nieo eiiaeainaoi?ieo aneio?iiieo aeaeaoi?a”
aeeiioaaeanue a?aeiia?aeii aei ieai?a Iaeanueeiai aea?aeaaiiai
iie?oaoi?/iiai oi?aa?neoaoo, i?ia?aie AeEIO Oe?a?ie

Iaoa i caaea/i aeineiaeaeaiiy. Iaoith ?iaioe ? noai?aiiy
iaoaiaoe/ieo iiaeaeae, aeai?eoi?a ? i?ia?ai oi?ioaaiiy e aiae?co
aeaioaeaee?nieo (neiao?e/ieo) aeaioacieo iaiioie c iiethnaie, ui
ia?aieeathoueny, (AeAeIII) ci?iiiai no?oio c o?aooaaiiyi aeiaeaoeiaeo
aa?iii?e iaai?oiiai iiey, c?o/ieo aeey ?aae?caoe?? ia no/anieo AII.
Aacith aeey oeueiai iai?yieo aeine?aeaeaiue ia?aiee AEAe.

Iniiai? caaea/? aeena?oaoe?eii? ?iaioe:

1. ?ic?iaea aeai?eoio eiii’thoa?iiai (aaoiiaoeciaaiiai) oi?ioaaiiy
AeAeIII;

2. Noai?aiiy i?aenenoaie aaoiiaoeciaaiiai i?iaeooaaiiy AEAe c
aeei?enoaiiyi o ieo ?ic?iaeaieo AeAeIII;

3. Aeine?aeaeaiiy neeaaeo aa?iii?e AeAeIII ? aea?? e?ieo i?e
aeaioa?iaiio aeeiiaii?;

4. ?ica’ycaiiy aeey ni?iuaiiy oaoiieia?? aeaioiaeaiiy AeAeIII ca ?aooiie
iaeiioa?iaiai e iaeii-aeaioa?iaiai aeeiiaiiy;

5. Iioei?caoe?y iaiioeiaeo aeaieo AEAe c o?aooaaiiyi aeiia oaoi?/iiai
caaaeaiiy.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a:

1. ?ic?iaeaia ? cai?iiiiiaaia iaoiaeeea oi?ioaaiiy neiao?e/ieo
aeaioacieo aeaioaeaee?nieo III c iaia?ieie /eneaie ia? iiethn?a i?e
aeaioaeaee?ni?e eiia?iaoe??, ui aeicaieeea iaea?aeoaaoe iia?
i?ea?iaeuei? oa aenieiaoaeoeai? noaie III;

2. ?ic?iaeaii niin?a iiaoaeiae iaiioie ?c iiaith noaiith eiiooaoe??,
yeee aeicaieea iaea?aeaoe aeai?eoi aeey aaoiiaoecaoe?? i?ioeano
oi?ioaaiiy III;

3. ?ic?iaeaia iiaa noaia eiiooaoe?? aeey aeaioaeaee?nieo III, ui aea?
iiaeeea?noue iaea?aeaoe iaiioee c eiao?oe??ioaie ?iciiae?eo ii??aiyieie
c iaeiioaeaee?nieie iaiioeaie ia aeaio /eneao ia? iiethn?a;

4. ?ic?iaeai? aeai?eoi oa i?ia?aia aaoiiaoeciaaiiai oi?ioaaiiy
neiao?e/ieo ca ?iai/eie aa?iii?eaie aeaioacieo aeaioaeaee?nieo iaiioie,
?aae?ciaai? ca aeiiiiiaith i?ia?ai EXCEL;

5. ?ic?iaeai? aeai?eoi oa i?ia?aia iioei?caoe?? iaiioeiaeo aeaieo;

6. Ia aac? aeaieo aeai?eoi?a ?aae?ciaai? i?aenenoaie aaoiiaoeciaaiiai
aiae?co aeanoeainoae aeaiooacieo aeaioaeaee?nieo iaiioie.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. I?aeoe/ia oe?ii?noue ?iaioe
iieyaa?: a i?aeaeuaii? aoaeoeaiino? i?ioeano i?iaeooaaiiy ? i?enei?aiiy
?ic?iaee iaiao?aeieo noai III; a ?icoe?aii? ooieoe?iiaeueieo
aeanoeainoae ? ai?iaaaeaeaii? iiaeo eiino?oeoe?e iaoei; o aeei?enoaii?
i?aenenoaie aaoiiaoeciaaiiai aiae?co aeaioacieo aeaioaeaee?nieo iaiioie.

Iniaenoee aianie caeiaoaa/a. ?ic?iaeai? aeai?eoi ? i?ia?aie
ia?aa??i/iiai ?ic?aooieo aeey aeaioaeaee?nieo eiiaeainaoi?ieo
aneio?iiieo aeaeaoi?a; aeei?enoaii oa iiaea?i?ciaaii aeai?eoi
aaeoi?ii-oaaee/iiai niiniao aeey oi?ioaaiiy AeAeIII, c aeiiiiiaith
i?ia?ai EXCEL ?ic?iaeaia i?ia?aia aaoiiaoeciaaiiai oi?ioaaiiy,
neiao?e/iiai ii ?iai/ei aa?iii?eai; ia aac? a?aeiieo ? ?ic?iaeaieo a
aeai?e ?iaio? aeai?eoi?a ?aae?ciaai? i?aenenoaie aaoiiaoeciaaiiai
neioaco oa aiae?co aeanoeainoae aeaioaeaee?nieo, aeaioacieo iaiioie;
?ic?iaeaii i?ea?iaeueio iaoiaeeeo oi?ioaaiiy neiao?e/ieo
aeaioaeaee?nieo, aeaioacieo iaiioie c iiethnaie, ui ia?aieeathoueny, c
iaia?ieie /eneaie ia? iiethn?a i?e aeaioaeaee?ni?e eiia?iaoe??, ui
aeicaiey? iaea?aeoaaoe iia?, aenieiaoaeoeai? noaie iaiioie c iiethnaie,
ui ia?aieeathoueny.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. Iniiai? iieiaeaiiy ? ?acoeueoaoe
?iaioe aeiiia?aeaeeny e iaaiai?thaaeeny:

Ia iaoeiai-oaoi?/ieo eiioa?aioe?yo iieiaeeo aeine?aeiee?a oaeoeueoaoo
aaoiiaoecaoe?? oa aeaeo?eo?eaoe?? i?iieneiaino? IAeIO (Iaeana — 1994),
ia iaoeiaiio nai?ia?? iaoeiai? ?aaee IAI Oe?a?ie c eiiieaenieo i?iaeai
“Iaoeia? iniiae aeaeo?iaia?aaoeee” ia eaoaae?? aeaeo?e/ieo iaoei IAeIO
(aa?acaiue, 1999), ia iaoeiaiio nai?ia?? iaoeiai? ?aaee IAI Oe?a?ie c
eiiieaenieo i?iaeai “Iaoeia? iniiae aeaeo?iaia?aaoeee” ia ?icoe?aiiio
iaoeiaiio nai?ia?? a?aeae?eo aeaeo?iiaoai?/ieo nenoai ?inoeoooo
aeaeo?iaeeiai?ee IAI Oe?a?ie (eenoiiaaea, 1999.).

Ioae?eaoe??. Iniiaiee ci?no aeena?oaoe?? a?aeia?aaeaii a 6 ioae?eaoe?yo
o iaoeiaeo oaoiaeo aeaeaiiyo.

No?oeoo?a ? ianya ?iaioe: Aeena?oaoe?y neeaaea?oueny c? anooio, i’youeio
aeaa oaenoo, aeniiae?a ii aeaaao, aeniiaeo, nieneo e?oa?aoo?e, ui
aeeth/a? 147 iaeiaioaaiue, aeiaeaoe?a. ?iaioa a caaaeueiiio ianyc?
neeaaea? 199 noi??iie; i?noeoue 101 noi??ieo iniiaiiai oaenoo; 35
oaaeeoeue, 58 ?enoie?a ? 3 aeiaeaoee.

INIIAIEE CI?NO ?IAIOE

O anooi? iaa?oioiaaia aeooaeuei?noue oaie aeena?oaoe?eii? ?iaioe,
aecia/ai? iniiai? iieiaeaiiy, ye? aeiinyoueny ia caoeno, ? iaaaaeaiee
ei?ioeee iien ci?noo ?iaioe.

