U.S. patent application number 13/752541 was filed with the patent office on 2013-06-06 for method and apparatus for locating a parallel arc fault.
This patent application is currently assigned to Astronics Advanced Electronic Systems Corp.. The applicant listed for this patent is Astronics Advanced Electronic Systems Corp.. Invention is credited to Vitaliy Mosesov, Frederick J. Potter.
Application Number | 20130141111 13/752541 |
Document ID | / |
Family ID | 42931933 |
Filed Date | 2013-06-06 |
United States Patent
Application |
20130141111 |
Kind Code |
A1 |
Potter; Frederick J. ; et
al. |
June 6, 2013 |
Method and Apparatus for Locating a Parallel Arc Fault
Abstract
Methods to determine the location of an arc fault include a
first method utilizing the inherent resistance per unit length of
the wire. A second and a third method utilize an inherent
inductance per unit length of the wire. The second method derives
the inherent inductance from the output voltage and a rate of
current rise. The third method derives the inherent inductance from
a resonant frequency of an oscillating current. The information is
useful to locate a fault emanating from a wire member of a wiring
harness used to distribute power about an aircraft.
Inventors: |
Potter; Frederick J.;
(Trumbauersville, PA) ; Mosesov; Vitaliy;
(Bellevue, WA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Astronics Advanced Electronic Systems Corp.; |
Kirkland |
WA |
US |
|
|
Assignee: |
Astronics Advanced Electronic
Systems Corp.
Kirkland
WA
|
Family ID: |
42931933 |
Appl. No.: |
13/752541 |
Filed: |
January 29, 2013 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
12583396 |
Aug 19, 2009 |
8395391 |
|
|
13752541 |
|
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Current U.S.
Class: |
324/523 |
Current CPC
Class: |
G01R 31/085 20130101;
H02H 3/042 20130101; H02H 1/0015 20130101; G01R 31/50 20200101;
G01R 31/086 20130101; G01R 31/52 20200101; G01R 31/008
20130101 |
Class at
Publication: |
324/523 |
International
Class: |
G01R 31/08 20060101
G01R031/08 |
Claims
1. A method to measure a distance to an arc emanating from a wire
having a voltage source and electronic circuit breaker at a first
end thereof and a load at a second end thereof, comprising the
steps of: obtaining an output voltage, V.sub.0, of said voltage
source and a peak current, I.sub.arc(peak), of said circuit;
calculating a resistance of said wire up to said arc from:
R.sub.wires=V.sub.0/I.sub.arc(peak); and utilizing an inherent
resistance per unit of length of said wire to determine a distance
from said voltage source to said arc.
2. The method of claim 1 wherein said wire is bundled in a wiring
harness having a plurality of parallel running wires and said
wiring harness is installed on an aircraft.
3. The method of claim 2 wherein said arc extends from said wire to
a second wire and R.sub.wires is the sum of the resistance of said
wire and said second wire from said voltage source to said arc.
4. The method of claim 2 including calculating a Critical Length of
said wire beyond which a short circuit current drops below a 10x
rating for said electronic circuit breaker whereby if said
electronic circuit breaker trips, then said distance to said arc is
less than said Critical Length.
5. The method of claim 2 wherein said arc extends from said wire to
an airframe of said aircraft and R.sub.wires is the resistance of
said wire from said voltage source to said arc.
6. The method of claim 1, wherein V.sub.o is obtained by measuring
the output voltage of the electronic circuit breaker.
7. The method of claim 1, further comprising estimating an error in
said distance determination, by assuming a value for resistance of
said arc R.sub.arc; and calculating the error as
R.sub.arc/R.sub.wires, the error being expressed as a
percentage.
8. The method of claim 1, further comprising estimating an error in
said distance determination, by estimating an arc current
I.sub.arc; assuming a value for resistance of said arc R.sub.arc;
and calculating the error as I.sub.arc*R.sub.arc/V.sub.0, the error
being expressed as a percentage.
9. The method of claim 8, further comprising using the value of
I.sub.arc(peak) for I.sub.arc to estimate a minimum error.
10. The method of claim 8, further comprising assuming R.sub.arc=0;
and calculating a critical length of said wire in accordance with
the wire gauge and a rating value for said circuit breaker.
11. The method of claim 10, wherein the critical length for said
wire gauge is the length for which a hard fault results in an
I.sup.2t trip at the circuit breaker.
Description
CROSS REFERENCE TO RELATED APPLICATION(S)
[0001] This patent application is a division of U.S. patent
application Ser. No. 12/583,396, titled "Method and Apparatus for
Locating a Parallel Arc Fault," that was filed on Aug. 19, 2009.
The disclosure of that patent application is incorporated by
reference in its entirety herein.
U.S. GOVERNMENT RIGHTS
[0002] N.A.
BACKGROUND
[0003] 1. Field
[0004] This invention relates to methods and systems to determine
the location of an arc fault between adjacent wires in a wiring
harness, such as used to provide power to widely separated
locations and components on an aircraft. More particularly, by
utilizing length dependent properties of the wires, such as
resistance and inductance, the distance to a remote parallel
arc-fault may be calculated.
[0005] 2. Description of the Related Art
[0006] Aircraft require electrical power delivered to widely
separated locations throughout the aircraft. Flight crucial
circuits include external lighting, instrument panels and
communications. Non-flight critical circuits include in-flight
entertainment systems and galleys. One or more generators on the
plane satisfy the aircraft electrical system requirements and
typically produce 115 volts AC, 400 hertz. Some present day
electrical components utilize 28 volts DC. Other voltage
requirements, such as 270 volts DC and variable frequencies, are
being considered for future aircraft. The electrical power is
delivered from the generators to the electrical systems through
wiring harnesses that contain bundles of wires. Such harnesses may
include in excess of 50 wires and have wires of variable lengths,
from under 5 feet up to several hundred feet in length.
