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ELEKTR TA’MINOTI TIZIMI TARMOG‘INING REAKTIV
QUVVAT TOKLARINI ELEKTROMAGNIT QURILMALARI
NOSIMMETRIK JARAYONLARNI MODELLASHTIRISH
A.B.Abubakirov
Z.A.Mawlenova
U.O.Muxammeddinova
Nukus davlat texnika universiteti, Nukus,
Uzbekistan, aziz1306@mail.ru
https://doi.org/10.5281/zenodo.15632201
ARTICLE INFO
ABSTRACT
Qabul qilindi: 01-June 2025 yil
Ma’qullandi: 07-June 2025 yil
Nashr qilindi: 10-June 2025 yil
Ushbu maqolada gibrid energiya manbali elektr
ta’minoti tizimi tarmoqlarida reaktiv quvvat
toklarining elektromagnit qurilmalari uchun yuqori
aniqlikni
ta’minlovchi
birlamchi
nosimmetrik
jarayonlarni yig‘ilgan va tarqoq parametrli graf
modellari hamda analitik ifodalari yordamida
modellashtirish amalga oshirilgan.
KEY WORDS
Reaktiv quvvat, graf model,
modellashtirish,
elektromagnit
qurilma, elektr taminoti, analitik
ifoda
Asosiy qisim.
Elektr ta’minoti tarmoqlaridan (ETT) oqayotgan uch fazali birlamchi
toklarni ikkilamchi kuchlanish, signal ko‘rinishiga o‘zgartirishda signal o‘zgartirish tamoyili
mavjud. Jumladan NIUFTO‘Qlarda uchta oddiy o‘lchovli cho‘lg‘am yoki yassi o‘lchovli
cho‘lg‘am qo‘llanilganda birlamchi toklar, o‘zgartirish zanjiri yoki tuzilmasi uning geometrik
shakli va o‘lchamlari hamda qo‘llanilgan signal o‘zgartirish tamoyili fizik –texnik effekt
asosidagi quyidagi algoritmlar asosida tadqiq etiladi:
a)
ETTT reaktiv quvvat manbasi ulangan neytrali izolatsiyalangan uch fazali reaktiv
quvvat tok elektr tarmog‘ining yig‘ilgan parametrli bir fazali bitta sezgir elementli
qurilmasining ikkilamchi kuchlanishini hosil qilish graf modeli shakllantirilgan (1- rasm).
1-rasm. Neytrali izolatsiyalangan uch fazali tok o‘zgartkich qurilmasining
ikkilamchi kuchlanishini hosil qilishning yig‘ilgan parametrli graf modeli
ETTT reaktiv quvvat manbasi elektr tarmog‘ining yig‘ilgan parametrli bir fazali bitta
sezgir elementli NIUFTO‘Qning chiqish kuchlanishini hosil qilish graf modeli asosida
shakllantirilgan analitik ifoda (1) ko‘rinishida bo‘ladi [2, 9]:
U
chiq
= W
IU
chiq
(IU
chiq
)I = К
IF
μ
П
μ
К
Ф
μ
U
chiq
I = (4.44fw
2
w
1
/R
μ
)I
,
(1)
bu yerda:
W
IU
chiq
(IU
chiq
) = К
IF
μ
П
μ
К
Ф
μ
U
chiq
– birlamchi tok I ni ikkilamchi kuchlanish
U
chiq
ga o‘zgartirish bo‘lagi orqali uzatish funktsiyasi;
К
IF
μ
– birlamchi tokni m.yu.k.ga zanjirlar aro o‘zgartirish koeffitsienti [1];
К
Ф
μ
U
chiq
– magnit oqimini kuchlanishga zanjirlar-aro o‘zgartirish koeffitsienti;
I – elektr tarmog‘ining birlamchi toki;
f - elektr tarmog‘ining tok chastotasi;
w
2
,w
1
– NIUFTO‘Q birlamchi va ikkilamchi chulg‘amlarining o‘ramlari soni;
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П
𝜇
= 𝑅
𝜇
−
𝜌𝐿
𝐹
- signal o‘zgartirish bo‘lagi (magnit) qarshiligi;
ρ - magnit o‘zak materialining solishtirma qarshiligi;
L – magnit oqimining yo‘li uzunligi;
F – magnit o‘zak yuzasi geometrik o‘lchami.