O ia?oiio ?icae?e? i?noyoueny iaeyae ? aiae?c e?oa?aoo?ieo aeaea?ae
(aeeth/ath/e iaoaioio e?oa?aoo?o) ii oai? aeena?oaoe??. I?iaiae?ciaaii
a?aeii? iaoiaee iiaoaeiae noai o?eoacieo III, a oaeiae iaeii- ?
aeaioacieo III. I?iaiae?ciaai? caaea/?, ?ic?aooiee ? iioei?caoe?y
iaeiioacieo aneio?iiieo aeaeaoi?a. Ca ?acoeueoaoaie aiae?co
noi?ioeueiaai? iaoa, iniiai? iai?yiee ? caaea/? aeaii? ?iaioe.

Ae?oaee ?icae?e i?enay/aiee iiaoaeia? aeaioaeaee?nieo aeaioacieo III.

Aeey iiaoaeiae AeAeIII canoiniaai? ?nioth/ee iaoiae ? niin?a iiaoaeiae
o?eoacieo III (aaeoi?ii-oaaee/iee niin?a i?e eiai a?aeiia?aeieo
ei?eaoaaiiyo).

Oi?ioaaiiy AeAeIII aeicaiey? iaea?aeoaaoe neiao?e/i? aeaioaci? III c
aoaeue-yeei ni?aa?aeiioaiiyi /enae iiethn?a i?e aeeiiaii? ianooiieo
oiia:

1. Iaiioeia? eiao?oe??ioe oac A ? A iathoue aooe ??ai? (KwA = KwA);

2. *enei aeoeaieo eioooeiaeo noi??i (AEN) o oacao A ? A ia? aooe
iaeiaeiaei (NA = NB);

3. I?inoi?iaee eoo c?ooaiiy i?ae a?nyie oac ia? aei??aithaaoe 90
aeaeo?e/iei a?aaeonai.

O?aoy oiiaa aeeiio?oueny caaaeaee i?e oe?eiio /ene? iac?a ia iiethn
? oaco (q). I?e ae??aiiio q ciaiaiiee ae??aiino? (d) ia ia? aooe e?aoiei
/eneo oac, oiaoi aeaii:

q = Z1/(2p.m) = Z1/(2p.2) = A(c/d) = (A.d+c)/d.

Aeoiaey/e c oeueiai aeaeii, ui /enea iac?a noaoi?a caeaaeaoue a?ae
/enae ia? iiethn?a iaiioee (p). O aeaiiio aeiaaeeo aiie iathoue aooe
e?aoi? /ioe?ueii (Z1/4 = oe./.). I?e iaio iaia?ieo /eneao ia?
iiethn?a iaiao?aeii, uia Z1/4 aoei /eneii oe?eei ? ia?iei, a a
ia?aeaeueieo a?eeao /enea eioooie iathoue aooe iaeiaeiaeie.

Oe? oiiae iathoue aeeiioaaoenue aeey eiaeiiai /enea iiethn?a.

Aaeoi?ii-oaaee/iee niin?a (AON) caniiaaiee ia ia?aoai?aii?
aaeoi?ieo ae?aa?ai iaciaeo A?N o oaaeeoe? AEN iaiioie.

Iiia?a AEN iaiioee iaiao?aeii caienoaaoe a iaaeao 180 a?aaeonieo oacieo
cii. C?ooaiiy i?ae iiia?aie AEN aiaeia?/ieo noiaioe?a A ? A neeaaea? 90
a?aaeon?a. *enei ai?eciioaeueieo ?yaee?a ?c iiceoeaieie iiia?aie AEN o
eiaei?e oac? aei??aith? p. Oaea ae e?euee?noue ?yaee?a AEN ? c
iaaaoeaieie ciaeaie.

I?eeeaae:

aeey Z1 = 24 ? 2p = 6. Ia/eneth?ii eoo c?ooaiiy i?ae aaeoi?aie A?N:

=360.p/Z1=360.3/24=45ae.a?aaeon?a.

?en. 2.1 Aaeoi?i? ae?aa?aie iaciaeo A?N aeey aeaioacii? iaiioee ?=3,
Z1=24

Iiia? a?ey aaeoi?a A?N — oea iiia? iaca aai AEN iaiioee, A, A, A’, A’ —
oacia? ciie.

sseui ?ic??caoe ae?aa?aio ii aa?oeeaeuei?e a?n?, ui ca?aa?oueny c
iiia?ii ia?oiai iaca, ? ?icai?iooe ia ieiueio, iaea?aeeii aaeoi?io
ae?aa?aio ia ieiuei?. Ia?ai?noeii i?ae ia?oo ae?oao iieiaeio ieinei?
ae?aa?aie aeey niieo/aiiy cii A c A’ ? A c A’. Oiaoi, ci?ieii iai?yiee
aaeoi??a A?N ia 180 a?aae.

Oeeo?e, ui ciaoiaeyoueny a iaei?e eieiioe?, ca?aathoueny ii oac? (+) aai
ciaoiaeyoueny a i?ioeoac? (-). Aeey /enea iiethn?a p = 3 oaaee/iee caien
AEN ia? ianooiiee aeaeyae:

Oaca A
Oaca A

1 2 3 3
4 5

9 10 11 11
12 –1

-5 –6 –7 -7
–8 –9

Iiaeia iaea?aeoaaoe iiia?e AEN aeey ?icoe?aii? ciie oace A ca
aeiiiiiaith oaeiai ae?aco:

Iiia?e AEN aeey ?icoe?aii? ciie oace A:

1- e ?yaeie: 1, 2,…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2-e ?yaeie: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picscalex1000100090000034a0100000200170000000000050000000902000000000400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,…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3-e ?yaeie: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,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,…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?-e: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000009000000320a20021802010000003100000109000000320a2002ff06010000003100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picscalex100010009000003cd0100000200170000000000050000000902000000000400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,…

[(E2 + 1) + (p – 1)
E1 ],

(2.1)

aea E1,
E2picscalex1000100090000035400000000001200000000000500000009020000000004
00000002010100050000000102ffffff00040000002e0118000500000031020100000005
0000000b0200000000050000000c02000220011200000026060f001a00ffffffff000010
000000c0ffffffc0ffffffe0000000c00100000b00000026060f000c004d617468547970
65000050000a00000026060f000a00ffffffff01000000000003000000000000626f6c00
ffffff00ffffff0000000000000000 — eiao?oe??ioe, aecia/ai? c ae?ac?a:

Canoiniao?ii neiao?oaaiiy /enae, ui ae?aaeathoue AEN uiaei
ai?eciioaeueii? a?n? oaaeeoe?, aeey ?iciiae?eo aeaioacii? iaiioee.

Aiaeia?/iei niiniaii iiaeia noi?ioaaoe oaaeeoe? AEN aeey aoaeue-yeiai
/enea iiethn?a o caaeaiiio /ene? iac?a.

Ia’?aeioth/e AEN aeey ??cieo /enae iiethn?a o caaaeueio oaaeeoeth
iaea?aeo?ii ?iciiae?ee aeaioaeaee?nieo III.

I?eeeaae:

2p1 : 2p2 = 6 : 4 o Z1/2 = 12,

oi?ioaaiiy iaiioee iieacaii a oaae.2.1.

Oaaeeoey 2.1

Oi?ioaaiiy III c 2?1 : 2?2 = 6:4

A 1 2 3

-5 -6 -7 -8

9 10 11 1 2 3 4

-7 -8 -9 -10

A 3 4 5 6

-7 -8 -9

11 12 -1 4 5 6 7

-10 -11 -12 -1

Aeey iaea?aeaiiy neiao?e/ii? aeaioacii? III a eiaei?e oac? aeae?ey?ii ii
12 AEN, ui caeiathoue ?aeaioe/ia iieiaeaiiy a?aeiinii a?aieoeue oacieo
cii (aeea. oaae. 2.1).