[0007] The bundled wires are individually coated with a polymer
insulator, such as polyimide. Over time, and due to environmental
factors such as heat, the insulation may wear away or crack
exposing an encased conductor. If two conductors are exposed in
close proximity, an electric current may arc from one conductor to
the other. Arcing may also occur between a single exposed conductor
and the airframe. This type of fault is referred to as a parallel
arc fault. Arcing can degrade insulation of adjacent wires and is a
fire hazard. Therefore, it is necessary to suppress the arc as
quickly as possible. Thermal circuit breakers were developed to
protect the wire insulation on aircraft from damage due to
overheating conditions caused by excessive over-current conditions.
The thermal circuit breakers are generally not effective to protect
against an arc fault. The arc fault is often an intermittent
problem occurring during a specific condition, such as in-flight
vibration of an aircraft frame. The arc is transient, frequently on
the order of milliseconds, such that a current overload and thermal
increase does not occur, rendering a thermal circuit breaker
ineffective.
[0008] A circuit interrupter that detects an arc fault and
interrupts the flow of current is disclosed in U.S. Pat. No.
5,682,101 to Brooks, et al. The patent discloses a method to detect
an arc fault by monitoring the rate of change of electrical current
as a function of time (di/dt) and generating a pulse each time
di/dt is outside a predetermined threshold. An arc fault signal is
sent to a circuit breaker or other safety device if the number of
pulses per a specified time interval exceeds a threshold. U.S. Pat.
No. 5,682,101 is incorporated by reference in its entirety
herein.
[0009] An electronic circuit breaker that detects arc faults
enhances aircraft safety, but does not assist in determining the
location of the fault. Wiring bundles on an aircraft may extend for
several hundred feet and are typically inaccessible, such as under
floorboards or extending through wing struts. Locating a fault is
time consuming and requires considerable effort to access the wire
bundle. U.S. Pat. No. 7,253,640 to Engel, et al. discloses a method
to determine a distance to an arc fault that employs the value of
the peak arc current, the wire resistance per unit length, and a
nominal peak line to neutral voltage value. A constant arc voltage
or an arc voltage as a function of the value of the peak current is
then provided to calculate the distance from the arc fault detector
to the arc fault. U.S. Pat. No. 7,253,640 is incorporated by
reference in its entirety herein.
[0010] Using wire resistance to locate an arc fault is of limited
value. The magnitude of resistance of the wires is typically in the
milliohm range while the resistance of the arc is unpredictable and
variable and can be from zero to tens of ohms. As a result, this
method is prone to large error.
[0011] There remains, therefore, a need for a method and system to
more accurately locate an arc fault to thereby more readily
facilitate repair of damaged insulation and wires.
BRIEF SUMMARY
[0012] The details of one or more embodiments of the disclosure are
set forth in the accompanying drawings and the description below.
Other features, objects and advantages will be apparent from the
description and drawings, and from the claims.
[0013] It is an object to provide herein methods and systems for
determining the location of an arc fault, such as emanating from a
wire member of a wiring harness of an aircraft. A first method
utilizes an inherent resistance per unit length of the wire. Second
and third methods utilize an inherent inductance per unit length of
the wire. The second method derives the inherent inductance from
the output voltage and a rate of current rise. The third method
derives the inherent inductance from a resonant frequency of an
oscillating arc current.
[0014] The first method includes the steps of measuring a distance
to an arc emanating from the wire by obtaining an output voltage
and a peak current, calculating a resistance of the wire up to the
arc from R.sub.wires=V.sub.0/I.sub.arc(peak) and then utilizing an
inherent resistance per unit of length of the wire to determine a
distance to fault.
[0015] The second method includes the steps of measuring a distance
to an arc emanating from the wire by obtaining an output voltage
and a rate of current rise as a function of time, di/dt,
calculating an inductance of the wire from
L.sub.wire=V.sub.source/(di/dt) utilizing an inherent inductance
per unit of length of the wire to determine a distance to
fault.
[0016] The third method includes the steps of measuring a distance
to an arc emanating from the wire by isolating the voltage source
from the wire with a decoupling inductor, inserting an output
capacitor between the decoupling inductor and a load, measuring a
resonant frequency of a current oscillating around a loop defined
by the output capacitor, the inductance of the wire, the arc and a
ground, calculating an inductance of the wire up to the arc and
utilizing an inherent inductance per unit of length of the wire to
determine a distance to fault.
[0017] A system to utilize the third method includes a voltage
source, a load, a wiring harness having a plurality of parallel
running insulated wires with at least one of the plurality of wires
electrically interconnected to the voltage source and to the load.
A decoupling inductor is disposed between the voltage source and
the wiring harness and is effective to provide RF isolation of the
voltage source from the wiring harness. An output capacitor is
disposed between the decoupling inductor and the wiring harness. An
output buffer is effective to store data related to a waveform
oscillating around a loop defined by the output capacitor, the
wire, an arc bridging the wire and a ground, and the ground
return.
BRIEF DESCRIPTION OF THE DRAWINGS
[0018] FIG. 1 illustrates in cross-sectional representation an
aircraft wiring harness as known from the prior art.
[0019] FIG. 2 illustrates a parallel arc fault between two wires
contained within the wiring harness of FIG. 1.
[0020] FIG. 3 is a circuit model of a parallel arc fault for
detection by wire resistance measurement in accordance with a first
embodiment.
[0021] FIG. 4 is block diagram of a system to locate an arc fault
detected by the wire resistance method.
[0022] FIG. 5 is a circuit model of a parallel arc fault for
detection by change in current (di/dt) as a factor of time in
accordance with a second embodiment.
[0023] FIG. 6 is block diagram of a system to locate an arc fault
detected by the di/dt method.
