Download Multi physical field coupling calculation of airflow

2016 China International Conference on Electricity Distribution (CICED 2016)
Xi’an, 10-13 Aug, 2016
Multi Physical Field Coupling Calculation of Airflow
Characteristics of SF6 Circuit Breaker Based on Actual Gas
Model
An Su, Xin Lin, Yalong Xia, Feiming Wang
School of Electrical Engineering, Shenyang University of Technology, Shenyang, 110870, China
Abstract—The Redlich-Kwong state equation of the
real gas and the governing equations of the flow field
were combined to solve the problem.The distribution of
physical parameters of the interrupter was attained
under the condition of the circuit breaker in small
capacitive current interruption by analysis of the 126kV
capacitor group SF6 gas circuit breaker arc
extinguishing chamber in air flow field, which is
according to enthalpy flow arc model and dynamic
model of non-equilibrium arc energy built by
microscopic parameters of plasma. The dielectric
recovery characteristic curves in arc contacts after the
arc extinguished were attained through the coupling
calculation in the field of electric and gas flow.
Calculation results show that: When the circuit breaker
is opening the small capacitive current, the effect of
breaking speed on arc burning time is very small and
arc extinguished in advance. The arc gap conductivity
is about 700S/m, and the thermal conductivity is about
1.1W/m·K at arc extinguishing time. The transient
recovery voltage is always lower than that of the
breakdown voltage, and the electric arc can
successfully break without reburning. To make the short
arcing time have a large arc distance, and the large
nozzle should be open enough to be strong for the gas
blowing condition, the optimum opening speed is
9.6m/s.
Index Terms—Circuit breaker; Redlich-Kwong state
equation; numerical calculation; gap breakdown margin
I. INTRODUCTION
SF6 gas circuit breaker parallel capacitor set special for
capacitor group in the power system is used, the
successful opening of capacitive small current is
realized by using the SF6's strong electronegative and
excellent thermo chemical properties, which can
effectively inhibit the over voltage and reduce the
critical wear rate[1]-[2]. Whether the SF6 breaker can
successfully open is relative to the recovery speed of
SF6 dielectric and voltage between contacts after the arc
extinguishes, the process refers to the transition from
conduction to insulation, including arc theory, plasma
physics, electromagnetic field theory, fluid mechanics,
thermodynamics and so on[3]-[4].The research on the
coupling calculation of breaking characteristics is of
great significance to the safety and stability of power
CICED2016
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Paper No CP1234
system as well as the reliable operation of circuit
breaker.
The study on breaking performance of the circuit
breaker is mainly divided into two aspects: test research
and simulation research. Because of the long cycle and
high cost, it is difficult to meet the actual requirements
of the project, therefore accurate calculation of arc
chamber pressure characteristics and dielectric recovery
performance is vital to the design of circuit breaker[5].
Gas property is the basic data for calculating the
breaking characteristics of SF6 circuit breakers, and
accurate gas parameters are necessary to ensure the
accuracy of the gas flow field[6].SF6 gas circuit breaker
in high pressure has large molecules and is in transonic
flow state during the breaking process with complex
flow path. The solution to the gas flow field of the
circuit breaker is the combination of the conservation
equation and the gas state equation, during which the
ideal gas state equation is used mostly, whereas the real
gas state equation is seldom used[7]-[9].The ideal gas
