lv circuitbreakers
TRANSCRIPT
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 1/27
CIRCUIT BREAKERSThe Switching Arc and Arc Modeling
Luigi Vanfretti – Friday, December 14th 2007
Final Exam (Presentation), Surge Phenomena in EPE
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 2/27
OUTLINE
Circuit Breakers
The Switching Arc
Mathematical Models of the Switching Arc
General Switching Arc Equations Cassie Model
Mayr Model
Arc-Circuit Interaction
U.Delft’s Arc Model Blockset Arc-Circuit Interaction Simulations
Cassie and Myar Models
References
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 3/27
CIRCUIT BREAKERS
Key equipment in power systems.
Function:
To isolate faulted sections of a network
Interrupt fault currents (up to the MVA rating of the
breaker)
Interrupt abnormal currents: due to nonlinear loads
(arc furnace), and other load variations.
Some history: First oil circuit breaker patented by J.N. Kelman in
1907 (Two contacts in an oil tank)
In 1957 T.E. Browne et al file the first patent for SF6
breakers.
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 4/27
FEATURES OF A CIRCUIT BREAKER
T YPES OF CIRCUIT BREAKERS
Features:
Good conductor when closed
Good insulator when opened
Fast switching capabilities (change from closed to open must be very
fast)
Doesn’t cause over-voltages when operating Reliable (opens when it has to!, stays closed otherwise)
Types: categorized by their extinguishing medium
Oil
Air Blast
SF6
Vacuum
We will focus on SF6 breakers
HV Circuits
(High Pressure Electric Arc)
MV Circuits
(Low Pressure Electric Arc)
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 5/27
THE ELECTRIC A RC AND CURRENT
INTERRUPTION PROCESS
A complex physical phenomena (not fully
understood)
Electric Arc: capable of changing from a
conducting to a non conducting state very fast.
Current Interruption (a simple description):1. High current is detected in the network
2. Control circuit sends a signal to action the movable contact
3. High-density current is established in a small contact surface
4. As the movable contact parts, a plasma channel isestablished (more details are explained latter)
5. As the movable contact continues to part, the arc is being
cooled down by the medium (gaseous or liquid)
6. When the contacts have fully separated, the arc has been
extinguished by the cooling process
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 6/27
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 7/27
THE PLASMA STATE
Molecular Energy exceeds Combination
Energy
Matter changes from SOLID LIQUID (melting)
Increase of Temperature Energy is added &
Var der Waals forces are overcomed
Matter Changes from LIQUID GAS
Increase of Temperature each molecule is
given more energy, so much, that the
dissociate into separate atoms
Temperature Increases Further energy
level is increased further!
Orbital electrons dissociate into free electros,
positve ions are left
TemperatureIncreases
5000 ºK - 6000 ºK
1800 ºK
T e m p e r a t u r e R e g i o n s f o r S F 6
4 ºK
C t ti C t ti
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 8/27
THE PLASMA STATE
Contraction
Zone
Contraction
Zone
Arc Column
e I
I
Electrons
Ions
Space ChargeZone
Space ChargeZone
C A T H O D E A
N ODE
For higher temperatures the conductivity increases rapidly.
Thermal ionization is caused by collisions between fast
moving electrons and protons, the slower moving positively
charged ions and the neutral atoms.
At the same time recombination process of the positive
charged electrons and positive charged ions into a neutral
atom occurs
Thermal equilibrium: rate of ionization = rate of
recombination.
What happens after the plasma is fully established?
Free electrons and heavier positive ions in the high temperature
channel make it (the plasma channel) highly conductive so current can
flow freely after contact separation, until extinguished.
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 9/27
S AHA ’S EQUATION
Thermal ionization can be used to
switch between a conducting state to a non
conducting state.
Relation of the pressure with the temperature
and the fraction of atoms that are ionized
Steep slope function of temperature reduction
of average kinetic energy level can be done by
cooling with cold gas.
Bring the arc channel from conducting to non-
conducting.
52
27
23.16 10
1
i V
e kT
f P T
f
19
23
: 1.6 10 , charge of
: ionization potential of the medium
: 1.28 10 , Boltzmann's Constanti
e e
V
k
Saha’s Eqn. for
Different Gasses
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 10/27
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 11/27
PLASMA CHANNEL
The potential gradient and the
temperature distribution can
be measured from the arc
channel. Potential along the arc
channel is a function of: arc
current, energy exchange
between plasma and medium,
pressure, flow velocity, and
physical properties of themedium.