Oaaeeoey 2.2

Oi?ioaaiiy iaeii-aeaioa?iai? AeAeIII c 2?1: 2?2 = 6:4

Oaca 2?=6 2?=4 1 2 3 4 A
-5 -6-7 -8 11 1212 3 4 9 10 11 12 -5 -6-7-8 -9-10 3 4 5
6 A -7 -8 -9 -10 2 345 6 7 11 12 -1 -2 -8 -9-10-11-12 -1

2?1 : 2?2 = 6:4

picscalex820100090000035ecc000007003e00000000000400000003010800050000000
b0200000000050000000c020100010004000000030108000400000003010800050000000
b0200000000050000000c0201000100050000000c02e302fb08050000000b02000000000
400000006010100040000000601020007000000fc020000000000000000040000002d010
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60000002403090028012b0124012f0124018e012d018e012d012f012801330128012b012
4012b0124012f01040000002d010200040000002d0103000400000006010100040000000
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b038e015f0392011604920116048a015f038a0163038e015b038e015b0392015f0392010
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1004202e100a502ea00a502ea004202e6004602e6003e02e1003e02e1004202040000002
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40841022c0841022c083d0228083d02040000002d010200040000002d010300040000002
d010000040000002d01010016000000240309002808a8022c08a4022c084102240841022
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40000002d010000040000002d0101001600000024030900ac06a402b006a8022808a8022
808a002b006a002b406a402ac06a402ac06a802b006a802040000002d010200040000002
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c06a402b406a402b4064102b0064602b0063d02ac063d02ac064102040000002d0102000
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d01010016000000240309004506460240064102c8044102c8044a0240064a023c0646024
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d010000040000002d0101001600000024030900c404a702c804ab024006ab024006a302c
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d01030004000000060101000400000006010200040000002d010000040000002d0101001
6000000240309003a04420235043e02bd023e02bd02460235044602310442023a0442023
a043e0235043e02040000002d010200040000002d010300040000002d010000040000002
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102aa02b902aa02b902ae02bd02ae02040000002d010200040000002d010300040000002
d010000040000002d0101001600000024030900bd023e02b9024202b902aa02c102aa02c
1024202bd024602bd023e02b9023e02b9024202040000002d010200040000002d0103000
4000000060101000400000006010200040000002d010000040000002d010100100000002
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40000002d01030004000000060101000400000006010200040000002d010000040000002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40000002d010000040000002d0101001000000024030600e2007402e2006f0267006f026
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d0101001000000024030600ab067702ab0673024206730242067b02ab067b02ab0677020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4696d6573204e657720526f6d616e20437972000070040000002d010500040000002d010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400000000009001000000cc0000020254696d6573204e657720526f6d616e20437972000
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500040000002d010400040000002d010500040000002d010400040000002d01050004000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500040000002d010400040000002d010500040000002d010400040000002d01050004000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40000002d01050005000000090200000000040000002e011800040000000201010007000
00021050100200026027107040000002d01040004000000f0010500040000002d0104001
7000000fb02ceff1400000000009001000000cc0000020254696d6573204e657720526f6
d616e20437972000070040000002d010500040000002d010400040000002d01050004000
0002d010400040000002d010500040000002d01040004000000f001050017000000fb02c
eff1400000000009001000000cc0000020254696d6573204e657720526f6d616e2043797
200cc65040000002d01050005000000090200000000040000002e0118000400000002010
1000700000021050100200026027d07040000002d01040004000000f0010500040000002
d01040017000000fb02ceff1400000000009001000000cc0000020254696d6573204e657
720526f6d616e20437972000070040000002d010500040000002d010400040000002d010
500040000002d010400040000002d010500040000002d01040004000000f001050017000
000fb02ceff1400000000009001000000cc0000020254696d6573204e657720526f6d616
e2043797200cc65040000002d01050005000000090200000000040000002e01180004000
000020101000700000021050100200026028a07040000002d01040004000000f00105000
40000002d01040017000000fb02ceff1400000000009001000000cc0000020254696d657
3204e657720526f6d616e20437972000070040000002d010500040000002d01040004000
0002d010500040000002d010400040000002d010500040000002d01040004000000f0010
50017000000fb02ceff1400000000009001000000cc0000020254696d6573204e6577205
26f6d616e2043797200cc65040000002d01050005000000090200000000040000002e011
80004000000020101000700000021050100200026029607040000002d01040004000000f
0010500040000002d01040017000000fb02ceff1400000000009001000000cc000002025
4696d6573204e657720526f6d616e20437972000070040000002d010500040000002d010
400040000002d010500040000002d010400040000002d010500040000002d01040004000
000f001050017000000fb02ceff1400000000009001000000cc0000020254696d6573204
e657720526f6d616e2043797200cc65040000002d0105000500000009020000000004000
0002e0118000400000002010100070000002105010020002602a307040000002d0104000
4000000f0010500040000002d01040017000000fb02ceff1400000000009001000000cc0
000020254696d6573204e657720526f6d616e20437972000070040000002d01050004000
0002d010400040000002d010500040000002d010400040000002d010500040000002d010
40004000000f001050017000000fb02ceff1400000000009001000000cc0000020254696
d6573204e657720526f6d616e2043797200cc65040000002d01050005000000090200000
000040000002e0118000400000002010100070000002105010020002602af07040000002
d01040004000000f0010500040000002d01040017000000fb02ceff14000000000090010
00000cc0000020254696d6573204e657720526f6d616e20437972000070040000002d010
500040000002d010400040000002d010500040000002d010400040000002d01050004000
0002d01040004000000f001050017000000fb02ceff1400000000009001000000cc00000
20254696d6573204e657720526f6d616e2043797200cc65040000002d010500050000000
90200000000040000002e0118000400000002010100070000002105010020002602bc070
40000002d01040004000000f0010500040000002d01040017000000fb02ceff140000000
0009001000000cc0000020254696d6573204e657720526f6d616e2043797200007004000
0002d010500040000002d010400040000002d010500040000002d010400040000002d010
500040000002d01040004000000f001050017000000fb02ceff140000000000900100000
0cc0000020254696d6573204e657720526f6d616e2043797200cc65040000002d0105000
5000000090200000000040000002e0118000400000002010100070000002105010020002
602c807040000002d01040004000000f0010500040000002d01040017000000fb02ceff1
400000000009001000000cc0000020254696d6573204e657720526f6d616e20437972000
070040000002d010500040000002d010400040000002d010500040000002d01040004000
0002d010500040000002d01040004000000f001050017000000fb02ceff1400000000009
001000000cc0000020254696d6573204e657720526f6d616e2043797200cc65040000002
d01050005000000090200000000040000002e01180004000000020101000700000021050
10020002602d507040000002d01040004000000f0010500040000002d01040017000000f
b02ceff1400000000009001000000cc0000020254696d6573204e657720526f6d616e204
37972000070040000002d010500040000002d010400040000002d010500040000002d010
400040000002d010500040000002d01040004000000f001050017000000fb02ceff14000
00000009001000000cc0000020254696d6573204e657720526f6d616e2043797200cc650
40000002d01050005000000090200000000040000002e011800040000000201010007000
0002105010020002602e107040000002d01040004000000f0010500040000002d0104001
7000000fb02ceff1400000000009001000000cc0000020254696d6573204e657720526f6
d616e20437972000070040000002d010500040000002d010400040000002d01050004000
0002d010400040000002d010500040000002d01040004000000f001050017000000fb02c
eff1400000000009001000000cc0000020254696d6573204e657720526f6d616e2043797
200cc65040000002d01050005000000090200000000040000002e0118000400000002010
100070000002105010020002602ee07040000002d01040004000000f0010500040000002
d01040017000000fb02ceff1400000000009001000000cc0000020254696d6573204e657
720526f6d616e20437972000070040000002d010500040000002d010400040000002d010
500040000002d010400040000002d010500040000002d01040004000000f001050017000
000fb02ceff1400000000009001000000cc0000020254696d6573204e657720526f6d616
e2043797200cc65040000002d01050005000000090200000000040000002e01180004000
00002010100070000002105010020002602fa07040000002d01040004000000f00105000
40000002d01040017000000fb02ceff1400000000009001000000cc0000020254696d657
3204e657720526f6d616e20437972000070040000002d010500040000002d01040004000
0002d010500040000002d010400040000002d010500040000002d01040004000000f0010
50017000000fb02ceff1400000000009001000000cc0000020254696d6573204e6577205
26f6d616e2043797200cc65040000002d01050005000000090200000000040000002e011
80004000000020101000700000021050100ed0026020708040000002d01040004000000f
0010500040000002d01040017000000fb02ceff1400000000009001000000cc000002025
4696d6573204e657720526f6d616e20437972000070040000002d010500040000002d010
400040000002d010500040000002d010400040000002d010500040000002d01040004000
000f001050017000000fb02ceff1400000000009001000000cc0000020254696d6573204
e657720526f6d616e2043797200cc65040000002d0105000500000009020000000004000
0002e01180004000000020101000700000021050100200026022208040000002d0104000
4000000f0010500040000002d01040017000000fb02bdff1b00000000009001000000cc0
000020254696d6573204e657720526f6d616e20437972000070040000002d01050004000
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90200000000040000002e011800040000000201010007000000210501007e00310019040
40000002d01040004000000f0010500040000002d01040017000000fb02bdff1b0000000
0009001000000cc0000020254696d6573204e657720526f6d616e2043797200007004000
0002d010500040000002d010400040000002d010500040000002d010400040000002d010
500040000002d01040004000000f001050017000000fb02bdff1b0000000000900100000
0cc0000020254696d6573204e657720526f6d616e2043797200cc65040000002d0105000
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1003d04040000002d01040004000000f001050003000000000000000000

a

?en.2.2. a Noaia eiiooaoei? iaeii-aeaioa?iai? III c 2?1 : 2?2 = 6:4

Ia ?en. 2.3 ? 2.4 iaaaaeai? iia? noaie eiiooaoe?? c 10 aea?aeieie
e?ioeyie, ui aeicaieythoue ia?aeeth/aoe iaiioeo ci?iith e?eueeino?
ia?aeaeueieo a?eie o oacao ? i?e oeueiio iaea?aeoaaoe aenie?
eiao?oe??ioe ?iciiae?eo aeey p1 ? p2.

