Научная статья на тему 'Analysis of shunt power track circuit without insulating joints'

Analysis of shunt power track circuit without insulating joints Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

CC BY
194
55
i Надоели баннеры? Вы всегда можете отключить рекламу.
Ключевые слова
LIMITING RESISTANCE / THE MODULUS AND THE ARGUMENT / THE INPUT IMPEDANCE OF THE RAIL LINE / THE EQUIVALENT CIRCUIT OF THE TRACK CIRCUIT

Аннотация научной статьи по электротехнике, электронной технике, информационным технологиям, автор научной работы — Aliev Ravshan Maratovich

This article describes how to the withdrawal the analytical expressions for determining the maximum value and critical space shunt power track circuits without isolating joints.

i Надоели баннеры? Вы всегда можете отключить рекламу.
iНе можете найти то, что вам нужно? Попробуйте сервис подбора литературы.
i Надоели баннеры? Вы всегда можете отключить рекламу.

Текст научной работы на тему «Analysis of shunt power track circuit without insulating joints»

Section 12. Transport

Aliev Ravshan Maratovich, Tashkent Institute of Railway Transport Engineers, Ph. D. technics, the Faculty organization of traffic and transport logistics

E-mail: silara@mail.ru

Analysis of shunt power track circuit without insulating joints

Abstract: This article describes how to the withdrawal the analytical expressions for determining the maximum value and critical space shunt power track circuits without isolating joints.

Keywords: limiting resistance, the modulus and the argument, the input impedance of the rail line, the equivalent circuit of the track circuit.

Working conditions of track circuits without isolating joints, as well as track circuits with insulated joints to a greater extent depends on the proper selection of the characteristics of limiting resistance. Limiting the magnitude of the resistance depends on the power consumed by the track circuit without isolating joints in both the normal and in the bypass mode wheel set supply end of the track circuit.

Research carried out for track circuits with insulating joints have shown [1] that for each track circuit there are modulus and argument of limiting resistance, in which the maximum power at the end of the rail bypass supply chain is the least Pkzmahn.

Invxl

To track circuits with insulating joints was calculated that the power Pkzmahn will take place under the condition that \Z\ = |z„| h - \<p<n\ =± 180° where Zx - input impedance between the track circuit start points of the rail line, Zo — limiting resistance.

The track circuits without insulating joints [2; 3] has a feature that the smallest calculation value when the maximum power supply bypass end is made with the influence of the two train shunts disposed on both sides of the feed end, as shown in the equivalent circuit of Fig. 3.

For the analysis of shunt power track circuit without isolating joints consider it the equivalent circuit in normal mode Fig.1, 2 in bypass mode the supply end Fig. 3, 4.

Invx2

Zo

Zg

Zv:

Znvx

tin

U

Figure 1. General scheme of substitution of the track circuit in the normal mode

Zg i _ invxl + Invx2

Zo

U

Zv:

Zn

Figure.2. The basic equivalent circuit of the track circuit in the normal mode

N

Z

vx1

In

Section 12. Transport

Invxl

Zy

Zg

Invx2

Zx

Zkzvx flkz

U

Figure 3. The general scheme of replacement track circuit in the presence of the mobile unit on the feeding end

Z-j _ Ikzvxl + Ikzvx2

g -

Zo

U

Ikz

Zk

Zk

Figure 4. The basic equivalent circuit of the track circuit in the presence of the mobile unit on the feeding end

Ze

-»--L

E

Znkzvx

Figure 5. Equivalent circuit of the track circuit

where Npt - four -pole supply limiting resistor between the end and the beginning of the track circuit, Zvxl — the input impedance of the adjacent track circuit from the supply end, Zvx 2 - the input impedance of the track circuit by the end of the relay, x — the distance from the rail line to the point of imposing the first shunt of train Rhl = 0, y — the distance from the rail line to the point of imposing the second of train shunt Rh 2 = 0, z — the resistance of rails, Zg — internal resistance of the power supply, Zo — limiter resistance.

The module argument limiting resistance and values of x and y, where is the smallest possible maximum power supply end of the bypass can be determined by equivalent circuits in the normal (Figure 2) and the bypass mode (4).

For the circuit shown in Figure 1.2 we can write: Un=in (Z + Z + Z„),

i = K( i„vxl + L 2),

where

For shunt mode power scheme Figure 3 we can write

U

Iz =

Z + Z + Z

g 0 I

U

kzvx 2

Ap

Z + Zk

o kzvx

* y + Bpm (Z * x + Z * y )

Cp *Z*x*Z*'

p m

(1)

(2)

(3)

(4)

^y + .pm(Z*x + Z*y)- (5)

The above equation corresponds to a known equivalent circuit Figure 5, which can significantly simplify the definition of conditions to ensure the smallest possible maximum power at the feeding end ofthe track circuit in the presence ofthe mobile unit.

In this scheme,

E = U = Ki (i + invx 2 )*(Zg + Zo + Znvx ), Z = Z + Z + Z ,

Z = Z - Z

nkzvx nvx kzvx

K =

cp z ,z 2

pm vsxl vx 2

+ Dm (Z

, + Z 2

vxl vx 2

AT Z ZZ

Z pT vxl v.

Z , + Z 2

vxl vx 2

- + bp (Z

! pm v vx

+ Z ,)

vx 2 '

Cm Z Z 2

pm vx l vx 2

+ Dp (Z , + Z 2)'

pm v vxl vx2'

Invxl - current, branching into the adjacent track circuit, Invx 2 - current flowing through this track circuit, Apm; Bpm; Cpm ;D pm - the coefficients of four - pole, replacement throttle transformer supply end.

