CC BY
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Section 13. Technical sciences
Karimov Rakhmatillo Choriyevich, Tashkent state technical university, Power faculty, «Power supply» chair, senior teacher E-mail: [email protected]
Research of the stabilizer of current taking into account the highest harmonicas in systems of power supply
Abstract: the method ofslowly changing amplitudes investigated the ferrorezonansny stabilizer of current allowing to support steadily current in loading at change of size both entrance tension, and loading resistance. Thus in calculations the highest harmonicas containing in the power supply and in the core of a ferromagnetic element are considered.
Keywords: autonomous inverter, converters of frequency, ferrorezonansny stabilizer of current, nonlinear inductance, the highest harmonicas, ferromagnetic element.
The increasing distribution of system of invariable current, the dual standard system of invariable tension, are promoted by need for it for such areas as an electrothermie, the electric drive, electrotechnology, pulse power industry, computer facilities, system of power supply [1; 2].
For example, use of this system in galvanotechnics gives the chance to increase labor productivity and quality of products, to reduce its prime cost in comparison with system of invariable tension. In this regard there is a problem of creation of more perfect, highly reliable, economic and universal electrotechnical devices transforming system of invariable tension to system of invariable current. Realization of system of invariable current is possible by means of various technical devices, for example, of the ferrorezonansny stabilizer of current.
With a wide circulation of independent inverters and converters of frequency in power supply systems of various
objects where the system of invariable current is also necessary, there was actual a creation of autonomous sources of current. Such sources find application in systems of railway automatic equipment, power supply of cable communication lines, in measuring and computer facilities, etc. Collaboration of the independent inverter and ferrorezonansny stabilizer of current allows to create an autonomous source of current, thus the rectangular shape of a curve of output tension of the inverter causes a number of features of the mode which should be considered at calculation of the ferrorezonansny stabilizer of current [3].
On the basis of the stated we investigate the ferrore-zonansny stabilizer of current which equivalent circuit is given in fig.1. taking into account the highest harmonicas of the power supply and induction of the core of a ferromagnetic element for R =0 case.
Fig. 1. Schematic diagram of the ferrorezonansny stabilizer of current
For simplification of the analysis of a chain we will accept assumptions:
- we approximate a curve of magnetization of a nonlinear element in the form of i = КФ3;
- we neglect streams of dispersion and we don’t consider loss in capacity;
- we will present a nonlinear ferromagnetic element the equivalent circuit consisting of nonlinear inductance connected in parallel and constant active conductivity which considers losses in the core.
For the considered chain ratios are fair:
43 I 4S II dw + , dt (1)
u=C! t2dt, (2)
+ i2, (3)
+ K V, dt (4)
• _ C d2T !l Cl dt3 '
here, i1 and i2 — the current proceeding on windings of linear inductance and via the C2 condenser.
Taking into account (4) equation (l) will assume an air: TT r Th3T r rThT3 d2T dT , .
U = LC + L(,K~dT + L°gdr + Тй ‘ (5)
dt dt dt dt
Entering replacement of variables:
„ T v U
r=at; X =—; Y = —,
T U
and having set up them in the equation (5), we will receive:
л, d3X n d2X dX3 dX
Y =—- + в—^ +------+ a—,
dr dr dr dr
here designations are accepted:
144
Research of the stabilizer of current taking into account the highest harmonicas in systems of power supply
g1Cl K '
; a = > U6 = Lfiia)^6; V 6 =
Cjffl g L0C1
Integration of the equation (5) brings to:
\Ydz= dX- + P — + X3 +aX + A. (6)
J dz2 dz (6)
We look for the decision (6):
X = Xlm SinT+ X3m Sin3T. (7)
If the feeding tension has a rectangular shape,
Y = — Ym sin(T+& + Z4 Ym sin(3т+ф). (8)
n 3n 4 '
As Х (t) — slowly changing function of time, under the terms of a method of slowly changing amplitudes we can write down:
^ dX dX d2X
X >> ; >>—2,
dz dz dz
taking into account it:
dX
— = Xm TOST + 3X3m С^Зт
dz
(9)
dX _ 2 dXim C0ST - xim sinr + 6 3m cost - 9X3m sin3z, (10)
dz dz dz
X3 = 3X 1m Sin T - 4X 1m Sin 3 + 3XLX3m Sin 3t -
3 3 3
- 4 X 1mX 3m sinT + 2 X 3mX1m sin T + ~ X 3^ Sin3T
_Th
n 9n
(11)
e 4 4
\Ydz =— Ym cos(t +ф)------Ym cos(3t +ф) + A1. (12)
J n 9n
Having substituted (19)-(12) in (6) and having grouped coefficients before identical trigonometrical functions, we will receive systems of the algebraic equations:
3 , з , з , 4
T X1m - Xm - ^ X\mX 3m + ~ X3mX1m + ^ = - ^m ^ Ф,
4 4 2 n
PX 1m =-Ym C°A
П
-9X3m - 1 X3lm + 3 XlX3m + 3 XL + «X3m = Ym sin ф,
4 2 4 9n
(13)
(14)
3PX3m = 9 Ym COsф.