?en.2.3. Noaia eiiooaoe?? aeaioacii? aeaioaeaee?nii? iaiioee c
ni?aa?aeiioaiiyi iiethn?a 2?1:2?2 i?e ?iaio? ia 2?1

Noaia ia? 8 a?eie ia?aieeaiiy. O eiaei?e oac? eioooeia? a?oie
c’?aeiothoueny iine?aeiaii. No??eeaie ia noai? (?en. 2.3) iieacaiee
iai?yiie no?oio o oacao i?e aieeaii? iaiioee ia 2p1.

Aeey ?iaioe iaiioee ia 2p2 eiaeia oaca c’?aeio?oueny a aea? ia?aeaeuei?
a?eee. Iai?yiie no?oio aeey oeueiai aeiaaeeo cia?aaeaii ioieoe?ieie
no??eeaie (?en. 2.4).

I?e ci?i? /enea ia? iiethn?a o a?eeao ia?aieeaiiy ci?iththoueny iai?yiie
? oaca no?oio.

?en.2.4 Aieeaiiy iaiioee ia 2?2

O?ao?e ?icae?e i?enay/aiee oi?ioaaiith ? aiae?co AeAeIII ca aeiiiiiaith
i?ia?aie EXCEL.

EXCEL — iaeia ?c nenoai aeaeo?iiieo oaaeeoeue (i?ia?aia aeaeo?iiieo
oaaeeoeue). Aiia ? ?ioa?aeoeaiei na?aaeiaeuai, ui aeicaiey? i?aoethaaoe
c /eneaie ? oaenoaie, ?icoaoiaaieie a oaaeeoeyo.

Aaoiiaoecoaaiiy iiaoaeiae AeAeIII c? noaiith eiiooaoe?? U/UU ia iniia?
aeai?eoio, iaaaaeaiiai a ae?oaiio ?icae?e?, a?aeaoaa?oueny a 17 aoai?a.
Ao?aeieie aeaieie ooo ? /enea iac?a noaoi?a (Z1) ? ni?aa?aeiioaiiy /enae
ia? iiethn?a (p1:p2). Aeai?eoi caiiaiaiiy ina?aaee?a noiaioe?a oaaeeoe?
ianooiiee:

1-e noiaiaoeue — (Z1 )-iiia?e iac?a noaoi?a a?ae 1 aei Z1/2;

2-e noiaiaoeue — (A1)- iiia?e AEN, ui aoiaeyoue o ciio oace A, i?e
ia?oiio /ene? ia? iiethn?a, oiaoi i?e ?1= 3;

3-e noiaiaoeue — ( A1)- iiia?e AEN, ui aoiaeyoue o ciio oace A, i?e
ia?oiio /ene? ia? iiethn?a, oiaoi i?e ?1= 3;

4-e noiaiaoeue — (A2)- iiia?e AEN, ui aoiaeyoue o ciio oace A, i?e
ae?oaiio /ene? ia? iiethn?a, oiaoi i?e ?2 = 2;

5-e noiaiaoeue — (A2)- iiia?e AEN, ui aoiaeyoue o ciio oace A, i?e
ae?oaiio /ene? ia? iiethn?a, oiaoi i?e ?2 = 2;

Aeai? aeey caiiaiaiiy ina?aaee?a 2, 3, 4 ? 5-ai noiaioe?a
?ic?aoiaothoueny ca oi?ioeaie (2.1). I?e a?aenooiino? cia/aiiy a
ae?aiacii? oeeo? a?ae 1 aei Z1/2, ina?aaeeai i?enaith?oueny “ioeue”.

6-e noiaiaoeue — (Aia)- iiia?e AEN, iaeiaeia? ca aaniethoiei cia/aiiyi
aeey oac A i?e ia?oiio ? ae?oaiio /eneao ia? iiethn?a, oiaoi i?e ?1= 3
? ?2 = 2, ooai?ththoueny a ?acoeueoao? ii??aiyiiy cia/aiue ina?aaee?a
2-ai ? 4-ai noiaioe?a.

7-e noiaiaoeue -(Aia)- iiia?e AEN, iaeiaeia? ca aaniethoiei cia/aiiyi
aeey oac A i?e ia?oiio ? ae?oaiio /eneao ia? iiethn?a, oiaoi i?e ?1= 3
? ?2 = 2, ooai?ththoueny a ?acoeueoao? ii??aiyiiy cia/aiue ina?aaee?a
3-ai ? 5-ai noiaioe?a.

8-e noiaiaoeue — ( A )- iiia?e AEN, ui i?e oi?ioaaii? iaiioee aoaeooue
aeeth/ai? o oaco A a on?o aa??aioao, aecia/athoueny ca aeaieie
ina?aaee?a iaeiiiiaiieo ?yaee?a 6-ai ? 7-ai noiaioe?a. sseui a ina?aaeeo
6-ai noiaioey — cia/oua oeeo?a, a 7-ai -“ioeue”, oi a ina?aaeie 8-ai
noiaioey caieno?oueny cia/aiiy ina?aaeea 6-ai noiaioey ? iaaiaee ca
iaeiaeiaeo cia/aiue a ina?aaeeao 6-ai ? 7-ai noiaioe?a a ina?aaeie 8-ai
noiaioey caieno?oueny “ioeue”.

9-e noiaiaoeue -(A)- yaey? niaith iiia?e AEN, ui i?e oi?ioaaii? iaiioee
aoaeooue aeeth/ai? o oaco A a on?o aa??aioao.

Oea a?aeaoaa?oueny aiaeia?/ii ii??aiyiiyi cia/aiue iaeiaeiaeo ?yaee?a
ina?aaee?a 6-ai ? 7-ai noiaioe?a. O?eueee oaia? /eneia? cia/aiiy
ina?aaeeai 7-ai noiaioey i?enaiththoueny ca ioeueiaiai cia/aiiy a
ina?aaeeao 6-ai noiaioey.

10-e noiaiaoeue-(AeI)- aea? iiia?e AEN, ui aoaeooue aeiiiaithaaoe oace
A i A o ??cieo aa??aioao iaiioie. sseui a ina?aaeeao iaeiiiiaiieo
?yaee?a 6-ai ? 7-ai noiaioe?a iaeiaeia? oeeo?e, oi ina?aaeeai 10-ai
noiaioey i?enaiththoueny iiia?e ?yaeea.

Iai?eeeaae, a ina?aaeeao 1-ai ?yaeea 6-ai ? 7-ai noiaioe?a oeeo?e 1,1.
Ioaea, ina?aaeeo 10-ai noiaioey i?enaith?oueny oeeo?a 1.

sseui a ina?aaeeao 6-ai ?yaeea — 0;0 , oi ina?aaeeo 10-ai noiaioey
i?enaith?oueny oeeo?a 6; yeui a ina?aaeeao 7-ai ?yaeea — 7;7, oi a
ina?aaeeo 10-ai noiaioey — 7; yeui a ina?aaeeao 8-ai ?yaeea — 0;0, oi a
ina?aaeeo 10-ai noiaioey — 8 ? o.ae.

11-e noiaiaoeue-(OA)- iiia?e AEN oace A c 8-ai noiaioey c aeiaeaaaiiyi
iiia??a aca?iicaeaaeieo AEN (yeui aiie ?).