Contraction
Zone
Contraction
Zone
Arc Column
e I
I
Electrons
Ions
Space Charge
Zone
Space Charge
Zone
C A T H O D E A
N ODE
Voltage
Gap Length x
arc V
cathode V
column V
anode V
Cathode: conducts current
carrying electrons to the arc
column.
Anode: collector of electrons
leaving the arc column.
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 12/27
M ATHEMATICAL MODELS OF THE
SWITCHING A RC
Arc Models:
Physical:
describe the physical phenomena
used in design
complex mathematics
Black box:
describe the behavior of the arc
used for simulation of arc-circuit interaction
Give the relation between the arc conductance and circuit
variables not used for design network studies
Parameter Models
more accurate black box models
parameters are obtained from complex functions and tables
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 13/27
GENERAL PHYSICAL MODEL Physical Models
Describe the entire physical process
Actually used for design of breakers
Based on fluid dynamics equations that obey the laws of
thermodynamics in conjunction with Maxwell’s equations
(Large number of differential equations).
There are three important expressions in these models
Conservation of: mass, momentum, and energy
Conservation of mass – continuity equation: Arc-plasma is a chemical reaction: conservation of mass and
rate equations for different chemical reactions are considered
in conjunction.
For local thermodynamic equilibrium, rate equations become
the equilibrium mass action laws – for a monotonic gas, this is
Saha’s equation.
Saha’s equation describes the degree of ionisation in the gas.
0 gas density gas flow velocitydiv u u t
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 14/27
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 15/27
CONSERVATION OF ENERGY
Special Case: conservation equations becomedecoupled Thermally and hydronamically fully developed and wall-
constricted arc with negligible axial pressure drop, the conditions
are in the z plane as follows
The energy equation becomes:
Used for qualitative evaluation of current increase or arc-channel
diameter reduction.
2grad( ) div( ) div ( ) ,h
u h E u K grad T R T r t
pressure enthalpy of gas thermal conductivitygas density electric field strength gas temperature
gas flow velocity electric conductivity radiation loss
arc radius
p h K
E T
u R
r
21
T Kr
r R E
r r
0 0 0z
r u h u z z
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 16/27
BLACK -BOX MODELS
Consist on one or two differential equations.
Arc is described by a mathematical equation relating
the arc conductance with the arc voltage and arccurrent
Classical models: Cassie, and Myar solutions to the
general arc eqn.
GENERAL A RC EQUATION
Arc conductance is a function of:
Power supplied to the plasma channel,
Power transported by cooling and radiation, and Time
1
, , arc
in out
arc
i g F P P t
u R
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 17/27
GENERAL A RC EQUATION
The arc conductance varies with the supplied power and the
transported power in the plasma channel. The stored energy in
the channel is
The instantaneous arc conductance can be defined as
The rate of change of the arc conductance, divided by the
instantaneous arc conductance is
Manipulation of the equations above gives the general arcequation
Solutions to this equation requires assumptions, black box
models are solutions to the equation each with different
assumptions.
0
t
in out Q P P dt
0
( )t
in out g F Q F P P dt
1 1 ( ) ( )dg dF Q d Q
g dt g dQ dt
ln( ) '( )
( ) in out
d g F Q P P
dt F Q
C M
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 18/27
C ASSIE MODEL Assumptions:
The arc channel has the shape of a cylinder filled with highly ionised gas at constant
temperature.
The cylinder is of variable diameter.
Consequences:
Heat content and conductance are constant per unit of volume.
The diameter of the plasma channel varies in diameter due to cooling.
Model:
Substituting into the general arc equation yields
Time constant: time for the arc channel diameter to change.
Applications: studying the behavior of the arc conductance in the high-currenttime interval at temperatures above 8000 Kelvin or more
00 0 0 0 0
0 0 0
( ) , '( ) , ,out
g Q Q g F Q Dg g F Q Q DQ P DP P
Q Q Q
Arc Conductance Energy Dissipated Energy
0 0
1 2
0 0 0 0
conductivity p.u. of vol., loss (cooling) p.u. of vol., arc channel diameter,
energy p.u. of vol., / static arc voltage
g P D
Q u P g
2/0 0
020 00
ln( ) ln( )1 , t arc
d g d g P u P g g
dt Q dt Q u
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 19/27
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 20/27
OTHER MODELS: H YBRID MODELS
Browne: uses Cassie equation for the high currentinterval, and Myar for current zero.