[0024] FIG. 7 is a circuit model of a parallel arc fault for
detection by inductance-capacitance-resistance (LCR) oscillation in
accordance with a third embodiment.
[0025] FIG. 8 is block diagram of a system to locate an arc fault
detected by the LCR oscillation method.
[0026] FIG. 9 illustrates di/dt as a function of the distance to
fault in accordance with the second embodiment.
[0027] FIG. 10A illustrates the percent error in the computation of
distance to fault from FIG. 9 when R.sub.arc is 1 ohm and FIG. 10B
illustrates the percent error when R.sub.arc is 2 ohms.
[0028] FIG. 11A illustrate a waveform from the second embodiment
when R.sub.arc is about zero and FIG. 11B illustrates a waveform
when R.sub.arc is 7.5 ohms.
[0029] FIG. 12 illustrates frequency as a function of the distance
to fault in accordance with the third embodiment.
[0030] FIG. 13 illustrates the percent error in the computation of
distance to fault from FIG. 12 when R.sub.arc is 0 ohm.
[0031] FIG. 14A graphs arc current, arc voltage and source voltage
for a 19 foot distance to fault and FIG. 14B graphs those
parameters for a 25 foot distance to fault.
[0032] FIG. 15A illustrates oscillation damping when the arc
resistance is 7.5 ohms, FIG. 15B when the arc resistance is 15 ohms
and FIG. 15C when the arc resistance is 30 ohms.
[0033] FIG. 16 is a waveform illustrating arc current and arc
voltage for a 19 foot distance to fault.
[0034] FIG. 17 is a waveform illustrating irregular arc
voltage.
[0035] FIG. 18 is a fast fourier transform (FFT) analysis of the
waveform of FIG. 14B.
[0036] FIG. 19 is a fast fourier transform analysis of the waveform
of FIG. 15B.
[0037] FIG. 20 is a waveform illustrating rapid voltage noise prior
to oscillation.
[0038] FIG. 21 is a waveform illustrating rapid voltage noise
around the resonant frequency.
[0039] FIG. 22 is a waveform illustrating a relatively weak
signal.
[0040] Like reference numbers and designations in the various
drawings indicated like elements.
DETAILED DESCRIPTION
[0041] FIG. 1 illustrates a wiring harness 10 in cross-sectional
representation. A restraining band 12 supports a bundle of wires
14. Each wire 14 has an electrically conductive core 16 sheathed in
an electrically insulating jacket 18. Typically, the jacket 18 is a
polymer, such as a polyimide. The bundle may contain in excess of
fifty wires 14.
[0042] With reference to FIG. 2, the bundles of wires 14 extend
throughout the aircraft and deliver power to widely separated
systems and components. The lengths of wires in the bundles may be
from under five feet to in excess of several hundred feet. The
bundles travel in areas where space is available, areas frequently
having limited accessibility, such as between a cabin floor 20 and
a ceiling 22 of a cargo hold. Individual wires 14' separate from
the bundle at required locations. For example, the wire 14' may
provide power to an in-seat power supply unit for an in flight
entertainment system.
[0043] If the insulating jackets 18 fail on two wires 14 in
proximity, an arc fault may occur. While an electronic circuit
breaker, as known from the prior art, is effective to stop the flow
of current in the affected wires, locating the fault and repairing
the fault in a potentially inaccessible location has, until now,
proven difficult. Following are three methods and systems to locate
the fault and facilitate repair.
[0044] A first method to estimate the location of an arc fault
utilizes wire resistance. A circuit modeling the harness is
illustrated in FIG. 3 and FIG. 4 is a block diagram of a system to
locate an arc fault by the wire resistance method.
[0045] The resistance of the wiring harness represented by
R.sub.wire 24 is the total of all resistance in series with the arc
26. If the arc 26 is to the airframe 28, than it is the resistance
of the single wire that is arcing, as shown in FIG. 3. If the arc
is between two wires, the resistance is the total resistance of
both wires. Uncertainty of the total resistance is one reason a
resistance measurement system is inaccurate.
[0046] The resistance of the arc represented by R.sub.arc 30;
[0047] The voltage of the source 32, e.g. generator output, is
represented by V.sub.source;
[0048] The in-series resistance of the electronic circuit breaker
(ecb) and the voltage source is represented by
R.sub.source+R.sub.ecb.
[0049] The resistance of the wire relates the current and the
voltage by Ohm's law:
R.sub.wire=V.sub.o/I.sub.arc(peak) (1)
[0050] Where I.sub.arc(peak) is peak measured current in the
circuit and V.sub.o is measured output voltage of the electronic
circuit breaker 34. The distance to fault (DTF) is then the
measured value for R.sub.wire 24 divided by the inherent resistance
per unit of length value for the wire gauge and composition.
[0051] Error in the circuit model of FIG. 3 comes from the unknown
arc resistance 30 that created voltage drop V.sub.arc across it. In
an ideal scenario, the voltage drop across the wires is equal to
the V.sub.o. However in reality, the arc resistance 30 will cause
V.sub.o to be divided between V.sub.wire and V.sub.arc introducing
an error. When I.sub.arc is at a maximum we can assume that arc
resistance is at a minimum and most of the V.sub.o is dropped
across the R.sub.wire reducing this error term to a minimum. The
percent error in a DTF calculation is given by:
% Error=(I.sub.arc*R.sub.arc/V.sub.0)*100% (2)
or as a ratio of resistances:
% Error=(R.sub.arc/R.sub.wire)*100% (3)
[0052] The magnitude of R.sub.wire 24 is typically in milliohms
range while R.sub.arc 30 is unpredictable and variable between 0
ohm and tens of ohms. Because of this possible error range, this
method has limited use. The method can, however, be used to do an
initial prediction where a fault might be located. If the peak arc
current is large enough where it can actually be caused by
resistance of the installed harness, an assumption can be made that
the arc resistance 30 is 0 ohm. This typically is a brief condition
that can occur during the arc fault when the faulty conductors
briefly weld themselves together. Fast response point of the ECB 34
can also be used to predict the section of the wire where the fault
occurred. If arc resistance 30 is at 0 ohms, every wire gauge will
have a critical length for which hard faults will always result in
an I.sup.2t (a common rating value for circuit breakers where I is
current and t is time) trip and never a fast response loop. This
information can be used to predict where the fault is located.