state equation ignores the molecular volume of gas,
assuming there is no interaction force between the
molecules, which is suitable for the calculation of small
molecules, low pressure gas. The Redlich-Kwong state
equation of the real gas considers the increasing effect
of gas molecular volume on the dynamic pressure of the
gas and the cohesion of intermolecular forces on
reduction of gas pressure, it also considers the influence
of temperature on molecular collision processes and
ignores the molecular shape, polarity, and ensures the
simplicity to improve the calculation accuracy, which is
more suitable for the calculation on SF6 gas with
macromolecules, non polarity, high pressure in circuit
breaker[10]-[11].
In this paper, the Redlich-Kwong state equation of the
actual gas was applied to the airflow field and electric
field coupling calculation of SF6 126kV circuit breaker,
based on the calculation on the distribution of electric
field in the arc chamber, the non equilibrium state arc
energy model was established, the distribution of
physical parameters in the arc chamber of circuit
breaker was calculated, and the breaking characteristics
of circuit breakers were analyzed according to
microscopic parameters of plasma and macroscopic
parameters of gas. The research results not only provide
a theoretical reference for the breaking characteristics
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2016 China International Conference on Electricity Distribution (CICED 2016)
of circuit breakers but also have a certain guiding
significance for the optimal design of circuit breakers.
II. CALCULATION MODEL
A. Research objects
Fig. 1 is a diagram of the structure of the SF6 gas circuit
breaker arc extinguishing chamber special for 126kV
capacitor group. During the opening process, the main
contact is separated from the arc contact, the current is
transferred to the closed static and dynamic arc contact,
and then the arc contact is separated to form arc. The
rated gas pressure ,rated back-to-back capacitor bank
breaking current circuit , arc contact distance and
super-path of the circuit breaker are 0.7MPa, 1600A,
150mm, 50mm, respectively. The curves of the speed
and route of the contact are showed in Fig.2.
1
3
2
4
5
Xi’an, 10-13 Aug, 2016
Kwong equation , high force coefficients in CR  K are a
function of the temperature T, which is superior to the
ideal gas state equation and meets the actual Onnes
equation highly.
In the calculation of arc energy, Joule heating is
considered without radiation heat transfer:
I
q   E 2  J 2 /   ( )2 / 
(5)
A
The relationship between the SF6 arc cross-section and
the current is given by LESLIE S.FROST[12]-[13]:
A
l
I/
pout
F 
Where A is arc cross-sectional area; l is arc length;
Pout is arc area downstream pressure; I is the current;
 is the conductivity, F is the enthalpy flow. In the
equation of F = ρch / P ,  is the density, h is enthalpy,
P is the pressure, c is the speed of sound, the
relationship between speed of sound and temperature is
as following:
c  800  0. 164T
6
8
7
1
0
9
1-SF6；2-Static main contact；3-Large nozzle；4- -Movable main contact；
5-Air chamber；6-Static arc contact；7-Shield；8-Small nozzle；9-Movable
arc contact；10-piston
12
行程/mm
s/mm
8
Main
contact trip
主触头行程
100
4
III. NUMERICAL CALCULATION
50
0
0
0.01
0.02
0.03
时间/s
t/s
0.04
0.05
0.06
0
Fig. 2. The curve of speed and distance of circuit breaker
B. mathematical model
SF6 gas Redlich-Kwong equation of state is:
P =
RT
a
V - b T 1 / 2V V +b 
(1)
Where P is the SF6 gas pressure; R is the gas constant;
V is the gas volume, the constant a and b are based
on the critical isotherms at the critical point.
a = 0.42748
RTc
R 2Tc2.5
b = 0.08664
Pc
Pc
(2)
Where Tc is the critical gas pressure, Pc is the critical
gas pressure. The formula(1) is deformed and expanded
in the form of summation of series:
RT
1
a
1
a