Avdonin, Hochrainer, Kopplin, Schwarz, and Urbanek:
capable of simulating dielectric breakdown
KEMA: based on experiments, capable of simulatingdielectric breakdown of the gaseous space between the
breaker contacts after current interruption.
Hybrid models calculate the conductance of the
channel with a Myar equation before current zero.During the intervals of pre-and-post current zero and
thermal-and-dielectric intervals the conductance is
obtained from the concentration of charged particles
and their drift velocity.
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 21/27
A RC-CIRCUIT INTERACTION
Interruption process: strong interaction between the
physical process between the contacts of the breaker and
the network connected at the terminals.
During current interruption, the arc resistance
increases from zero to infinite (ideally) in microseconds After current interruption, the TRV (transient recovery
voltage) builds up across the circuit breaker contacts.
The TRV is thus formed by local oscillations and
reflected voltages.
The hot gas in the breaker does not change to aninsulating state instantaneously the arc resistance is
finite and a small current can still flow: post arc current.
Illustrate this interaction with the ARC Model Blockset.
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 22/27
THE A RC MODEL BLOCKSET: U. DELFT
Features
Operates within V.2. and V.3. of the
SimPowerSystems toolbox for MATLAB/Simulink.
Seven different arc models.
Ideal for arm model comparisons.
Highly accurate
Current limitations:
The blockset complies with V.2. of SimPowerSystems,
it can be updated to V.3. using the “psbupdate”command (available only in V.3.).
It is incompatible with V.4. (directory, graphical, and
other issues). Updated not available from U. Delft as
of Dec. 2007.
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 23/27
Arc Model Blockset
© january 2001Electrical Power Systems
Delft University of Technology
Schwarz arc model
Schavemaker arc model
Modifi ed Mayr arc model
Mayr arc modelKema arc model Habedank arc model
Cassie arc model
A RC MODEL BLOCKSET
Simple Test Circuit Schematic
voltage current
+-
v
+i-
Cassie arc mode l
• Simple Test Circuit
• Models in the Blockset:
L
C RArc
Model S
V
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 24/27
SIMULATIONS SET UP
Two different arc models:Cassie, Myar.
Simulate breaker
interruption for two cases:
Case 1: Breaker opens att = 0
Case 2: Breaker opens at
t = 9 ms
Observe the behavior at highcurrent and current zero
Compare differences with the
models
[vsw]vsw1
voltage
[vma]vma
[vca]vca
[isw]isw
[ima]ima
[ica]ica
current
+ -
v
+ -
v
+ -
v
Schavemaker arc mo del
Mayr arc model
[vsw]
[vma]
[vca]
[isw]
[ima]
[ica]
+ i
-
+ i
-
+ i
-
Cassie arc model
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 25/27
0 0.005 0.01 0.015 0.02-4
-2
0
2
4
6
8x 10
4
Time (sec)
A r c V o l t a g e ( V ) ,
A r c C u
r r e n t ( I )
VMyar
IMyar
0.0167 0.0167 0.0167 0.0167 0.0167 0.0167
0
0.2
0.4
0.6
0.8
Time (sec)
A r c V o l t a g e
2 0 K V (
V ) , A
r c C u r r e n t ( I )
VMyar
IMyar
8.328 8.33 8.332 8.334 8.336 8.338 8.34
x 10-3
-0.8
-0.6
-0.4
-0.2
0
Time (sec)
A r c V o l t a g e
2 0 K V (
V ) ,
A r c C u r r e n t ( I )
VMyar
IMyar
SIMULATION RESULTS (C ASE 1)
0 0.002 0.004 0.006 0.008 0.01
-8
-6
-4
-2
0
2
4x 10
4
Time (sec)
A r c V o l t a g e ( V ) ,
A r c C u r r e n t ( I )
VMyar
IMyar
Zero Crossing
Arc Voltage
Extinguishing Peak
Post Arc
Current
TRV
SIMULATION RESULTS (C ASE 2)
Zero Crossing
Arc Voltage
Extinguishing Peak
Post Arc
Current
TRV
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 26/27
8/11/2019 LV CircuitBreakers
http://slidepdf.com/reader/full/lv-circuitbreakers 27/27