(6)

(7)

iНе можете найти то, что вам нужно? Попробуйте сервис подбора литературы.

(8)

Equation (6) can be written as follows:

E Ki ( nvxl + 1 nvx2 ^ + + Zkzvx ^ + (Znvx Zkzvx^^ (9)

Replace the value Zg + Z + Zkzvx and -

their values according to the equation (7) and (8), we obtain

E = K (i )* ( + Z^x) (10)

or taking out the brackets ZAzvx obtain

E = K (ii invx 2 )* |l + if- I (11)

N

Designating

by Kc and make the change in the

equation (11), we obtain

E Ki ( \ nvxl ++ 1 nvx 2 ^ Z nkzvx + Kc ^

Short-circuit power is given by:

p =

(12)

(13)

Substituting the value of E in equation (12) into equation (13) yields

- Ki(Invxl + InvJ2* Zlkzvx *|(1 + Kc)\

-x-!-L (14)

Pkz =-

^kz Ki ( 1 nvxl + 1nvx 2^ Z nkzvx K |(1 + Kc

(15)

If x, y = const in equation (13) with the change Zo will change only one complex value Kc = \Kc\e'{(p' ).

To find the minimum unit value of Pkz a given argument ço and a constant (çe -pnk2 ) determine the value of the module .

Equating modules left and right sides of the equation (15), we obtain.

PK3 nvxl + 1nvx Ki Znkzvx [ + | + 2 C°s (pp Pnkz^ ](16)

Kc

Examining equation (16) to the max. and min. relatively K we obtain:

\K\ =1 or

= 1

Hence \Z\ = |Z„,z„|.

Thus, the lowest power at the end of the rail bypass supply chain for any argument limiting resistance q>0 and any values of variables x and y will be provided

Z + Z + Z. = Z - Z.

g o kzvx nvx kzvx

Substituting equation (16) instead of Kc its optimal value — one — get the equation (17) for calculating the lower end of the power supply bypass for given values , x and y.

= 2(1 ! +1 2)

2* K2* *[1 + cos (-yAz )].(17) From equation (17) shows that when x, y = const and variables maximum power at bypass takes the smallest value with increasing difference of the arguments Pe -Pnkz up to ±180° when cos-pnkl) = cos (±180°)= — 1. In this case PZmin = 0. Such a case does not occur practically.

The optimum value of the module Zo at which maximum power is minimum is determined by the equation:

Z + Z + Zk = Z . .

g 0 kzvx nkzvx

Equating squares models left and right sides of the equation and solving it with respect to |Zo |, we get:

Z = -[Z cos( -pg) + ^ cos( -ykz)]±^ (18)

±J\Z cos(m — m ) + Z cos(m -m, )\ + Z\ -(Z + Z, )2

g \ 0 g J kzvx \'0 T kz / nkzvx v g kzvx'

For large negative values of the argument maximum power occurs upon application of the shunt not in the supply end and at a distance from it.

To determine this distance, we use the equation (13)

i= £.

kz Z

Substituting into this equation instead E and Ze their values from the equations (6) and (7), we obtain:

12 K2\Z + Z + Z I2

Pkz =

I ,+1

nvxl nv

Z + Z + Z,

(19)

After substituting in the equation (19) instead of Zkz its value from equation (5), we obtain:

Pz =

I ,+1

nvxl nv

K2 Z + Z + Z

A m * Z * x * Z * y + B (Z * x + Z * y )

(20)

Z + Z +

Cpm * Z * x * Z * y + Dpm (Z * x + Z * y)

As can be seen from equation (20) when changing the x and y vary only the denominator when the smallest value whose power supply bypass end is maximum. Consequently, it suffices to study at max. and min. Only the denominator of equation (20).

Z. = Z + Z +

ob g 0

If we denote

Apm * Z * x * Z * y + BT (Z * x + Z * y) CT * Z * x * Z * y + Dpm (Z * x + Z * y ) Z * x * Z * y

(21)

we get:

Z * x + Z * y

= l * z, then make the change,

. A * l * z + B ZL = Z + Z +- pT pT

CT * l * z + DT

p p

(22)

We denote in equation (22)

A *z = a ;B =b;C *z = c ; D = d, Z+Z=m.

pm pm pm pm g 0

Make replacement, we obtain:

a, . a * i+b

Z. = mob

(23)

(24)

c*l + d

or Zob (c * l + d) = m (c * l + d) + a * l + b Performing transformation, we obtain:

Z„ (c * l + d) = Ml + N, (25)

where M = mc + a, N = md + b.

Equating the squares of the moduli left- and right sides of the equation (25) and carrying out the conversion, we get: Z 2 = M 2l2 + 2MNcos (-q>N) + N2 0 c2l2 + 2cdlcos (qqc -qd) + d2 Examining equation (26) to the max. and min. relatively l, we get:

where Qj =

Qo =

-=HQ.

M 2d2 - c2 N2

(27)

cdM2 cos (<pc -çd ) - c2MNcos(çM -Çn ) ' d2MNcos(yM -çN)-cdN2 cos(<pc -çd) cdM2 cos (ppc -Pd ) - c2MNcos(Pm -Pn ) '

The expression obtained allows to define the value of l at different values Zg, Zo and . After determining the value l

Z * x * Z * y

of the expression

iНе можете найти то, что вам нужно? Попробуйте сервис подбора литературы.

Z * x + Z * y

for various combinations of y.

- = l * z value of x is determined

i Надоели баннеры? Вы всегда можете отключить рекламу.