V 1 b
T bV 1  b
T bV
V
V
RT RTb
a
RTb 2
ab

 2 
 3 
 
V
V
V
TV 2
TV 3
P

RT
V
(3)
 1

a  1  2
ab 
1  V  b 
  2 b 
  
T TR V 
T TR



BR  K  b 
In the solution of the control equation, the parameters
of the gas in different states f  P, T  were obtained by
using two interpolation methods.
2
2 
(8)
f  P,T  - f  Pi ,T  
弧触头行程
Arc
contact trip
Speed of arc
弧触头速度
contact
Speed of
主触头速度
main
contact
v/(m/s)
速度/(m/s)
150
a
,
T TR
CR  K  b 2 
ab
T TR
(4)
A. Calculation of physical parameters of arc quenching
chamber
When the coupling numerical calculation was
performed, the first kind of boundary condition was
imposed on the moving arc contact and the moving
main contact: 1 =1V, The first kind of boundary
condition was the static main contact and the static arc
contact with loading:  2 =0V[14]-[15]. The initial
velocity of the gas is 0, the gas pressure is 0.7MPa, the
initial temperature is 293K.
The finite element volume method was used to discrete
the mathematical model of the SF6 gas, the arc energy
of arc contact was loaded by self programming, arc
conductance was calculated simultaneously through the
temperature and pressure in arc plasma area monitored
by programs, the simulation process can be used to
describe the dynamic development trend of arc during
the opening of circuit breaker. Assuming the SF6 circuit
breaker phases was 1/2π, the distribution of the
physical property parameter in the arc extinguishing
chamber under the unsteady flow were calculated under
the average speed of arc contact is respectively 5.7m/s,
6.72m/s, 7.68m/s, 8.64m/s, 9.6m/s, when the capacitive
small current was 1600A. Figure 3 shows the
distribution of the physical parameters in the arc
quenching chamber at different speed.
(4) is the second and third force coefficient of Redlich
CICED2016
Session 3
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 f  Pi ,T 
f  P,T  =   
i=0  i=0,i  j f  Pi ,T  - f  Pj ,T  


Fig. 1. Structure of arc quenching chamber
200
(6)
Paper No CP1234
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2016 China International Conference on Electricity Distribution (CICED 2016)
(a)Electric field
(b)Density
Xi’an, 10-13 Aug, 2016
increases. However, the influence of breaking speed on
arcing time is not obvious, the arcing time varies
between 4.25ms and 4.33ms, and the range is not large.
In the process of opening and breaking of the circuit
breaker with the small 1600A capacitive current, there
is a certain degree of advance quenching phenomenon
in the process because of the lower arc energy and the
smaller breaking current, in addition, due to the short
arcing time, the large nozzle of circuit breaker has not
yet opened in the process of opening the small current,
therefore, the arc extinguishing ability of the circuit
breaker is mainly determined by the pressure difference
between chamber and the hollow tube when contact
separates.
Table.1 Arc parameters at different speeds
Breaking
Moment of
Arcing
Arc Extinguish
speed (m/s) separation(ms) time(ms)
distance(mm)
5.76
27.56
21
4.33
(c)Temperature
(d)Pressure
6.72
23.62
4.28
27
7.68
20.67
4.25
32
8.64
18.37
4.3
37
9.6
16.53
4.27
41
B. Study on the dielectric recovery characteristic of
circuit breaker
According to the simulation model of the gas flow field
and electric field of the fast grounding switch, the
characteristic curve of dielectric recovery was
calculated. In a slightly inhomogeneous electric field,
the breakdown criterion of SF6 gas can be expressed by
the following formula[16]:
 Ecrit =1.167 