Ia?aa??ea iayaiino? aca?iicaeaaeieo iiia??a AEN i?iaiaeeoueny a
niaoe?aeuei?e oaaeeoe? i?ia?aie Excel. Aiia iaiao?aeia aeey iaea?aeaiiy
aa??aio?a neiao?e/ieo aeaioaeaee?nieo iaiioie ia iaio /eneao iiethn?a.

12-e noiaiaoeue-(OA)- iiia?e AEN oace A c 9-ai noiaioey c aeiaeaaaiiyi
iiia??a aca?iicaeaaeieo AEN.

13-e noiaiaoeue — (AeI)- iiia?e AEN 10-ai noiaioey ca aeiyoeii
aca?iicaeaaeieo iiia??a AEN.

14-e noiaiaoeue-(1-e aa?. A)- iiia?e AEN (ii aaniethoiiio cia/aiith)
oace A aeey ?1=3 ? ?2=2 ia?oiai aa??aioo iaiioee.

15-e noiaiaoeue-(1-e aa?. A)- iiia?e AEN (ii aaniethoiiio cia/aiith)
oace A aeey ?1=3 ? ?2=2 ia?oiai aa??aioo iaiioee.

16-e noiaiaoeue- (2-e aa?. A)- iiia?e AEN (ii aaniethoiiio cia/aiith)
oace A aeey ?1=3 ? ?2=2 ae?oaiai aa??aioo iaiioee.

17-e noiaiaoeue- (2-e aa?. A)- iiia?e AEN (ii aaniethoiiio cia/aiith)
oace A aeey ?1=3 ? ?2=2 ae?oaiai aa??aioo iaiioee.

I?ia?aia a EXCEL aaoiiaoeciaaiiai oi?ioaaiiy aeaioaeaee?nieo iaiioie
aeicaieeea iaea?aeoaaoe iia? neiao?e/i? aa??aioe aeaioaeaee?nieo
iaiioie.

Oaaeeoe? a EXCEL aeicaieythoue aiae?coaaoe oae? aeanoeaino? iaiioie:

— neiao??th iaiioee ii ?iai/?e ? aeiaeaoeiaeo aa?iii?eai aeey aeaio
/enae ia? iiethn?a;

— aieea e?ieo iaiioie ia aa?iii?/iee neeaae ? ia ni?aa?aeiioaiiy
?iaeoeoe?e o iia?o?yiiio caci?? aeaioaeaee?nii? iaiioee;

— ia?aa??eo a?aenooiino? ??cieoeaaeo A?N o ia?aeaeueieo a?eeao iaiioie o
noaiao c aeaiia ia?aeaeueieie a?eeaie.

I?ia?aia a EXCEL oaeiae aeeiio? ?ic?aooiee eiao?oe??io?a ?iciiae?eo,
iaiioeiaeo eiao?oe??io?a oac A, A i?e ia?aiiio e?ioe? iaiioee, aecia/a?
eooe c?ooaiiy inae oac ii a?aeiioaiith aei a?n? i?aeeiao, a oaeiae
iaiioeia? eiao?oe??ioe aeey i?yieo ? cai?ioiio aa?iii?e iaai?oiiai iiey.
I?e ?ic?iaoe? i?ia?aie aa?iii?/iiai aiae?co iaienai? niaoe?aeuei?
ei?enooaaeuei? ooieoe?? a iiaeoeueieo eenoao iiaith Visual Basic, ca
aeiiiiiaith yeeo anoaiiaeththoueny caeaaeiino?, ui aeicaieythoue aea?aoe
noaio iaiioee ? ?aeiiaiaeoaaoe e?ie, a oaeiae i?iaiaeeoe a?ao?/io
?ethno?aoe?th ?acoeueoao?a aa?iii?/iiai aiae?co aeaioaeaee?nii? iaiioee
aeey I?N -o aa?iii?e.

Oi?ioaaiiy ? aiae?c AeAeIII ca aeiiiiiaith i?ia?ai EXCEL aeicaieythoue
anaa?/ii i?iaiae?coaaoe aa??aioe iaiioie ? aea?aoe aa??aio, ni?eyoeeaee
ca ??aiai iaiioeiaeo eiao?oe??io?a ? ca aiie?ooaeith ?iai/eo ? -o
aa?iii?e I?N.

*aoaa?oee ?icae?e i?enay/aiee ieoaiiyi iioei?caoe?? iaiioeiaeo aeaieo
i?e i?iaeooaaii? aeaioacieo aeaioaeaee?nieo AAe.

I?e oeueiio aecia/athoueny /enea aeoe?a iaiioie (WA, WB) ? ?ii?noue
eiiaeainaoi?a (Cp) aeaioaeaee?niiai aneio?iiiiai eiiaeainaoi?iiai
aeaeaoia (AEAe). Oea cae?enith?oueny ia iniia? ae??oaiiy iioei?caoeieii?
caaea/? a ?ioa?aeoeaiiio ?aaeei? c IAII i?e aeaii??iiio a?aeia?aaeaii?
oaoi?ei-aeiiii?/ieo oa?aeoa?enoee AEAe o aeaeyae? e?i?e ??aiiai ??aiy ia
ae?ai? aeenieath.

Noai?aiiy aeaioacieo aeaioaeaee?nieo AEAe ?c iaiao?aeieie ?iai/eie
aeanoeainoyie iiaeeeaa i?e aeei?enoaii? aaiiao??? iaeiioaeaee?nieo iaoei
oeyoii i?iaeooaaiiy ?o ia aea? /anoioe iaa?oaiiy i?e iioei?caoe??
iaiioeiaeo aeaieo.

Caaea/a ae??oo?oueny ia iniia? i?eioeeio aeaeiiiiceoe??, oiaoi oeyoii
?icaeaee ?? ia aea? iacaeaaei? iaeia a?ae iaeii? ie?ai? caaea/?. Iaeia
c ieo — oea aecia/aiiy noaie aeaioaeaee?nii? iaiioee, ui caeaaeeoue a
iniiaiiio a?ae /enea iiethn?a ? iac?a, a ae?oaa — aecia/aiiy
iioeiaeueiiai /enea aeoe?a oac A ? A ? ?iiino? eiiaeainaoi?a i?e
caaeaieo oaoi?/ieo aeiiaao.

I?e oeueiio iniiaieie oaoi?/ieie aeiiaaie ?: e?aoiino? ioneiaiai (Ei) ?
iaeneiaeueiiai (Ei) iiiaio?a, a oaeiae ?ici?? iai?oae ia eiiaeainaoi??
i?e oieinoiio oiae? (Uei). sse e?eoa??e iioei?caoe?? i?eeiathoueny cos ?
?ici?? cai?ioiiai iiey, ui ia? aooe i?i?iaeueiei. Oeueiio a?aeiia?aea?
iaeneiaeueii iiaeeeaee EEAe. Ca ea?iaai? ci?ii? i?eeiathoueny /enea
aeoe?a o oacao A i A iaiioie. O yeino? ea?iaaieo ci?iieo ooo i?eeiyo? WA
? KT = WB/WA, a oaeiae cia/aiiy ?iiino? eiiaeainaoi?a (N?).

O aeaioaeaee?nieo AEAe caaea/a iioei?caoe?? ua a?eueo oneeaaeith?oueny ?
iiaea aooe aecia/aia ye aaaaoie?eoa??aeueia, oiio ui ? aea? /anoioe
iaa?oaiiy, ia eiaei?e c yeeo ia? aooe caaacia/aiee iaeneiaeueii
iiaeeeaee EEAe. Oiio aeiiae oi?ioeththoueny o oaeiio aeaeyae?: ciaeoe
WA, ET, N?, ui aiaeiiaiaeathoue e?eoa??yi

WA > 0, EO > 0, N? > 0 ,

aea
picscalex148010009000003b10000000200170000000000050000000902000000000400
000002010100050000000102ffffff00040000002e011800050000003102010000000500
00000b0200000000050000000c02a002e0011200000026060f001a00ffffffff00001000
0000c0ffffffb0ffffffa0010000500200000b00000026060f000c004d61746854797065
0000800010000000fb0240fe0000000000009001010000020002001053796d626f6c0002
040000002d01000009000000320aa0011e000100000068000c0117000000fb0220ff0000
000000009001000000cc0002001054696d6573204e657720526f6d616e2043797200ccdd
040000002d01010004000000f001000009000000320a10021e0101000000f00070000a00
000026060f000a00ffffffff01000000000010000000fb021000070000000000bc020000
00cc0102022253797374656d00cc040000002d01000004000000f0010100030000000000
000000000000000000000000000000000000 — EEAe ca aeaii? /anoioe iaa?oaiiy
(?en. 4.1, 4.2).