[0053] A second method to estimate the location of an arc fault 26
utilizes inductor di/dt 36. A circuit modeling the harness with the
wire inductance L.sub.wire 38 and wire resistance R.sub.wire 24 in
series is illustrated in FIG. 5. FIG. 6 is a block diagram of the
system to locate an arc fault by the inductor di/dt method. The
system is similar to that illustrated in FIG. 4 for the wire
resistance method except that the microprocessor 40 does a
different set of calculations using the same basic data.
[0054] R.sub.arc 30 is the resistance of the arc 26.
[0055] V.sub.source is the source 32 voltage.
[0056] R.sub.source is the source 32 resistance.
[0057] R.sub.ecb is the resistance of an electronic circuit breaker
34.
[0058] R.sub.source+R.sub.ecb are in series resistance of the
circuit breaker and the voltage source.
[0059] Before a parallel arc fault event, an initial condition is
established by the current flowing from the source 32 into the load
42. When an arc 26 strikes at some distance from the circuit
breaker 34, it forms a closed loop defined by L.sub.wires,
R.sub.wires, R.sub.arc, V.sub.source, R.sub.source and R.sub.ecb.
The circuit can be described by analyzing a step response typical
of an LR circuit. Due to the influence of L.sub.wires, the arc
current does not rise to its final value instantaneously. The rate
of current rise, di/dt 36, is a function of inductance and voltage
drop across L.sub.wires:
L.sub.wires=V.sub.source (di/dt) (4)
Or
di/dt=V.sub.source/L.sub.wires (5)
[0060] A more accurate equation takes into account the voltage drop
associated with its series resistance:
V.sub.source-i(t)R.sub.source-i(t)R.sub.ecbi(t)R.sub.wire-i(t)R.sub.arc=-
L.sub.wires*di/dt (6)
where:
[0061] i(t) is current flowing through the harness at time, t.
[0062] R.sub.arc is resistance of an arc 26 when the arc
strikes.
[0063] As a first order approximation, we assume that R.sub.ecb and
R.sub.source are sufficiently low so that V.sub.source=V.sub.o.
[0064] We can also assume that R.sub.wires<<R.sub.arc and can
be approximated to be 0 ohms.
[0065] The equation for the inductance of the wires 38 is then
given by:
L.sub.wires=(V.sub.source-i(t)R.sub.arc)/(di/dt) (7)
In the absence of R.sub.arc 30, the rate of current rise di/dt 36
is simply a ratio of V.sub.source/L.sub.wires. However, resistance
of an arc 30 is an unknown and unpredictable value resulting in an
error term in the equation given by i(t)R.sub.arc as a voltage drop
across the arc 26 itself. The instant when the switch closes the
original steady state I.sub.load current is maintained through the
arc setting the initial condition. That current will establish
initial voltage drop across the arc resistance 30. The actual
current I(t) is given by:
I(t)=(V.sub.source/R.sub.arc)+(I.sub.load-(V.sub.source/R.sub.arc))exp(R-
.sub.arc/L.sub.wires)*t (8)
and the actual di/dt is given by:
di/dt=((V.sub.source-R.sub.arc*I.sub.load)/L.sub.wires)exp(R.sub.arc/L.s-
ub.wires)*t (9)
di/dt is dependent on the length of the closed loop, one segment of
which is the arc fault. Therefore, knowing di/dt enables a
calculation of the DTF by calculating the inductance of the fault
loop: V.sub.source.times.dt/di=L.sub.wire. For a particular wire
gauge and type, there is a constant inductance per linear foot, K
(.mu.H/ft). Then calculate the distance to the fault:
DTF=1/2(L/K).
[0066] As seen from the equations, the actual rate of current rise
in the circuit is not a constant value, rather the current
increases exponentially approaching V.sub.source/R.sub.arc as final
value. A percent error in distance to fault calculations can be
thought of as the difference between expected and actual voltage
across L.sub.wires. That difference is the voltage across
R.sub.arc. If V.sub.source is the expected voltage drop when
R.sub.arc=0 ohm, then:
%
Error=-(i(t)R.sub.arc)/V.sub.source)*100%=[((V.sub.source-R.sub.arc*t.-
sub.oad)exp(R.sub.arc/L.sub.wires)*t)/V.sub.source]*100% (10)
Percent error in measuring di/dt and thus in distance to fault
computation depends on several variables: the resistance of the
arc, initial load current and time of measurement. Resistance,
R.sub.arc, can be viewed as the sum of every in-series resistance
shown in Equation 6 for more accurate error prediction.
[0067] A third method to estimate the location of an arc fault
utilizes the resonant frequency of LCR oscillation. A circuit
modeling the harness 10 with oscillating circuit 44 is illustrated
in FIG. 7. FIG. 7 shows a simplified schematic of the source 32,
electronic circuit breaker 34, harness 10 and load 42 system.
L.sub.decoupling is an output inductor 46 at the output of the
circuit breaker 34 that serves as a decoupling element separating
in frequency the source 32 from the harness 10
(L.sub.decoupling>>L.sub.wires) at high frequencies. Before
the parallel arc fault event 26 strikes, there is an initial steady
state condition where the load 42 draws current from the source 32
(I.sub.load). At this point, the output capacitor 48 of the circuit
breaker 34, C.sub.out is fully charged to the V.sub.o voltage. When
the arc 26 strikes, an LCR loop is formed by C.sub.out,
L.sub.wires, R.sub.wires+R.sub.arc. Due to the presence of the
output inductor 46, the circuit to the left of V.sub.o is
effectively decoupled from an AC perspective.