U b  Ecrit / E1V
(e)Conductivity
(f)Thermal conductivity
Fig. 3. Parameter distribution of arc extinguishing chamber at
quenching moment
It can be seen from the graph that at arc extinguishing
time, arc gap conductivity is about 700S/m, and the
thermal conductivity is about 1.1W/m·K. The greater
the speed, the greater the pressure value in the upper
reaches of the small nozzle, and the more the pressure
difference between the upper and the lower reaches of
the arc, with the greater gas blowing intensity at the
moment of extinguishing, the convection heat transfer
between air and electric arc is more obvious, and the
arc energy diffusion is more adequate. When the circuit
breaker breaking phase is 1/2π, the different parameters
corresponding to the arc velocity are shown in table 1.
According to the calculation results, it can be seen that
the breaking speed directly affects the time of the arc
contact and the distance of the arc extinguishing. With
the increase of the breaking speed, the time of the
contact shortens and the distance between the arc
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(9)
Where Ecrit is the value of the critical breakdown
electric field strength; U b is the Critical breakdown
voltage; E1V is the electric field intensity distribution
when the contact voltage is 1 V. When the electric field
strength between contacts shows E > Ecrit , effective
ionization coefficient γ>0, arc gap may be break
down.The critical breakdown voltage distribution of arc
extinguishing chamber is calculated in Figure 4.
Fig. 4. Critical breakdown voltage distribution in arc
extinguishing chamber
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2016 China International Conference on Electricity Distribution (CICED 2016)
62271-100:2008 IEC regulates the capacitor group
circuit breakers of rated voltage 126kV, requirements of
transient recovery voltage (TRV) are:
uc  1.95  1.4  2 / 3  126kV  281kV (10)
t  8.7ms
The results through the calculation show that under
different opening speed, the curves of the dielectric
recovery characteristics of arc gap and transient
recovery voltage changing with open distance were
obtained in Fig.5, comparing the breaking voltage
under different breaking angles and TRV under circuit
breaker breaking with small capacitive current, it can be
concluded that breakdown voltage of the breaks of
circuit breaker is always higher than the value of
transient recovery voltage, which can successfully
break the arc without reburning. Fig.6 is curves of arc
gap breakdown margin changing with open distance
under different speeds in the process of breaking.
Because the arc current is very small under short arcing
times, the small current arc energy and arc radius are
very small, as the influence of arc energy on the
recovery of the post arc dielectric is relatively small,
different breaking speeds mainly affect the electric field
distribution at the moment of extinction and gas
blowing intensity after large nozzle opening, thus
affecting the dielectric recovery rate in short time after
arc extinguishing and the value of the breakdown
margin after large nozzle opening. the faster the speed,
the faster the medium recovery rate after arc
extinguishing, and the lower the breakdown margin of
the large nozzle, the influence of the breaking speed on
the early and late stage of the recovery of the medium is
opposite. Considering the dielectric recovery
characteristics of the circuit breaker, the short arcing
time should have a large arc distance, and the large
nozzle should be open enough to be strong for the gas
blowing condition, so the optimum opening speed is
9.6m/s.
1500
5.76m/s
6.72m/s
7.68m/s
8.64m/s
9.6m/s
TRV5.76m/s
TRV6.72m/s
TRV7.68m/s
TRV8.64m/s
TRV9.6m/s
电压/kV
U/kV
1000
500
0
0
25
50
75
开距/mm
k/mm
100
125
150
Fig. 5. Curve of the dielectric recovery characteristics in the
opening process
5.76m/s
6.72m/s
7.68m/s
8.64m/s
9.6m/s
15
裕度
Margin
IV CONCLUSION
Based on the structure of the circuit breaker arc
extinguishing chamber, the dielectric recovery
characteristic of the capacitive small current breaking
of the SF6 126kV circuit breaker was analyzed by the
coupling calculation of electric field and flow field, and
the following conclusions were drawn:
(1) When the breaking phase was 1/2π under the
condition of breaking 1600A small capacitive current,
the average speed of the arc contact respectively 5.7m/s,
6.72m/s, 7.68m/s, 8.64m/s, 9.6m/s, corresponding to
the burning arc time were 4.33ms, 4.28ms, 4.25ms,
4.3ms, 4.27ms. The effect of breaking speed on arc
burning time is very small, but it has large effects on
the circuit breaker pneumatic process and arc
extinguishing time distance. Because of the low arc
energy and the small breaking current, there exists arc
extinguishing in advance in the process of breaking.
(2) The arc gap conductivity is about 700S/m, and the
thermal conductivity is about 1.1W/m·K at arc
extinguishing time. With the greater speed, the
convection heat transfer between air and electric arc is
more obvious, and the arc energy diffusion is more
adequate.
(3) To make the short arcing time have a large arc
distance, and the large nozzle should be open enough
to be strong for the gas blowing condition, the optimum
opening speed is 9.6m/s.
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An Su was born in China in 1991. He is a master graduate student of
Shenyang University of Technology. Currently, focuses on the
research of high voltage and insulation test technology.
E-mail:[email protected]
Xin Lin was born in China in 1961. She is a professor and doctoral
supervisor, research direction for high voltage and insulation
technology, high voltage electrical appliances, intelligent electrical
appliances, etc.
CICED2016
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Paper No CP1234
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