I?eioeeiiaei o oaeeo caaea/ao ? oa?aeoa? aeiionoeii? iaeano? (AeI), ai
a?i aecia/a? iaeiicia/i?noue ??oaiiy ? iiaeeea?noue eiai iaea?aeaiiy.
Aeoiaey/e c oeeo iiiyoue, ii?iae?caoe?y aeai?eoi?a neioaco e
iioei?caoe?? AEAe cia/ii oneeaaeith?oueny.

No/ani? IAII aeicaieythoue oni?oii ae??ooaaoe aeaio caaea/o a
?ioa?aeoeaiiio ?aaeei? i?e aeaii??iiio a?aeia?aaeaii?
oaoi?ei-aeiiii?/ieo oa?aeoa?enoee AEAe ia ae?ai? aeenieath o aeaeyae?
e?i?e ??aiiai ??aiy aeey aeaio ?aaeei?a.

Ne?ae cacia/eoe aeoaea aaaeeeaee aniaeo. IAII aeeiio? ?ic?aooiee o
aecia/aiiio aenia?eiaioaeueiiio iie? ci?ie ea?iaaieo ciiiieo ? ia?iaey?
?acoeueoaoe aenia?eiaio?a (oeeo ?ic?aooie?a), a eiino?oeoi?, aiae?coth/e
oe? aeai?, i?eeia? a?aeiia?aei? ??oaiiy.

O iaoiio aeiaaeeo aeey aeaioaeaee?nieo AEAe caaea/a ae??oo?oueny ia
iniia? i?eioeeio noia?iiceoe??, oiaoi oeyoii iaeeaaeaiiy aeaio
iacaeaaeieo ??oaiue iioei?caoe?eieo caaea/ aeey aeaio ??cieo /anoio
iaa?oaiiy. Ooai?th?oueny aea? caeaaeiino? WA (ET) ? ?o aeiionoei?
iaeano?, eiaeia c yeeo ooai?th?oueny ia?aoeiaiiyi e?i?e ??aiiai ??aiy
oa?aeoa?enoee: Ei, Ei ? Uei (?en. 4.3.).

Aeey ae??oaiiy caaea/? ia iniia? i?eioeeio noia?iiceoe??, nii/aoeo a
?ioa?aeoeaiiio ?aaeei? ae??oo?oueny ia?oa /anoeia caaea/? neioaco, oiaoi
caaea/a caaacia/aiiy iaii?iaei?o AeI ? ?o niieo/aiiy aeey aeaio /anoio
iaa?oaiiy ca iaeiaeiaeo cia/aiue eiao?oe??io?a o?ainoi?iaoe??. C
caaeaieie iaiaaeaiiyie c oaoi?/iiai caaaeaiiy aecia/athoueny caaaeuei?
cia/aiiy ea?iaaieo ciiiieo. Iio?i ciaoiaeeoueny caaaeueia aeiionoeia
iaeanoue ?c ia?aoeiaiiy AeI aeey aeaio /anoio iaa?oaiiy, ii ye?e
i?eeia?oueny iioeiaeueia ??oaiiy.

?en 4.1. E?i?? iaeiiai ??aiy e?eoa???a, iaiaaeaiiy oa aeiionoeii?
iaeano? iaiioeiaeo aeaieo i?e 2?=4 oa N?=30 ieO

?en. 4.2. E?i?? iaeiiai ??aiy e?eoa???a, iaiaaeaiiy oa aeiionoeii?
iaeano? iaiioeiaeo aeaieo i?e 2?=6 e N?=22 ieO

?en.4.3. E?i?? iaeiiai ??aiy e?eoa???a, iaiaaeaiiy oa aeiionoeii?
iaiioeiaeo aeaieo aeaioaeaee?niiai AEAe 6/4 , N?=30ieO i?e 2?=4 oa
N?=22ieO i?e 2?=6

??oaiiy iioei?caoe?eieo caaea/ ia iniia? aeaii??ii? ?ioa?aeoeaiino?
aeicaiey?:

— ciaioeoe ?ici??i?noue iioei?caoe?eii? caaea/? ? caanoe ?? aei
aa??aoe?? o?eueee ?ici??o ?iiino? eiiaeainaoi?a;

— iaoe iioei?caoe?eio nenoaio, ?iaa??aioio aei ci?ie oaoi?ei-aeiiii?/ieo
aeiia;

— i?iaeooaaoe aeaioaeaee?ni? AEAe c aeineoue aenieei EEAe ia iaio
/anoioao iaa?oaiiy.

I’yoee ?icaeie i?enay/aiee aenia?eiaioaeueiei aeine?aeaeaiiyi ?
aei?iaoaaiiyi iaeaoiiai c?acea aeaeo?iaeaeaoia, ni?iaeoiaaiiai ia aac?
na??eii? iaoeie AII-71-4. I?e oeueiio aeeiio?oueny:

— ia?aa??ea i?aoeacaeaoiino? aeaioaeaee?niiai AEAe;

— aeine?aeaeaiiy aieeao cia/aiiy ?iai/iai eiiaeainaoi?a ia
aeaeo?iiaai?oi? ? aeaeo?iiaoai?/i? aeanoeaino? iaoeie;

— ciyooy ?iai/eo oa?aeoa?enoee AEAe.

Aeine?aeaeaiiy neeaaeaeeny c e?eueeio aoai?a:

1. Aeei?enoiaoth/e ?ic?iaeai? i?ia?aie ia?aa??i/iiai ?ic?aooieo ?
iioei?caoe?? iaiioeiaeo aeaieo (aeea. ?icae?e 4.), a oaeiae
aaoiiaoeciaaii? iiaoaeiae AeAeIII (aeea. ?icae?e 3.) i?e i?iaeooaaii?
aeaioaeaee?nieo AEAe, iiia?aaeiuei aoee i?iaaaeai? aeaeo?iiaai?oi?
?ic?aooiee aa??aio?a AEAe i?e ?=2 ? ?=3 c ??cieie iaiiooaaeueieie
aeaieie ? ??cieie ?ici??aie eiiaeainaoi??a; cae?enithaaany iiooe
iioeiaeueiiai aa??aioa iaiioee. Ca io?eiaieie aeaieie aoa aeaioiaeaiee
iaeaoiee c?acie aeaioaeaee?niiai AEAe;

2. Aenia?eiaioaeuei? aeine?aeaeaiiy iaeaoiiai c?acea iieyaaee a
cae?eniaii?:

2.1. Aeine?aeo oieinoiai oiaeo, ui aeeiioaaany i?e iino?eiiio cia/aii?
eiiaeainaoi?a ? ci?iiiio cia/aii? aeeaey/i? iai?oae. Ca io?eiaieie
?acoeueoaoaie aoee iiaoaeiaai? caeaaeiino? Io, ?i, coso = f( Uo ), a
oaeiae ciaoiaeeeeny ao?aoe ?no + ?iao = f( Uo ). Ooo oa?aeoa? iaai?oiiai
iiey AEAe caeaaeaa a?ae aaee/eie eiiaeainaoi?a;

2.2. Aeine?aeaeaiiy ?iai/eo oa?aeoa?enoee aeaeaoia. Aeey oeueiai ye
iaaaioaaeaiiy aoei aeei?enoaia aeaeo?iiaai?oia aaeueii. Ca aeiiiiiaith
no?iaineiia aecia/aeany /anoioa iaa?oaiiy aeaeaoia. Ao?aoe ? EEAe
anoaiiaethaaeeny ca iaoiaeii iiae?eo ao?ao. Oa?aeoa?enoeee ci?iaeeny
i?e ??cieo iai?oaao ? i?e ??cieo ?iiinoyo ?iai/eo eiiaeainaoi??a.
Io?eiai? ?acoeueoaoe i?aeoaa?aeaeothoue ?c aeinoaoiueith oi/i?noth aeai?
?ic?aooie?a ? iaiao?aei? aeanoeaino? aeaioaeaee?niiai eiiaeainaoi?iiai
aeaeaoia.