[0068] At this instant we can examine the portion of the circuit
formed by C.sub.out-L.sub.wires-R.sub.wires-R.sub.arc only. Output
capacitor 48 C.sub.out starts to transfer stored energy via
in-series resistance R.sub.wires and R.sub.arc to the inductor 50
formed by L.sub.wires. When all the stored energy is transferred to
the inductor 50, the inductor 50 starts to charge back the output
capacitor 48 with opposite polarity. The cycle continues creating
an oscillating current 44 that decays exponentially due to the
presence of R.sub.wires and R.sub.arc. The frequency of this
oscillation is a function of L.sub.wires and C.sub.out. The
resonant frequency range is set by the initial value of the output
capacitor 48. The higher the initial value, the lower the resonant
frequency range. While higher frequency ranges are advantageous,
providing greater sensitivity (change in frequency per foot) and
longer oscillation time, the advantages come at the expense of
increased hardware complexity. Also, a smaller initial value may
increase the effect of an error introduced by parasitic capacitance
of the harness 10. An exemplary initial value for the output
capacitor is between 1 and 15 nF and a preferred range is between 2
and 5 nF.
[0069] Oscillating circuit 44 behavior can be described by
analyzing the natural response of a typical LCR circuit. Damping
factor, a, ideal resonant frequency .omega..sub.o and damped
resonant frequency .omega..sub.d (actual resonant frequency
adjusted from ideal due to damping factors) are given by:
.omega..sub.o=1/(L.sub.wires*C.sub.out).sup.0.5 (11)
.alpha.=(R.sub.wires+R.sub.arc)/(2*L.sub.wires) (12)
.omega..sub.d=(.omega..sub.o.sup.2+.alpha..sup.2).sup.0.5 (13)
Under-damped oscillation will occur if the combined in-series
resistance of the wires 24 and of the arc 30 is less than the
critical resistance value:
.omega..sub.o.sup.2>.alpha..sup.2 (14)
or
(R.sub.wires+R.sub.arc)<2*(L.sub.wires/C.sub.out).sup.0.5
(15)
[0070] For the typical length wire contained in wiring harness 10,
resistance 24 is in milliohms range and can be omitted from
equation 15 causing the arc resistance 30 value to be the decisive
factor whether or not oscillation will occur. We estimate the worst
case value for the right side of the inequality to be somewhere
around 7.5 ohms (assuming the output capacitance 48 to be no more
than 0.1 .mu.F and the minimum wire inductor 50 to be 1.4 .mu.H)
which is about 5 feet of AWG 14 wire. The worst case arc resistance
30 must be less than that to satisfy the equation.
[0071] Equations for the current and voltage in the under-damped
LCR circuit are given by:
I.sub.osc(t)C.sub.le.sup.-.alpha.t
cos(.omega..sub.dt)+C.sub.2e.sup.-.alpha.t sin(.omega..sub.dt)
(16)
V.sub.0=I.sub.osc(t)(R.sub.wire+R.sub.arc)+L.sub.wire*dI.sub.osc/dt
(17)
[0072] Constants C.sub.1 and C.sub.2 are set from the initial
current condition in the circuit. At the time t=0, current through
the wire inductor 50 is I.sub.load setting the constant C.sub.1
equal to I.sub.load. C.sub.2 can be found by taking a derivative of
the I.sub.osc(t) and equating that to the (dI.sub.osc/dt) from the
voltage Equation 17 at the instant when output capacitor 48 starts
discharging into wire inductor 50. At this instant voltage
V.sub.o-(R.sub.wire+R.sub.arc)I.sub.load is dropped across the wire
inductor 50 and series resistance 24, 30 producing:
C.sub.2=(V.sub.0-(R.sub.wire+R.sub.arc)*I.sub.load)/.alpha.*L.sub.wire
(18)
Where [(R.sub.wire+R.sub.arc)*I.sub.load] is an initial voltage
across the wire and the arc resistance 30 is at the instant the arc
strikes. This voltage is a result of initial steady state
I.sub.load. Another useful parameter is the total time of the
oscillation as amplitude drops to 10% of the initial maximum. This
is found by setting the damping coefficient equal to 0.1 and
solving for time t (0.1=e.sup.-.alpha.t).
t.sub.max-10%=4.6L.sub.wire/(R.sub.wire+R.sub.arc) (19)
[0073] Unlike the method for locating a fault using inductor di/dt
described above, as seen from Equation 16, in the present method
the frequency of oscillation does not depend on initial load
current I.sub.load or time meaning that the DTF may be accurately
determined by the resonant frequency. Using fixed value output
capacitor 48 of the ECB 34 as C and solving for L, wire inductance,
=(1/.omega.).sup.2)/C. As with the di/dt method, for a particular
wire gauge and type, there is a constant inductance per linear
foot, K (.mu.H/ft). Then calculate the distance to the fault:
DTF=1/2(L/K). The percent error in resonant frequency introduced by
the arc resistance 30 can be estimated from the difference between
ideal resonant frequency .omega..sub.o and the actual resonant
frequency .omega..sub.d:
%
Error=100%*[(.omega..sub.d-.omega..sub.0)/.omega..sub.0=100%*{[1-(C.su-
b.out*C.sub.arc.sup.2)/4L].sup.0.5-1} (20)
[0074] Constraints in the design of hardware for utilizing the LCR
oscillation method include:
[0075] LCR oscillation event happens once, in a brief time period
<50 .mu.S. The circuit must be ready to respond and process the
signal first.