b)
ETTT reaktiv quvvat manbasi ulangan neytrali izolatsiyalangan uch fazali reaktiv
quvvat tok elektr tarmog‘ining tarqoq parametrli uch fazali uchta sezgir elementli NIUFTO‘Q
ikkilamchi kuchlanishini hosil qilingan graf modeli shakllantirilgan (2- rasm).
2-rasm. Neytrali iziolyatsiyalangan uch fazali tok o‘zgartkich qurilmasining
ikkilamchi kuchlanishini hosil qilishning tarqoq parametrli graf modeli
Tarqoq parametrli uch fazali uchta sezgir elementli NIUFTO‘Qning graf modeli asosida
chiqish kuchlanishini shakllantirish uchun toklar orqali m.yu.k larni hosil qilingan analitik
ifoda (2) ko‘rinishlarida bo‘ladi [8, 9]:
{
𝐹
𝜇11
−𝐹
𝜇12
П
𝜇11
+
𝐹
𝜇11
−𝐹
𝜇21
П0
𝜇11
+
𝐹
𝜇11
−𝐹
𝜇13
П
𝜇13
= 𝐾
𝐼
𝐴
𝐹
𝜇11
𝐼
𝐴
;
𝐹
𝜇21
−𝐹
𝜇11
П0
𝜇11
+
𝐹
𝜇21
−𝐹
𝜇31
П
𝜇21
= 0;
𝐹
𝜇12
−𝐹
𝜇11
П
𝜇11
+
𝐹
𝜇12
−𝐹
𝜇22
П0
𝜇12
+
𝐹
𝜇12
−𝐹
𝜇13
П
𝜇12
= 𝐾
𝐼
𝐵
𝐹
𝜇12
𝐼
𝐵
𝐹
𝜇22
−𝐹
𝜇12
ПO
𝜇12
+
𝐹
𝜇22
−𝐹
𝜇31
П
𝜇22
= 0;
𝐹
𝜇13
−𝐹
𝜇12
П
𝜇12
+
𝐹
𝜇13
−𝐹
𝜇22
П0
𝜇13
+
𝐹
𝜇13
−𝐹
𝜇11
П
𝜇13
= 𝐾
𝐼
𝐶
𝐹
𝜇13
𝐼
𝐶
𝐹
𝜇23
−𝐹
𝜇13
П0
𝜇13
+
𝐹
𝜇28
−𝐹
𝜇13
П
𝜇23
= 0;
𝐹
𝜇31
−𝐹
𝜇21
П
𝜇21
+
𝐹
𝜇31
−𝐹
𝜇22
П
𝜇22
+
𝐹
𝜇31
−𝐹
𝜇23
П
𝜇23
= 0.
(2)
Bu yerda: Sezgir element o‘ramlari soniga bog‘liq koeffitsientlar (
𝑤
𝑎
,
𝑤
𝑏
, 𝑤
𝑐
) -
𝐾
𝐼
𝐴
𝐹
𝜇11
,
𝐾
𝐼
𝐵
𝐹
𝜇12
,
𝐾
𝐼
𝐶
𝐹
𝜇13
; birlamchi toklar-
𝐼
𝐴
,
𝐼
𝐵
,
𝐼
𝐶
; magnit o‘zak (sterjen) va havo oraliq magnit
parametrlari qarshiliklari -
П
𝑖𝑗
, П𝑂
𝜇𝑖𝑗
; qurilma magnit o‘zagidagi (sterjen) m.yu.k. lar -
𝐹
𝜇𝑖,𝑗
.
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Hosil qilingan yetti noma’lumli tenglamalar tizimidan, noma’lumlar bo‘lgan m.yu.k.lar
magnit o‘zgartirish bo‘lagida tarqalishi magnit parametrlarga mos ravishda aniqlanadi va
m.yu.k.larning qiymatlari uzatish funktsiyalari miqdorlarini belgilaydi.
