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11
ИРКУТСКИЙ ГОСУДАРСТВЕННЫЙ УНИВЕРСИТЕТ ПУТЕЙ СООБЩЕНИЯ
форме, что позволило создать автоматически значительную часть базы данных.
БИБЛИОГРАФИЯ
1. Мартьянов В. И. Логико-эвристические методы сетевого планирования и распознавание ситуаций // Проблемы управления и моделирования в сложных системах : тр. Междунар. конф. Самара, 2001. С. 203-215.
2. Мартьянов В. И. Симонов А. С. Анализ и проектирование трассы автомобильной дороги // Современные технологии. Системный анализ. Моделирование. 2008. № 4(20). С. 16-23.
3. Новиков Ф. А. Дискретная математика для программистов : учеб. для вузов. 2-е изд. Спб. : Питер, 2005. 364 с.
4. Зубов В. С. Справочник программиста : базовые методы решения графовых задач и сортировки. М. : Филинъ, 1999. 256 с.
He Renwang
УДК 621.33
CALCULATION OF FAULT CURRENT ON ELECTRIC TRACTION NETWORK WITH SERIES COMPENSATORS
1. Introduction
Series compensators are frequently used to improve the voltage distribution in electric traction networks. It is necessary to calculate the short-circuit current through these compensators for relay protection, system reliability analysis or other purposes. Yet it is unusually complicated to accomplish the calcula-tion[1-5]. The paper presents a novel approach to this problem.
2. Mathematical Model
Fig.1 shows a fault on power traction systems.
Traction substation
,C|
I i
d2i R + RT di
dT X-(t = ct)
■ XT dT
+
Xci
1
du
X + XT X
-XT dT'
(1)
Fig. 1. Fault on power traction system with compensators
Its equivalent circuit is shown in Fig.2. According to Kirchhoffs laws, the fault current i can be expressed as follows:
Fig. 2. Equivalent circuit of fault on power traction system with compensators
where R, X, XC are the resistance, inductive reactance and capacitive impedance on the line respectively, while RT, XT are the resistance and reactance of the transformer respectively.
3. Calculation of Fault Current
There are inductors with iron cores inside the transformers. Since the load current of on a contact line is usually more than 600 amperes, and the fault current would be much larger, the magnetic saturation should be considered. The magnetic flux can be expressed in higher-degree polynomial
Ф=Е
a
• 2 k+1
(2)
k=0
According to Faraday's law of induction, the voltage will be
.Td0 di ^Tdi u = N— = N—— = N—S0
So =
dt dф di
di dt
dt
= £ (2k + 1)ak
k=0
МЕХАНИКА. ТРАНСПОРТ. МАШИНОСТРОЕНИЕ. ТЕХНОЛОГИИ
where N is the number of turns in a winding. Thus, equation (1) can be rewritten as
u = uR + uL + uC + u ,
R L C n~
uR = (R + RT ) i, di
__
~dz~ ~XUl
(5)
duC
1
i( m ) _ ■
-u
( m-1)
u
X
( m-1) _
•( m-2)
(oC
u
u
R (m-1) _ (R + Rr )i(m-1), (m-1) _(N(iS0)(m-1),
m -1
(N X C^i
Л_0
uL( m-1) _ u(m-1) - uC ( m-1) - uR
(m-Ä-1) ^ (Л) (m-1)
- u
(m-1)
(6)
Using equation (3) and equation (4), the current can be rewritten as:
i( m) _-
X
u(m-1) - (R + RT )i(m-1)-
■(m-2)
(C
-(N x Cm-1
(m-Л-Х) s (Л)
(7)
(cosT)(p) Т_0 _A(,) _
0 (p _ 2Л +1),
1 (p _ 4Л),
-1 (p _ 4Л + 2),
(Л_ 0,1,2,-)
then
,( m-1)
T_0 _ A(m-1)Um ,
define
se_ (Si-1)f) (£_ 1,2, •••Д).
From equation (4):
S0 _ ^ = X (2k + 1)aki
di k _0
2k
or rewrite as
)(1) _ ( s )(1)(i)(1) _
dr co C
un =CNU-
ax
Derive the m th or (m-1) th derivative of i with respect tor in equation (5): 1
(«' (i)T_ ВДТ, (S0)T2) _ (ЗДТТ,
(S0)T0) _ ( S1 (i ^ k0 -1) _
k0-1
X Ckl (i)(k0 -kl ) S(k')
k _0
л-1 k -1
(S^ Ckk2-1 (i )( k1 -k2) S
( k2) 2 '
k2 _0
k,-1
(SJ^ _ X Cfe(i)(k^+{)S1+1(k-2) _ (i)TS1+1,
k,+1 _0
thus
ST _ (Л-1) _
Л k(-1-1 n Л
_ПИП-
(2k +1) ! (ig X^1
(kf-1 -k()
1=1 tl 1=1 -kr -1)!(2k-A-1)!at//-A-1' (10) Applying equation (10) in equation (7), the fault current can be expressed as
X
u(m-1) - (R + RT)i(m-1) - —i(m-2)-(C
(11)
(N (Л-1)!ЕИЕЕИ 1
(2k + 1)!(i)T S-1
( kS-1-ks)
Suppose the starting value of fault current is i(0)=I0, and the voltage of the equivalent source is u=Umcosrnt =Um cost. Noticing
(8)
(9)
i=0 hi fci 1=1 kr (kr_i - kr- 1) !(2k -1 -1)!«/-A-1 _ 4. Conclusions
The fault current on a power traction system with series compensators can be calculated by equation (11).