[0076] LCR oscillation event happens much earlier than actual
electronic circuit breaker trip. It is preferred to have a reliable
way to recognize and trigger on the event prior to an ECB 34
trip.
[0077] The circuit must be able to process frequencies of at least
3 Mhz. An ability to process higher frequencies is beneficial.
[0078] Preferably, the waveforms may be stored for diagnostic
purposes.
[0079] Digitizing, storing and processing the waveform offers a
potential solution. Once the waveform is digitized and stored in
the memory it can be processed at a later time when a relatively
slow host processor is ready to analyze the data (e.g. when the
electronic circuit breaker 34 is tripped and the host processor is
idle again). A system block diagram is shown in FIG. 8. The output
capacitor 34 sets the frequency range of operation. The signal is
first filtered with an analog bandpass filter 52 that is tuned to a
frequency range where LCR oscillation is expected to occur, such as
in the range of between 585 kHz and 3 MHz. This filter 52 also
serves as an antialiasing filter before an A/D converter 54. Output
of the bandpass filter 52 is fed into the A/D converter 54
constantly sampling at 6-10 Ms/s. The A/D converter 54 writes
directly into a circular buffer memory without requiring processor
involvement.
[0080] In a worst case scenario circular buffer 56 must be large
enough to store the waveform data from the instant the arc 26
occurs to the time when the ECB 34 recognizes the event and trips.
At this point the event trigger 58 will send a stop signal 60 to
the A/D converter 54. This time window can be anywhere from tens of
microseconds to hundreds of milliseconds depending on the fault
conditions. At the 6 Ms/s rate, a 10 bit A/D converter 54 will
constantly deliver 750 kBytes of data for every 100 ms into the
circular buffer 56 to be processed in the event of trip. For a 10
Ms/s rate, that number will double.
[0081] Another approach is to implement an analog event trigger 58
circuit that will stop 60 the A/D converter 54 independent of
microprocessor 40 when LCR oscillation 44 is detected. This circuit
can be as simple as a rectifier, averager/integrator and a
comparator that will constantly monitor the output of the band pass
filter 52. Reducing the trigger time will reduce the total waveform
sample size. As soon as the microprocessor 40 is ready to process
the data, it will use a built in algorithm (such as fast fourier
transform analysis (FFT) with ability to locate frequency peaks) to
perform the distance to fault (DTF) evaluation and transfer the
waveform data to an external host as needed.
[0082] Success of the methods described above in locating an arc
fault in real time depends on the arc fault event itself, magnitude
of R.sub.arc and arc voltage. The percent error in method two,
utilizing inductor di/dt, is a function of initial load current,
resistance of the arc and time. When R.sub.arc is approximately 0
ohms, the expected vs. measured di/dt was within 2% error
indicating that this method will work if R.sub.arc is close to 0
ohms or when conductors are briefly welded together to produce low
section feeding into the electronic circuit breaker that adds
inductance as well as any internal inductors that are in series
with the harness.
[0083] Unlike the first method, utilizing wire resistance, and the
second method, an apparent advantage of method three, utilizing the
resonant frequency of LCR oscillation, is that the distance to
fault computation depends less on resistance of an arc and does not
depend on load current, time or wire sections feeding to the
electronic circuit breaker. From the experimental data that
follows, we conclude that method three offers the most potential as
a solution for real time distance to fault measurements. However,
it is also the most complex of three to implement.
[0084] The first method is the easiest to implement. But since with
this method of distance to fault determination depends only on
resistance of the wires, a significant error can potentially be
introduced by the unknown arc resistance that falls in series with
the resistance of the wires. Despite that, this technique can still
be used to initially predict the distance range or section of the
wire where the fault is located by using the peak current draw
during the arc fault event to report one of the two possible
outcomes: fault occurred within critical distance length of the
wire or fault location is uncertain. Minimum hardware, if any at
all, changes would be required to implement the first method into a
current electronic circuit breaker.
[0085] Advantages of the methods and systems described above will
become more apparent from the Examples that follow:
EXAMPLES
Example 1
Wire Resistance Method
[0086] The data below was collected to determine the critical wire
length point for different wire gauges and electronic circuit
breakers fast trip points. The fast response trip point was set at
10.times. and the input voltage set at 28V DC. The critical length
point of the wire is derived directly from the resistance value
beyond which the short circuit current drops below the 10.times.
rating of the circuit breaker. This point can be defined as a
critical resistance.
R.sub.critical resistance=V.sub.0/10.times.ECB Rating (21)
Critical length of the wire with given AWG can be calculated
by:
Critical Length=R.sub.critical 0/R per unit length (22)
Resistance per unit of length is a characteristic of a wire having
a given AWG. Table 1 shows some Critical Resistance and Critical
Length values for ECBs and measured wire gauges.
TABLE-US-00001 TABLE 1 ECB Resistance per Critical Critical Rating
Gauge ft. Resistance Length (Amps) (AWG) (mOhms/ft) (Ohms) (ft) 2.5
18 6.38 0.92 144 7.5 16 4.02 0.31 77 15 14 2.53 0.15 61 25 10 1.00
0.092 92 30 8 0.63 0.077 121
[0087] Table 1 can be used to compute critical length with any
combination of ECB 10.times. rating and wire gauge. As an example
for a 15 A breaker using 16 AWG wire:
TABLE-US-00002 ECB Rating AWG MOhms/foot Critical resistance
Critical length 15A 16 .02 0.15 37 feet
Suggesting if electronic circuit breaker results in a hard trip,
the fault is within 37 feet of wire.