Birlamchi elektr toklari - I
A
, I
B
, I
C
, m.yu.k. -
F
μ11
,
F
μ12
,
F
μ13
, magnit oqimlari -
Ф
𝜇11
,
Ф
𝜇12
,
Ф
𝜇13
va chiqish ikkilamchi kuchlanishlariga – U
1
, U
2
, U
3
, o‘zgartirish jarayonidagi
bog‘liqliklarning analitik ifodalari (3), (4) va (5) shakllantiriladi:
U
1
= К
Ф
µ11
U
1
Ф
μ11
;
(3)
Ф
μ11
=
F
μ11
−F
μ21
ПO
μ11
;
F
μ
11
= К
I
A
F
𝜇11
I
A
.
U
2
= К
Ф
µ12
U
2
Ф
𝜇12
;
(4)
Ф
μ12
=
F
μ12
−F
μ22
ПO
μ12
;
F
μ12
= К
I
B
F
𝜇12
I
B
.
U
3
= К
Ф
µ13
U
3
Ф
𝜇13
;
(5)
Ф
μ13
=
F
μ13
−F
μ23
ПO
μ13
;
F
μ13
= К
I
C
F
𝜇13
I
C
.
Yuqoridagi ifodadan foydalanib m.yu.k. lar hosil qilingan magnit oqimlari orqali
quyidagicha (6), (7) va (8) ikkilamchi kuchlanishlarini hosil qilish mumkin.
U
1
= К
Ф
μ11
U1
(
К
IAFμ11
ПO
μ11
I
A
−
F
μ21
ПO
μ11
) ;
(6)
U
2
= К
Ф
μ12
U
2
(
К
IAFμ12
ПO
μ12
I
B
−
F
μ22
ПO
μ12
) ;
(7)
U
3
= К
Ф
μ13
U
3
(
К
ICFμ13
ПO
μ13
I
C
−
F
μ23
ПO
μ13
) ;
(8)
bu yerda: “
К
Ф
μ11
Ua
,
К
Ф
μ12
U
b
,
К
Ф
μ13
U
c
- Ikkilamchi chiqish kuchlanish va magnit
oqimlarning o‘zaro bog‘liqlik koeffitsienti” [2-7].
с) GEMli neytrali izolatsiyalangan uch fazali elektr tarmog‘iga reaktiv quvvat manbasi
ulangan hajmsimon tarqoq parametrli uch fazali uchta sezgir elementli qurilmaning
ikkilamchi kuchlanishini hosil qiliuvchi graf modeli shakllantirilgan (3- rasm).
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3- rasm. Neytrali izolyatsiyalangan uch fazali tok o‘zgartkich qurilmasining
ikkilamchi kuchlanishini hosil qilishning hajmsimon tarqoq parametrli graf modeli
Hajmsimon tarqoq parametrli uch fazali uchta sezgir elementli NIUFTO‘Qning graf
modeli asosida chiqish kuchlanishini shakllantirish uchun toklar orqali m.yu.k larni hosil
qilingan analitik ifoda (9) ko‘rinishlarida bo‘ladi [6]:
{
𝐹
𝜇11
−𝐹
𝜇12
П
𝜇11
+
𝐹
𝜇11
−𝐹
𝜇121
П0
𝜇11
+
𝐹
𝜇11
−𝐹
𝜇13
П
𝜇13
+
𝐹
𝜇11
−𝐹
𝜇41
П1
𝜇11
= 𝐾
𝐼
𝐴
𝐹
𝜇111
𝐼
𝐴
;
𝐹
𝜇21
−𝐹
𝜇11
П0
𝜇11
+
𝐹
𝜇21
−𝐹
𝜇31
П
𝜇21
+
𝐹
𝜇21
−𝐹
𝜇51
П1
𝜇21
= 0;
𝐹
𝜇12
−𝐹
𝜇11
П
𝜇11
+
𝐹
𝜇12
−𝐹
𝜇22
П0
𝜇12
+
𝐹
𝜇12
−𝐹
𝜇13
П
𝜇12
+
𝐹
𝜇12
−𝐹
𝜇42
П1
𝜇12
= 𝐾
𝐼
𝐵
𝐹
𝜇12
𝐼
𝐵
;
𝐹
𝜇22
−𝐹
𝜇12
ПO
𝜇12
+
𝐹
𝜇22
−𝐹
𝜇31
П
𝜇22
+
𝐹
𝜇22
−𝐹
𝜇52
П1
𝜇22
= 0;
𝐹
𝜇13
−𝐹
𝜇12
П
𝜇12
+
𝐹
𝜇13
−𝐹
𝜇22
П0
𝜇13
+
𝐹
𝜇13
−𝐹
𝜇11
П
𝜇13
+
𝐹
𝜇13
−𝐹
𝜇43
П1
𝜇13
= 𝐾
𝐼
𝐶
𝐹
𝜇13
𝐼
𝐶
;
𝐹
𝜇23
−𝐹
𝜇13
П0
𝜇13
+
𝐹
𝜇28
−𝐹
𝜇13
П
𝜇23
+
𝐹
𝜇23
−𝐹
𝜇53
П1
𝜇23
= 0;
𝐹
𝜇31
−𝐹
𝜇21
П
𝜇21
+
𝐹
𝜇31
−𝐹
𝜇22
П
𝜇22
+
𝐹
𝜇31
−𝐹
𝜇23
П
𝜇23
+
𝐹
𝜇31
−𝐹
𝜇61
П1
𝜇31
= 0.
(9)
Birlamchi elektr toklari - I
A
, I
B
, I
C
, m.yu.k. -
F
μ11
,
F
μ12
,
F
μ13
, magnit oqimlari -
Ф
𝜇11
,
Ф
𝜇12
,
Ф
𝜇13
va chiqish ikkilamchi kuchlanishlariga – U
1
, U
2
, U
3
, o‘zgartirish jarayonidagi
bog‘liqliklarning analitik ifodalari (10), (11) va (12) shakllantiriladi:
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U
1
= К
Ф
µ11
U
1
Ф
μ11
;
(10)
Ф
μ11
=
F
μ11
−F
μ21
ПO
μ11
+
𝐹
𝜇11
−𝐹
𝜇41
П1
𝜇11
;
F
μ
11
= К
I
A
F
𝜇11
I
A
.
U
2
= К
Ф
µ12
U
2
Ф
𝜇12
;
(11)
Ф
μ12
=
F
μ12
−F
μ22
ПO
μ12
+
𝐹
𝜇12
−𝐹
𝜇42
П1
𝜇12
;
F
μ12
= К
I
B
F
𝜇12
I
B
.
U
3
= К
Ф
µ13
U
3
Ф
𝜇13
;
(12)
Ф
μ13
=
F
μ13
−F
μ23
ПO
μ13
+
𝐹
𝜇13
−𝐹
𝜇43
П1
𝜇13
;
F
μ13
= К
I
C
F
𝜇13
I
C
.
Yuqoridagi ifodadan foydalanib m.yu.k. lar hosil qilingan magnit oqimlari orqali
quyidagicha (13), (14) va (15) ikkilamchi kuchlanishlarini hosil qilish mumkin.
U
1
= К
Ф
μ11
U1
(
К
IAFμ11
ПO
μ11
I
A
−
F
μ21
ПO
μ11
−
F
μ41
П1
μ11
) ;
(13)
U
2
= К
Ф
μ12
U
2
(
К
IAFμ12
ПO
μ12
I
B
−
F
μ22
ПO
μ12
−
F
μ42
П1
μ12
) ;
(14)
U
3
= К
Ф
μ13
U
3
(
К
ICFμ13
ПO
μ13
I
C
−
F
μ23
ПO
μ13
−
F
μ43
П1
μ13
) ;
(15)
Xulosa.