REFERENCES
1. Tomislav B. Sekara, Jovan C. Mikulovic. Optimal non-active power compensation under non-sinusoidal conditions // Electrical Engineering. 2006. V. 88 P. 423-429
2. Zhou Yun-fei, Song Bao, Chen Xue-dong. Position-force control with a lead compensator for PMLSM drive system // Int. J Adv Manuf Tech-nol. 2006. V. 30 : 1084-1092.
3. Arshunin S. A., Zinakov V. E., Kadi-Ogly I. A. Asynchronous turbogenerators and compensators as a means of improving the operating capability of the Moscow power system // Power Technology and Engineering. 2008. V. 42, No. 1.
4. Zhang X.-P. Robust modeling of the interline power flow controller and the generalized unified
power flow controller with small impedances in 5. Fikret Caliskan. Robust quadratic stable dynamic power flow analysis // Electrical Engineering. output compensator // Electrical Engineering. 2006. V. 89. P. 1-9. 2008. V. 90. P. 181-187.
He Bolin, Yu Yingxia, Li Qiuping УДК 669.7/.8
PREPARATION OF THE POROUS CERAMICS OF AI2O3-TIB2 SYSTEM BY SELF-PROPAGATING HIGH-TEMPERATURE SYNTHESIS METHOD
The porous ceramics is a new kind of functional material. These ceramic materials have many good properties and been attracted great interest for wide application in many fields such as chemical industry, information technology, biomaterial engineering, environmental protection and so on[1-3]. There are many homogeneous porosity which dispersed in base ceramic materials. They have the advantages of lower density, the BET surface area, physical surface characteristics, selecting permeability for liquid and gas, energy absorbing, damping, and so on. Forthmore, the porous ceramic materials have high temperature corrosion resistance, higher chemical stability and size stability. By making advantages of homogeneous porosity, the porous ceramics can be manufactured into filters, separating equipment, etc. By making advantages of energy absorbing property, they can be used for sound absorbing materials, shock absorption materials. By making advantages of high value of the BET surface area, they can be used for porous electrode, catalyst supports, heat exchanger, gas sensor. By making advantages of lower density and heat conductivity, they can be used as heat-insulation material and light structural materials.
Self-propagating High-temperature Synthesis
Today, the methods preparing porous ceramics are appending producing pore techniques, froth techniques, organic forth-dipping techniques, and sol-gel method [4,5]. Self-propagating high-temperature synthesis (SHS) is developed from Russia [6,7]. The method is based on the use of the heat released during exothermic reactions in order to preheat raw materials and to obtain a self-sustained system.
In this paper self-propagating high-temperature synthesis method is carried out to fabricated the porous ceramics and Al2O3-TiB2system is used for research object by adjusting the state of reaction mate-
rials, including raw materials chemistry composition, reaction materials grain size, raw sample density and so on. Many porous ceramic products with different shapes such as circle plate, and cylinder, etc, have been fabricated by author with porosity of 45%-68%, and pore sizes of 1-400 ^m. 1 Experiment conditions and process
1.1 Reaction system
10Al + 3TiO2 + 3B2O3 ^ 5Al2O3 + 3TiB2.
For the porous ceramics of Al2O3-TiB2 system, the range of porosity and pore size is great. The porosity and pore size are easy alternated and controlled. In the Al2O3-TiB2 system, high combustion temperature is one of features during the combustion process. The highest temperature in Al2O3-TiB2 system is 223 0oC and higher than the melting point of Al2O3. The Al2O3 and TiB2 in the system can be thoroughly sintered. Another feature is that the combustion materials are easy formed in the combustion process. The combustion materials are not easy dela-minated and can be ignored easily. It does not effect the ignore point to add different kind and quantity of additions and the system can combusted thoroughly. It gives the convinince to alternate and control the pore size by adding some additions.
1.2 Raw materials
Al powder: industrial, grain size 45-175 ^m; TiO2 powder: industrial, rutile, grain size smaller than 45^m; B2O3 powder: industrial, grain size smaller than 175^m.
1.3 Raw materials
The raw materials are mixed according to chemical mole ratio of the composite system for 4 hours, and some additive is added. After being sieved, mixed and dried, the reactive mixtures were filled up the stainless steel die by pressing or librating to shape.