Example 2
Using Inductor di/dt Method
[0088] The experimental set up was 17 feet of 14 AWG wire. The
inductance of AWG 14 wire was measured to be 283.8 nH per foot. The
17 feet of AWG 14 wire had an inductance of 4.82 .mu.H and
R.sub.wire was 0.067 ohm. The voltage source delivered 28V DC. For
the purposes of initial evaluation it was assumed that a typical
aircraft AC voltage source appears as a DC source for the duration
of the di/dt events described herein. The half cycle time of the
400 Hz source frequency is 1.25 ms which is much greater than the
typical range for the time content of LR circuit (<10 .mu.S)
Behavior of the setup can be predicted by using previously derived
equations. di/dt rise time vs. distance to fault when R.sub.arc=0
ohm is illustrated in graph form in FIG. 9.
[0089] The FIG. 9 distance to fault graph is a non-linear curve
with a maximum resolution (change in di/dt per foot) of 3.9
amps/.mu.Sec per foot at 5 feet and a minimum resolution of
0.006863 amps/.mu.Sec per foot at 120 feet. The percent error in
computing distance to fault for the above setup with 17 feet of AWG
14 wire is given by Equation 10 and plotted on FIGS. 10A and 10B.
These graphs are plotted for different value of initial load
current (0, 5, 10, 20 amps). On FIG. 10A, R.sub.arc is 1 ohm and on
FIG. 10B, R.sub.arc is 2 ohms.
[0090] The percent error graphs show that measured di/dt value will
deviate by more than 15% from ideal at t=1 .mu.sec when R.sub.arc
is 1 ohm and I.sub.load is 0 amp. With increased initial load
current the error will increase further. The expected di/dt with 17
feet of AWG 14 wire and R.sub.arc=0 ohm is di/dt=28V/4.8 .mu.H=5.8
A/.mu.Sec. FIGS. 11A and 11B show the captured waveforms showing
the i(t) for the R.sub.arc.about.0 ohm (FIG. 11A) and 7.5 ohm (FIG.
11B) with I.sub.load at 3 amps (FIG. 11A) and 0 amp (FIG. 11B).
With presence of R.sub.arc, the di/dt is distorted from ideal. With
7.5 ohms R.sub.arc and 3.0 amps for I.sub.load, di/dt is measured
to be 3.25 amps/.mu.Sec approximated by a line from 0-1 .mu.Sec
time period which results in a 43% error. When R.sub.arc is near 0
ohms, di/dt was measured to be 6 Amps/.mu.Sec which deviates by 2%
from the expected value.
Example 3
Resonant Frequency of LCR Oscillation
[0091] The set up included 19 feet and 25 feet of 14 AWG wire. The
inductance of the AWG 14 wire was 283.8 nH per foot. The 19 feet of
AWG 14 wire had an inductance of 5.62 .mu.H with R.sub.wire=0.072
ohm. The 25 feet of AWG 14 wire had an inductance of 7.09 .mu.H of
inductance with R.sub.wire=0.145 ohm. The voltage source was DC at
28V with L.sub.decoupling=5 mH. It was assumed that the typical
aircraft AC voltage source may be considered a DC source for the
LCR oscillation events evaluated. The half cycle time of a 400 Hz
source frequency is 1.25 ms which is much greater than the typical
duration of an LCR oscillation, which is typically 20-30
.mu.Sec.
[0092] The initial value for C.sub.out was 9.89 nF forcing the LCR
resonant frequency range to be around 272 kHz-1.3 MHz for AWG 14
wire of 5 ft-120 ft distance range. There was a significant decay
in amplitude of oscillation of the captured waveforms indicating
that energy was dissipated elsewhere in the circuit (most likely
through the L.sub.decoupling and source). Choosing a smaller value
of C.sub.out, and corresponding higher frequency range, has a
number of advantages. It provides greater change in frequency per
foot (.DELTA..omega..sub.o/ft), reduces the % Error that can
potentially be introduced by R.sub.arc as seen from Equation 20,
and increases the Critical Resistance value. A higher frequency
range will also allow longer oscillation time (less energy is
leaked through L.sub.decoupling) which results in higher signal to
noise ratio in frequency domain. At higher resonant frequencies we
can keep L.sub.decoupling relatively small, saving space and
reducing power dissipation of the ECB. But these advantages will
come at the expense of increased hardware complexity (faster A/D
converters, larger storage memory, longer processing time, etc).
Also, a smaller value for C.sub.out can potentially increase the
effect of an error introduced by parasitic capacitance of the
harness that appears in parallel to C.sub.out.
[0093] The experiment was repeated with C.sub.out of 2.17 nF
forcing the frequency range to be 585 kHz-2.86 Mhz with improved
results. The data that follows relates to this latter case. Before
data collection, behavior of the set up was estimated using the
above formulas. The worse case critical resistance point occurs
with minimum inductance wire at 5 ft. From Equation 15, this is
equal to 51.0 ohms. In other words, in order for the oscillation to
occur on the entire distance range (5 ft-120 ft) of the AWG 14 wire
the series resistance R.sub.arc+R.sub.wires (or simply
.about.R.sub.arc) must be less than 51.0 ohm. Frequency range vs.
distance to fault is plotted on FIG. 12 and is given by
f.sub.o=.omega..sub.o/2.pi.. The frequency vs. distance graph is a
non-linear curve with greatest change in frequency per foot being
284.5 kHz/ft at 5 feet and the smallest being 2.4 kHz/ft at 120
feet with an assumption that the typical harness length on an
aircraft is between 5 and 120 feet.
[0094] Expected resonant frequency at 25 feet is 1/(7.09 .mu.H*2.17
nF).sup.0.5=8.06*10.sup.6 rad/sec=1.283 MHz. Expected critical
resistance at 25 feet is 114.3 ohms.
[0095] Expected resonant frequency at 19ft. is 1/(5.62 .mu.H*2.17
nF).sup.0.5=9.05*10.sup.6 rad/sec=1.442 MHz. Expected critical
resistance at 19 ft is 101.8 ohms.