9n
Their decision concerning Xlm and X3m represents a complex challenge, however if to assume that X3m/X1m << l. that (13) and (14) can be given the following look:
3 , 3 ,
4X, - Хш - 4XLX3m +«Xm
-{px 1,
= Y_
81-
-9X,_ -1 XL + 3 XLX. + aX,,
= | - Y
(15)
+ (3PX3m )
If to consider that X23m values and р are negligible, from (15)
amplitude of the third harmonica will be defined so:
—Xl (a -1)2 + — Xm (a -1) - — Xl 81 54 81
X 3m =-
Xl -(9,3-a)- 72 X 1m
(16)
We will calculate the established decision (6) from (13) and (14):
Y =
( 1 3 3 \
-x +- x L + - x L X. +- X L X. +
+aX 1m +aX3m - 9X3m + 3 X3m
40
9n
• (17)
+ [^‘(Xim + 3X 3,
For determination of dependence of i =f№ it is necessary to find i2 from (1) and (2):
12 C2l0 dt2 + C2 dt2.
(18)
The current proceeding on a chain, we will define from expression (3) taking into account (4) and (18):
(19)
• - m + CT (C + C л
I - C1C2L0 —— + C2L0g-j- + (c, + C2)+
dt dt dt
d4 d2T3
+g^d7 + C2L°K~kp- + ^T-
Entering replacement of variables: w i
X = —; Z = -; z=gt. i6
We have:
ry_d2X Qd 2X d 2X dX d2X3 V3
Z -—~y + P~TT + P~TX + Pai~T~ + , 2 +aiX , (20)
dz dz dz dz dT
here designations are accepted:
p = a+a{, a = 1 2; i6 = Cf,.
We will define derivatives from X taking into account that X (t) — slowly changing function of time: dX d2Xim dXlm .
--- _ 3----C0ST - 3 Vm_ slnT - Xim COST +
dz3 dz2 dz lm
+9 d Xlm cost - 27 dX3m sln 3z - 27X3m cos3z,
(21)
dz2
d4X . d3X„
dz
-cost - 6-
-dX
dT
dX
dT
-cost +
dT dTt
d 3X d 2X
+X1m sinT +12---3mcos3T -54----Asin3T -
dT
-78 dX3m cos3t + 51X3m sin3T, dT
dz2
(22)
d2X3 9 dX2„
dz2
2 dz
-cost— X2m sinr —
9 dX2,
9 3
+4 Xlm sin3T + 25X3
4
dX
2 dT
-cos3t-
dT
2m cos 3t + 25X2mdXmcos 3t -
dXlm sinT- 3 X2
dT
dX 3m
” dT dX„
-cost -
-9X2mX3m sin 3t" X3m , _
2 dT 2
3 dX 3
- - X 3m -7м- cost + - X2mX 3m sinT + 3X 1i—fm cost + 2 -t 4 -t
+6X-Xзmcost - -3XLX-sinT + — -X3mcos3T -
(23)
-T
27 X3 • 3
- — X3m sin3T.
2 -t
Having substituted expressions (9)-(11), (21)-(23) in the equation (20), we will define the maximum Zm value:
2
+
2
2
2
2
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Section 13. Technical sciences
Th =
x„ (1 -p)+43Xl (aa -1)+43Xlx,m (1 - a)+43Xlxlm a -1)
x3m (51 - 9p)+Xl 144 - 4a 1+XlmX3m I 3a1 - 91+43 XlXI a - 9)
[„pa -1)]2 +
+[X зтв3(а - 9);
(25)
Fig. 2. Volt-ampere characteristic of the ferrorezonansny stabilizer of current
On expressions (17) and (24) in fig. 2. the volt-ampere stabilization of current in quite wide range of change of en-characteristic of the ferrorezonansny stabilizer of current is trance tension is observed. constructed; here at certain ratios of parameters of a chain
References:
1. Milyakh A. N., Volkov I. V. Systems of invariable current on the basis of inductance-capacitor converters. - Kiev: Naukova thought, 1974. - Р. 216.
2. Gubanov V. V. Power semiconductor converters with output stabilizers. - L.: Energy., 1972. - Р. 133.
3. Kadyrov T. M., Alimov H. A. The Analysis of a double-circuit chain taking into account the highest harmonicas. - AN UZSSR, STN. - 1979. - № 3. - Р. 17-22.
4. Karimov R.Ch. Research nonlinear dynamic chains with thyristor elements in system of power supply, the collection of materials IV of the International scientific conference “Current Trends Technical Sciences" - Kazan, Oktyabr 2015. - Р. 30-33.
5. Karimov R.Ch. Research nonlinear dynamic chains with diode elements in system of power supply, the collection of materials IV of the International scientific conference “Current Trends Technical Sciences" - Kazan, Oktyabr 2015. - Р. 33-35.
Khayitoy Yozil Kkasimovich, Tashkent city, Uzbekistan, National University of Uzbekistan named after Mirzo Ulugbek, Lecturer of the Faculty of Geology and Geography E-mail: [email protected]
On the cleaning of waste water from textile factories using Pistia Stratiotes L.
Abstract; In this article the study of the ecological and biotechnical features of cultivation of the aquatic plant — Pistia Stratiotes L. on the waste water from the weaving factories in the Buchara province. In the composition of the waste water there were not detected the dissolved oxygen; the average values of BOD 5 and oxidability were 155.4 and 115.1 mg 02/l, respectively, the smell was 5 points, the colour — from yellow to brown. In the result of cultivation of Pistia Stratiotes L. in the waste water of the weaving factory the quantity of the dissolved oxygen increased up to 8.0-10.0 mg/l, the quantity of BOD5 and oxidability decreased up to 14.4 and 21.0 mg 02/l, respectively — i. e.,
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