Yuqoridagi formulalardan ko‘rinib turibdiki hosil qilingan magnit yurituvchi
kuchlar orqali va nosimmetrik holatda m.yu.k. hosil qilgan magnit maydonga kiritilgan sezgir
element (yassi plastinkaga o‘ralgan chulg‘am) sezish diapazonida ikkilamchi chiqish
kuchlanishini olishimiz mumkin. Agar nosimmetrik holat yuz bermasa ya’ni fazalar aro
simmetriya bo‘lsa bu holatda ikkilamchi chiqish kuchlanishi nolga teng bo‘ladi.
Foydalanilgan adabiyotlar:
1.
Siddikov I.X., Abubakirov A.B., Kurbaniyazov T.U., Bekimbetov M.N., Uch fazali tokning
nosimmetrikligini kuchlanishga o‘tkazuvchi elektromagnitli o‘zgartirgich // Patent RUz (UZ)
№ FAP 02157 U.S. 27.05. 2022 y.
2.
Abubakirov A.B. Analysis of cloud computing of digital monitoring of nonlinear values and
parameters of electric networks // Journal of Engineering and Technology (JET),
ISSN(P):2250-2394; ISSN(E): Applied Vol. 12, Issue 2, Dec 2022, 35–44.
3.
Azizjan Abubakirov, Timur Kurbaniyazov and Muratbay Bekimbetov. Analysis of three-
phase asymmetrical currents in the secondary voltage of signal change sensors in the
power supply system using graph models // E3S Web of Conferences 525, 03013 (2024),
GEOTECH-2024, -T. №1.
4.
Azizjan Abubakirov, Naurizbek Eshmuratov, Gulayim Esemuratova, and Muzaffar Nazarov.
Electromagnetic converter of reactive power and monitoring of high-voltage induction motors
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// E3S Web of Conferences 525, 03016 (2024), GEOTECH-2024, -T. №1.
5.
I.Kh.Siddikov, P.D.Chelyshkov, A.B.Abubakirov, N.M.Nazhimatdinov, R.Zh.Tanatarov.
Structure of control sensors of multi-phase reactive power currents in power supply systems
// Agribusiness, Environmental Engineering and Biotechnologies» IOP Conference Series:
Earth and Environmental Science 839 (5), 052045. pp. 1-9. doi:10.1088/1755-
1315/839/5/052045. (AGRITECH-V - 2021). Publication Year: 2021.
https://iopscience.iop.org/article/10.1088/1755-1315/839/5/052045/pdf
6.
A. Djalilov, O. Matchonov, A. Abubakirov, J. Abdunabiev, A. Saidov. System for measuring
and analysis of vibration in electric motors of irrigation facilities // Agricultural Engineering
and Green Infrastructure Solutions. IOP Conference Series: Earth and Environmental Science,
Volume 868, International Conference on Agricultural Engineering and Green Infrastructure
Solutions
(AEGIS
2021)
12th-14th
May
2021,
Tashkent,
Uzbekistan.
https://iopscience.iop.org/article/10.1088/1755-1315/868/1/012032
7.
I.Siddikov, A.B.Abubakirov, R.Seytimbetov, Sh.Kuatova, Yu.Lezhnina. Analysis of current
conversion primary sensors dynamic characteristics of a reactive power source with
renewable energy sources into secondary voltage // Part 1. E3S Web of Conferences 281,
09028. CATPID-2021. Publication Year: 2021.
8.
I.Kh.Siddikov,
M.A.Anarbaev,
A.A.Abdumalikov,
A.B.Abubakirov,
M.T.Maxsudov,
I.M.Xonturaev. «Modelling of transducers of nonsymmetrical signals of electrical nets» //
International Conference On Information Science And
9.
Communications Technologies Applications, Trends And Opportunities
10.
// Publication Year: 2019, Page(s): 1–6. http://WWW.ICISCT2019.Org
11.
I.X.Siddikov, A.B.Abubakirov, A.J.Allanazarova, R.M.Tanatarov, Sh.B.Kuatova //
Мodeling the secondary strengthening process and the sensor of multiphase primary currents
of reactive power of renewable electro energy supply // Solid State Technology, Volume: 63
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