O aeiaeaoeao i?noyoueny: A) ei?enooaaeuei? ooieoe?? a i?ia?aiao EXCEL;
A) aeo?aeiee eiae i?ia?aie ia?aa??i/iiai ?ic?aooieo AEAe oa iioei?caoe??
iaiioeiaeo aeaieo; A) i?eeeaaee o?aaiaioieo eeno?a ia iniia? i?ia?aie
EXCEL aeey aaoiiaoeciaaii? iiaoaeiae oa aiae?co aeanoeainoae noai
iaiioie AEAe.

AENIIAEE

1. Ia nueiaiaei? iaaecae/aeii aeooaeueieie ? caaea/? iiaea?i?caoe?? oa
?aiiioo iaeii-, aeaioaeaee?nieo aeaeo?iaeaeaoi?a. I?ioa aaoiiaoecaoe?y
iaoiaeee ?ic?aooieo aoaeoeaii? oaoi?ee iaiioie oa ?io? aeaoae?
a?aenooi?. Canoinoaaiiy aaeoi?ii-oaaee/iiai niiniao ?ic?iaeaiiai
aaoi?ii, aeey iiaoaeiae aeaioacieo, iaeii-aeaioa?iaeo III aeicaieeoue
cia/ii ni?inoeoe i?ioean ?ic?iaee oa aeaioiaeaiiy aeaioaeaee?nieo
iaiioie.

2. Cai?iiiiiaaia iaoiaeeea aoaeoeaiiai i?iaeoiiai oi?ioaaiiy neiao?e/ieo
aeaioacieo aeaioaeaee?nieo III aeicaiey? iiaoaeiao iaiioie c iaia?ieie
/eneaie ia? iiethn?a o aeaioaeaee?ni?e eiia?iaoe??.

3. ?ic?iaeaia iiaa noaia eiiooaoe?? aeey aeaioacieo III, ui aea?
iiaeeea?noue iaea?aeoaaoe iaiioee c aenieeie eiao?oe??ioaie ?iciiae?eo,
aeecueeeie aei aiaeia?/ieo eiao?oe??io?a iaeiioaeaee?nieo iaiioie ia
iaio /eneao ia? iiethn?a.

4. ?ic?iaeaiee i?ea?iaeueiee niin?a iiaoaeiae iaiioie ?c iiaith noaiith
eiiooaoe?? aeicaieea iiaoaeoaaoe aoaeoeaiee aeai?eoi aeey aaoiiaoecaoe??
i?ioeano oi?ioaaiiy III.

5. Iiaoaeiaai? ca aeiiiaith ?ic?iaeaieo niinia?a aeaioaeaee?ni?
iaiioee ca aaee/eiaie iaiioeiaeo eiao?oe??io?a ia?aaeuothoue ia 7-15 %
a?aeii? iaiioee.

6. ?ic?iaeaiee aeai?eoi aaoiiaoeciaaiiai oi?ioaaiiy neiao?e/ieo, ii
?iai/ei aa?iii?eai, aeaioacieo aeaioaeaee?nieo iaiioie, ?aae?ciaaiee ia
aac? i?ia?ai EXCEL, aeicaiey? ciaioeoe o?oaeiaeo?aoe ?ic?iaieea iaiioie.

7. Cai?iiiiiaaiee aeai?eoi ae??oaiiy iioeiecaoe?eii? caaea/? aeey
aecia/aiiy aeaieo AEAe iaiioeiaeo ? iaiioie c iiethnaie, ui
ia?aieeathoueny ia iniia? aeaii??ii? ?ioa?aeoeaiino?, yea aeicaiey?:

ciaioeoe ?ici??i?noue iioei?caoe?eii? caaea/? ? caanoe ?? aei aa??aoe??
eeoa cia/aiiy ?iiino? eiiaeainaoi?a; iaoe iioei?noe/io nenoaio,
?iaa??aioio aei ci?ie oaoi?ei-aeiiii?/ieo aeiia; i?iaeooaaoe
aeaioaeaee?ni? AEAe ?c aeineoue aenieeie EEAe ia iaio /anoioao
iaa?oaiiy.

8. Iieacaii iiaeeea?noue noai?aiiy aenieiaoaeoeaieo aeaioaeaee?nieo
AEAe c iaea?aeaiiyi iaiioie i?e niieo/aii? oac U/UU, i?e i?i?iaeueiiio
??ai? (ye i?aaeei, a?aenooiino?) ??cieoe? A?N o ia?aeaeueieo a?eeao.

9. Cae?eniaia i?iaeooaaiiy ?yaeo aa??aio?a noai aeaioacieo iaiioie c
iiethnaie, ui ia?aieeathoueny, i?aeoaa?aeaeo? aoaeoeai?noue ?ic?iaeaieo
niinia?a.

10. Io?eiai? iia? aa??aioe noai III c aenieeie cia/aiiyie iaiioeiaeo
eiao?oe??io?a iiaeooue aooe ?aeiiaiaeiaai? aeey aeei?enoaiiy a
eiiaeainaoi?ieo aeaeaoiao c iaoith ?icoe?aiiy ?o ooieoe?iiaeueieo
iiaeeeainoae.

11. ?acoeueoaoe aeine?aeaeaiue ? aei?iaoaaiue iaeaoiiai c?acea
aeaioaeaee?niiai AEAe i?aeoaa?aeeee iniiai? oai?aoe/i? iieiaeaiiy ?
?ic?aooieia? ni?aa?aeiioaiiy, ui iathoue iinoea o ?iaio?.

12. ?ic?iaeaia iiaith N? i?ia?aia ?ic?aooie?a AEAe aeei?enoiao?oueny a
iaa/aeueiiio i?ioean? ia eaoaae?? aeaeo?e/ieo iaoei IAeIO i?e ae??oaii?
caaaeaiue iaoeiai-aeine?aeiiai oa?aeoa?o, i?e eo?niaiio ? aeeieiiiiio
i?iaeooaaii? aeey ia?aa??i/iiai ?ic?aooieo i iioei?caoe?? iaiioeiaeo
aeaieo, ?ic?iaoe? iiaeo ? aiae?c? a?aeiieo noai ye iaeiioaeaee?nieo, oae
? aeaioaeaee?nieo iaiioie aneio?iiieo eiiaeainaoi?ieo aeaeo?iaeaeaoi?a.

Nienie iioae?eiaaieo i?aoeue ca oaiith aeena?oaoe??:

1. Aaeeeiaa E. ss., Aeeaoeeo Iaae?o Eoia. Iino?iaiea aeaoooaciuo
iiethni-ia?aeeth/aaiuo iaiioie.// Yeaeo?iiaoeiino?iaiea e
yeaeo?iiai?oaeiaaiea: ?ani. iaaeaaae. iao/.- oaoi. na.- Eeaa: Oaoieea.-
1995.- ?.47.- N. 83-86.

2. Aaeeeiaa E. ss., *aeeianeee A. I., Aeeaoeeo Iaae?o Eoia.
Iioeiecaoeey iaiioi/iuo aeaiiuo aeaoonei?inoiuo aneio?iiiuo
eiiaeainaoi?iuo aeaeaaoa-eae.// Aeaeo?iiaoeiiaoaeoaaiiy oa
aeaeo?iiaeaaeiaiiy: ?ani. iiaeaiae. iaoe. oaoi. ca.- Eeia: Oaoiiea.-
1997.- ?. 49.- N. 79-82.

3. Caoa?ia I. E., Aaeeeiaa E. ss., Aeeaoeeo Iaae?o Eoia.
Aaoiiaoece?iaai-iia oi?ie?iaaiea aeaoonei?inoiuo aeaoooaciuo iaiioie n
i?eiaiaieai Excel.// Aeaeo?iiaoeiiaoaeoaaiiy oa aeaeo?iiaeaaeiaiiy:
?ani. iiaeaiae. iaoe. oaoi. ca.- Eeia: Oaoiiea.- 1998.- ?. 50.- N.
87-91.

4. Aeeaoeeo Iaae?o Eoia. Aiaeec naienoa aeaoonei?inoiuo
aeaoooaciuo iaiioie n iiiiuueth Excel.// Aeaeo?iiaoeiiaoaeoaaiiy oa
aeaeo?iiaeaaeiaiiy: ?ani. iiaeaiae. iaoe. oaoi. ca.- Eeia: Oaoiiea.-
1998.- ?. 51.- N. 54-57.

