10-04-2012, 03:48 PM
CIRCUIT BREAKERS
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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
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.
FEATURESOFACIRCUITBREAKERTYPESOFCIRCUITBREAKERS
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 SF6breakers
HV Circuits
(High Pressure Electric Arc)
MV Circuits
(Low Pressure Electric Arc)
THEELECTRICARCANDCURRENTINTERRUPTIONPROCESS
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 is established (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
THESWITCHINGARC
Electric arc is used for interruptionswitching arc.
What is an electric arc?
A plasma channel(the 4thstate of matter)between the breaker contacts formed after a gas dischargein the extinguishing medium.
How is an electric arc formed in a confined closure (circuit breaker)?
Before contacts separate a high current density is produced at the small surface contact area the material of the contacts melts!
The melting material explodes producing a gas discharge in the extinguishing medium
As the breaker parts, the magnetic energy stored in the inductances of the system force current to flow
Plasma channel is established…
THEPLASMASTATE
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 leftTemperature Increases
5000 ºK -6000 ºK
1800 ºK
Temperature Regions for SF64 º
K
THE PLASMA STATE
Contraction
Zone
Contraction
Zone
Arc Column
e I
I
Electrons
Ions
Space Charge
Zone
Space Charge
Zone
CATHODE
ANODE
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.
SAHA’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 nonconducting.
5
2
2
7
2 3.16 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 Constant
i
e e
V
k
Saha’s Eqn. for
Different Gasses
SMALL TIME CONSTANTS
Temperature change to interrupt current cannot
be immediate, however, it can be very fast due to
the characteristic of the extinguishing medium
as seen from Saha’s equation.
The time it takes to cool down the plasma
channel is called conductivity time constant,
which depends on
Ion-electron recombination speed
Particle-velocity distribution
Consequence:
For the electric transient, the circuit arc is assumed
to be in the thermal-ionization equilibrium
108 sec
1010 sec
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 the
medium.
Contraction
Zone
Contraction
Zone
Arc Column
e I
I
Electrons
Ions
Space Charge
Zone
Space Charge
Zone
CATHODE
ANODE
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.
MATHEMATICALMODELSOFTHESWITCHINGARC
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 designnetwork studies
Parameter Models
more accurateblack box models
parameters are obtained from complex functions and tables
GENERALPHYSICALMODEL
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.
0gas densitygas flow velocitydivuut
GENERALPHYSICALMODEL
Conservation of momentum (Navier-Stokes equation)
Arc-plasma is electrically conducting in the momentum equation interaction with magnetic fields from the arc or generated outside are taken into account.
Conservation of energy:
Resistive heat dissipation of electric energy calculated with Ohmn’s law: volumetric heat generation term
Arc-plasma is strongly radiatingradiation transport of importance for energy equation
A portion of the radiated energy is reabsorbed by the plasma radiation-transfer equation or tabulated value fro the net emission coefficient.
gas densitygradgradpressuregas flow velocityuuupput
CONSERVATIONOFENERGY
Special Case: conservation equations become decoupled
Thermally and hydronamically fully developed and wall-constricted arc with negligible axial pressure drop, the conditions are in the zplane as follows
The energy equation becomes:
Used for qualitative evaluation of current increase or arc-channel diameter reduction.
2grad()div()div(),huhEuKgradTRTrtpressureenthalpy of gasthermal conductivitygas densityelectric field strengthgas temperaturegas flow velocityelectric conductivityradiation lossarc radiusphKETuRr21TKrrRErr000zruhuzz
BLACK-BOXMODELS
Consist on one or two differential equations.
Arc is described by a mathematical equation relating the arc conductance with the arc voltage and arc current
Classical models: Cassie, and Myar solutions to the general arc eqn.
GENERALARCEQUATION
Arc conductance is a function of:
Power supplied to the plasma channel,
Power transported by cooling and radiation, and
Time
1,,arcinoutarcigFPPtuR
GENERALARCEQUATION
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 arc equation
Solutions to this equation requires assumptions, black box models are solutions to the equation each with different assumptions.