[0096] If we assume that the R.sub.arc is zero ohms, the percent
error in computing the distance to fault is given by Equation 20
and is plotted on FIG. 13.
[0097] FIG. 14 displays the arc current, arc voltage and V.sub.o at
19 foot (FIG. 14A) and 25 foot (FIG. 14B) fault locations. The
frequency of the oscillation was measured to be 1.47 Mhz for the 19
foot fault location and 1.25 Mhz for the 25 foot fault location,
with arc resistance near 0 ohm. The arc resistance was monitored by
monitoring the arc current and the arc voltage behavior. In order
to see the effect of arc resistance on overall waveform, R.sub.arc
was adjusted by using low inductance carbon composition resistors
in series with an arc itself. Increasing R.sub.arc also increases
the arc voltage. FIGS. 15A, 15B and 15C display the obtained
waveforms from the 25 ft fault locations.
[0098] Although an expected critical resistance for R.sub.arc is
above 100 ohms, the waveforms (FIGS. 15A, 15B and 15C) illustrate
that at 30 ohms of arc resistance the oscillation is already
severely damped. At R.sub.arc=30 ohms, the percent error in
resonant frequency and corresponding distance to fault is minimal,
less than 5%. The measured frequency of resonant oscillation was
1.25 Mhz, slightly less than the expected value of 1.28 Mhz,
resulting in 2.3% error. An observed sharp decay in amplitude of
the captured waveforms cannot be entirely attributed to the
in-series arc and wire resistance only. Energy stored in the LCR
loop has many ways of escaping. Some of it is dissipated through
L.sub.decoupling and eventually through the source itself. Although
L.sub.coupling presents relatively large impedance to LCR loop for
our frequency range, a portion of the energy will inevitably be
dissipated through it. Furthermore, inductance of the
L.sub.coupling is not a fixed value. A sharp rise of short circuit
current that the arc creates will start to saturate the core of the
L.sub.copuling causing its inductance and thus its impedance to
drop. This effect further dampens the amplitude of the resonant
oscillation.
[0099] Given the nature of the high current arc, at the instant
when a fault occurs, the arc voltage does not always drop to zero
volts in a step function. A zero volt arc voltage drop is usually a
brief short circuit condition during the arc fault event. On a
microscopic scale, motion on the faulty wires, vibration forces,
melting and rapid evaporation of metal all have a direct effect on
behavior of the arc voltage and thus arc resistance Waveforms on
FIG. 16 show the arc current and arc voltage captured during one of
the parallel arc faults on a 19 foot arc fault location. In this
example, the arc voltage drops exponentially from the instant a
fault occurs rather than in a step. Arc resistance follows the same
curve dropping to about 1.3 ohms when oscillation occurs. In cases
like this, where the arc resistance R.sub.arc does not drop in a
step function from infinite to zero, the damping factor will be
increased (and no longer be a static parameter) effectively
reducing the amplitude decay rate. However, the drop of R.sub.arc
is fast enough to have a minimum effect on the resonant frequency
of oscillation. V.sub.o waveform shows that the frequency of
oscillation is still 1.42 Mhz which is within 1% of the expected
frequency.
[0100] FIG. 17 illustrates another example of captured waveform
where arc voltage behaves irregularly before dropping to 0 volts.
LCR oscillation occurs 20 .mu.Sec from the instant of arc strike.
The amplitude of oscillation is significantly lower than in
previous cases. This is expected since initial energy stored in
C.sub.out is dissipated by an arc prior to the actual oscillation
event. In all the cases, with the set up used, presence of LCR
oscillation will occur if the arc resistance rapidly drops below 30
ohms at some point during arc fault event.
[0101] Frequency content of the captured waveforms can be examined
by applying a fast fourier transform analysis (FFT). FIG. 18 shows
an FFT waveform obtained from the time domain waveforms of FIG. 14B
and FIG. 19 shows an FFT waveform obtained from the time domain
waveforms of FIG. 15B. The sampling rate used to generate these
waveforms was 10 Ms/s and corresponds to general mid to upper range
A/D converters on the market. The FIG. 18 waveform shows FFT of the
frequency waveform where R.sub.arc is near 0 ohm. The FIG. 19
waveform shows FFT of the waveform with R.sub.arc=15 ohms. The
frequency peak occurs at 1.29 Mhz and is clearly visible in both,
however there is at least 14 dB reduction in magnitude due to 15
ohms added arc resistance.
[0102] FIGS. 20, 21 and 22 show FFT (on right hand side) for
several random waveforms of V.sub.o (on left hand side) obtained at
a 25 foot arc fault location. FFT was applied to the "raw" signal
without any preconditioning or filtering. The sample size for the
FFT covers the entire waveform in a time domain as shown on the
left. The frequency peak value in all of the waveforms was 1.30 Mhz
which is within 2% of the expected value. FIG. 20 illustrates rapid
voltage noise prior to oscillation. FIG. 21 illustrates rapid
voltage noise introduced halfway through the signal producing broad
frequency noise around the resonant frequency. FIG. 22 illustrates
a relatively weak signal.
[0103] FFT effectively isolates the frequency of interest from the
background noise induced by the sporadic behavior of the arc
voltage and can serve as one of the methods of determining the
frequency in real time. Its performance can be improved by limiting
the scan region to include only the location where actual LCR
oscillation occurs. Simplest way to achieve that is by introducing
a band-pass filter at the input tuned to the frequency range of
interest. Analog band pass filter at the input will attenuate all
the frequencies outside the expected range improving the FFT
performance.
[0104] One or more embodiments of the present invention have been
described. Nevertheless, it will be understood that various
modifications may be made without departing from the spirit and
scope of the invention. Accordingly, other embodiments are within
the scope of the following claims.
* * * * *