5. Caoa?ia I. E., Aaeeeiaa E. ss., *aeeianeee A. I., Aeeaoeeo
Iaae?o Eoia. Iioeiecaoeeiiiua caaea/e i?e i?iaeoe?iaaiee aeaoonei?inoiuo
iaeiioaciuo aneio?iiiuo yeaeo?iaeaeaaoaeae.// Aeaeo?iiaoeiiaoaeoaaiiy oa
aeaeo?iiaeaaeiaiiy: ?ani. iiaeaiae. iaoe. oaoi. ca.- Eeia: Oaoiiea.-
1998.- ?. 51.-N. 30-33.

6. Aaeeeiaa E. ss., Aeeaoeeo Iaae?o Eoia. Aeaoonei?inoiua
aeaoooaciua ia-iioee n iiaie noaiie eiiiooaoeee.// Iao/. e I?ieca.
I?aeo. Ca.- Iaeanna: o?oaeu Iaeanneiai Iieeoaoie/aneiai Oieaa?neoaoa.-
1998.- Aui. 1(5), 1998.- N. 228-230.

Aiioaoei?

Iaae?o Eoia Ae?ao?eo. Iaiioee c iiethnaie, ui ia?aieeathoueny aeey
iaeiioacieo aeaioaeaee?nieo eiiaeainaoi?ieo aneio?iiieo aeaeaoi?a —
?oeiien.

Aeena?oaoe?y ia caeiaoooy a/aiiai nooiaiy eaiaeeaeaoa oaoi?/ieo iaoe ca
niaoe?aeuei?noth 05.09.01.- aeaeo?e/i? iaoeie ? aia?aoe. — ?inoeooo
aeaeo?iaeeiaiiee IAI Oe?a?ie, Ee?a, 1999.

Aeaia aeena?oaoe?eia ?iaioa ? oai?aoe/ieie oa aenia?eiaioaeueiei
aeine?aeaeaiiyi c iaoith iiaea?i?caoe?? aneio?iiieo eiiaeainaoi?ieo
aeaeaoi?a. ?icaeyaeathoueny: neioac ? oi?ioaaiiy noai aeaioacieo
aeaioaeaee?nieo iaiioie c iiethnaie, ui ia?aieeathoueny (AeAeIII);
aiae?c aeanoeainoae aeaieo iaiioie ca aeiiiiiaith i?ia?ai EXCEL; aiae?c
oei?a iioei?caoe?eieo caaaeaiue i?e i?iaeooaaii? iaeii- ? aeaioacieo
aeaioaeaee?nieo aeaeo?iaeaeaoi?a. ?ic?iaeai? i aei?iaoaai? iiaa noaia
eiiooaoe?? aeey aeaioacieo III ? niin?a iiaoaeiae iaiioie ca iiaith
noaiith eiiooaoe??. ?ic?iaeai? iiaith NI i?ia?aia ? i?aei?ia?aie iiaith
VISUAL BASIC aeey ae??oaiiy caaaeaiue iaoeiaiai ? aeine?aeieoeueeiai
oa?aeoa?o, ia?aa??i/iiai ?ic?aooieo, iioei?caoe?? iaiioeiaeo aeaieo ?
aiae?co aeanoeainoae iaiioie i?e i?iaeooaaii? iiaeo ? a?aeiieo noai ye
iaeiioaeaeeinieo, oae ? aeaioaeaee?nieo iaiioie AEAe.

Eeth/ia? neiaa: aeaioaeaee?ni?, aeaioaci?, iaiioee c iiethnaie, ui
ia?aieeathoueny, aeoeai? eioooeia? noi??i?, /enei ia? iiethn?a,
e?eoa?i?, iaiaaeaiiy, ea?iaai? ci?ii?, aeiionoei? iaeano?, noaia
eiiooaoe??, aiaeic, iioeiicaoeiy.

Iaae?o Eoia Aeeaoeeo. Iiethniia?aeeth/aaiua iaiioee aeey iaeiioaciuo
aeaoonei?inoiuo eiiaeainaoi?iuo aneio?iiiuo aeaeaaoaeae. — ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/?iie noaiaie eaiaeeaeaoa oaoie/aneeo
iaoe ii niaoeeaeueiinoe 05.09.01 — yeaeo?e/aneea iaoeiu e aiia?aou —
Einoeooo yeaeo?iaeeiaieee IAI Oe?aeiu, Eeaa, 1999.

Ianoiyuay aeenna?oaoeeiiay ?aaioa i?aaenoaaeyao niaie
oai?aoe/aneea, yenia?eiaioaeueiua enneaaeiaaiey a oeaeyo iiaea?iecaoeee
aneio?iiiuo eiiaeainaoi?iuo aeaeaaoaeae. ?anniao?eaathony: aiaeec e
oi?ie?iaaiea noai aeaoooaciuo aeaoonei?inoiuo iiethniia?aeeth/aaiuo
iaiioie (AeAeIII); aiaeec naienoa aeaiiuo iaiioie n iiiiuueth i?ia?aii
EXCEL; aiaeec oeiia iioeiecaoeeiiiuo caaea/ i?e i?iaeoe?iaaiee iaeii e
aeaoooaciuo aeaoonei?inoiuo yeaeo?iaeaeaaoaeae. ?ac?aaioaiu e
ai?iae?iaaiu iiaay noaia eiiiooaoeee aeey aeaoooaciuo III e niinia
iino?iaiey iaiioie n iiaie noaiie eiiiooaoeee. ?ac?aaioaiu ia ycuea NE
i?ia?aiia e iiaei?ia?aiiu ia ycuea VISUAL BASIC aeey ?aoaiey caaea/
iao/iiai e enneaaeiaaoaeueneiai oa?aeoa?a, iiaa?i/iiai ?an/aoa,
iioeiecaoeee iaiioi/iuo aeaiiuo e aiaeeca naienoa iaiioie i?e
i?iaeoe?iaaiee iiauo e ecaanoiuo noai eae iaeiinei?inoiuo, oae e
aeaoonei?inoiuo iaiioie AEAe.

Eeth/aaua neiaa: aeaoonei?inoiua, aeaoooaciua,
iiethniia?aeeth/aaiua iaiioee, aeoeaiua eaoooa/iua noi?iiu, /enei ia?
iiethnia, e?eoa?ee, ia?aie/aiey, oi?aaeyaiua ia?aiaiiua, aeiionoeiua
iaeanoe, noaia eiiiooaoeee, aiaeec, iioeiecaoeey.

Pedro Kuma Diatilo. Pole-changing windings of single-phase,
double-speed condenser-type asynchronous induction motors.- Manuscript.

Thesis for the doctor’s degree by speciality 05.09.01.- Electrical
machines and apparatus.- The Institute of electrodynamics of National
Academy of Sciences of Ukraine, Kyiv, 1999.

The present thesis represents theoretical, experimental researches
with the purposes of modernization of asynchronous condenser-type
motors. Considered are: analysis and formation of two-phase double-speed
pole-changing windings (TDPCW) circuits (schemes); analysis of
properties of datas of windings with the help of the program EXCEL;
analysis of types of optimizations of problems at designing one and
two-phase double-speed induction motors. The new switching chart for
two-phase PCW and way of build-up of windings with a new switching chart
designed and approved.

The techniques of designing on single-speed and double-speed
condenser-type induction motors with the usage of computer programing
language C «“IEAAe”» are created.

The types of optimizations problems are stated at designing one and
two-phase, double-speed induction motors. The theoretical fundamentals
and program of optimization of windings of datas of examined machines,
are set up.

On using Visual Basic language, algorithm and program of formation
of the automized symmetrics on working harmonics of two-phase,
double-speed windings, was designed, implemented with the help of the
program Excel and a subsystem, permitting to carry out: — analysis of a
symmetry of a winding on working and nius () harmonics for two pairs of
poles; — analysis of influence of step of spools on the harmonical
composition MMF and on a relation of induction in an air gap of a
double-speed winding; — check of absence in the difference of EMF at
switching a winding with a connecting circuit of phases in two parallel
branches.

Designed with the program language C program and subsystems on the
language Visual Basic for problem solving of scientific and exploratory
character, proven calculation, optimization of windings of datas and
analysis of properties of windings at designing the new and known
circuits (schemes) both single-speed, and double-speed windings ACM.
Their application is effective at a stage of formation and choice of
variants two-phase PCW depending on the requirements shown to designed
condenser-type motor.

This thesis (work) can be utilised also in an electric machine
industry at development of new types of machines and in the educational
process, in course and degree designing at preparation of the engineers
for electromechanics.

Keywords: double-speed, two-phase, pole-changing of a winding,
active bobbin sides, number pair of poles, criterion, limitations
controlled variables, valid areas, switching chart, analysis, formation,
optimization.

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