CIRCUIT BREAKER AND METHOD FOR
SENSING CURRENT INDIRECTLY FROM BIMETAL VOLTAGE
AND DETERMINING BIMETAL TEMPERATURE AND
CORRECTED TEMPERATURE DEPENDENT BIMETAL RESISTANCE
BACKGROUND OF THE INVENTION
Field of the Invention
This invention pertains generally to circuit interrupters and, more
particularly, to circuit breakers including a bimetal in series with separable contacts.
The invention also pertains to methods for determining bimetal temperature and/or
bimetal resistance.
Background Information
Circuit breakers are used to protect electrical circuitry from damage
due to an overcurrent condition, such as an overload condition or a relatively high
level short circuit or fault condition. In small circuit breakers, commonly referred to
as miniature circuit breakers, used for residential and light commercial applications,
such protection is typically provided by a thermal-magnetic trip device. This trip
device includes a bimetal, which heats and bends in response to a persistent
overcurrent condition. The bimetal, in turn, unlatches a spring powered operating
mechanism, which opens the separable contacts of the circuit breaker to interrupt
current flow in the protected power system.
In certain circuit breaker applications (e.g., without limitation, arc fault
detection), the voltage across the thermal bimetal element is employed as an indirect
measurement of the circuit breaker load current. Sensing current with a bimetal
element is complicated by the variation of that element's impedance as a function of
temperature. This variation results in inaccuracies in the measurement of the
amplitude of the measured current. For example, the bimetal element's impedance
can vary as much as about 70% with temperature over the normal operating range of
the circuit breaker depending upon the type of bimetallic material used.
As is typical with most metals, the bimetal impedance has a positive
temperature coefficient (PTC). In other words, resistance increases with temperature.
If the design of the circuit breaker electronics assumes that the bimetal resistance is
constant, then any resistance-temperature variation of the bimetal can introduce error

BRIEF DESCRIPTION OF THE DRAWINGS
A full understanding of the invention can be gained from the following
description of the preferred embodiments when read in conjunction with the
accompanying drawings in which:
Figure 1 is a block diagram of a circuit breaker in accordance with the
present invention.
Figure 2 is a block diagram in schematic form showing the electrical
model and the thermal model employed by the processor of Figure 1.
Figure 3 is a flowchart of an algorithm for the electrical and thermal
models of Figure 2.
Figure 4 is a flowchart of an electrical and thermal model algorithm in
accordance with another embodiment of the invention.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
As employed herein, the statement that a part is "electrically
interconnected with" one or more other parts shall mean that the parts are directly
electrically connected together or are electrically connected together through one or
more electrical conductors or generally electrically conductive intermediate parts.
Further, as employed herein, the statement that a part is "electrically connected to"
one or more other parts shall mean that the parts are directly electrically connected
together or are electrically connected together through one or more electrical
conductors.
The present invention is described in association with an arc fault
circuit breaker, although the invention is applicable to a wide range of circuit
interrupters.
Referring to Figure 1, a circuit breaker 2 includes a housing 4,
separable contacts 6 and a bimetal 8 electrically connected in series with the separable
contacts 6. The bimetal 8 includes a temperature dependent resistance 10 (Figure 2)
and an output 12 having a voltage 14 (Figure 2) representative of current 16 (Figure
2) flowing through the separable contacts 6. An operating mechanism 18 is structured
to open and close the separable contacts 6. A temperature sensor (T) 20 is disposed
distal from the bimetal 8 and includes an output 22 having a signal 24 representative
of ambient temperature.

A trip circuit 26 cooperates with the operating mechanism 18 to trip
open the separable contacts 6. The trip circuit 26 includes a first circuit 28 providing
a real-time thermal model function 29 and a second circuit 30 providing a trip
function 31 (e.g., without limitation, arc fault detection (AFD)). The first circuit 28
includes a first input 32 electrically interconnected with the output 12 of the bimetal 8
to input the voltage 14 (Figure 2) representative of the current 16 (Figure 2) flowing
through the separable contacts 6, and a second input 34 electrically interconnected
with the output 22 of the temperature sensor 20 to input the signal 24 representative of
ambient temperature. As will be discussed below in connection with Figures 2-4, the
real-time thermal model function 29 is structured to provide a corrected temperature
dependent resistance 36 (Figures 3 and 4) of the bimetal 8 as a function of the bimetal
voltage 14 (Figure 2) and the signal 24 representative of ambient temperature. In
turn, the thermal model function 29 provides an output 38 including a bimetal current
value 40 which is a function of the bimetal voltage 14 and the corrected temperature
dependent bimetal resistance 36. The AFD trip function 31 includes an input 42
having the current value 40 and an output 44 structured to actuate the operating
mechanism 18 in response to predetermined current conditions.
Examples of suitable arc fault detectors are disclosed, for instance, in
U.S. Pat. No. 5,224,006, with a preferred type described in U.S. Pat. No. 5,691,869,
which is hereby incorporated by reference herein.
Example 1
The first circuit 28 includes a suitable processor (uP) 46 structured to
repetitively execute an iterative algorithm (58 of Figure 3 or 58' of Figure 4) as the
real-time thermal model function 29. The uP 46 includes or cooperates with an
analog-to-digital converter (ADC) 48 and is structured to periodically input the
voltage 14 representative of current flowing through the separable contacts 6 and the
signal 24 (e.g., without limitation, voltage) representative of ambient temperature. As
will be discussed below in connection with Figures 2-4, the uP 46 measures bimetal
voltage 14 and circuit breaker ambient temperature, employs the thermal model
function 29 to estimate bimetal temperature 50 (Figures 3 and 4) and bimetal
electrical resistance 36 (Figures 3 and 4), and derives the circuit breaker current 86
(Figures 3 and 4) from these quantities. In particular, the uP 46 senses the voltage 24

representing ambient temperature and the bimetal voltage 14 using the ADC 48, and
processes that information using the algorithm 58 of Figure 3 or 58' of Figure 4 to
provide the circuit breaker current 86.
Example 2
The ambient temperature is within the circuit breaker housing 4. The
uP 46 employs the temperature sensor 20 (e.g., without limitation, a thermistor,
disposed distal (i.e., a suitable distance in order to measure ambient temperature) from
the bimetal 8) to sense the circuit breaker internal ambient temperature. Then, the uP
46 employs the bimetal voltage 14 (Figure 2) and a thermal model 51 (Figure 2) of the
bimetal 8 and the circuit breaker 2 to estimate the transient bimetal temperature rise
52 (Figure 2) above the circuit breaker internal ambient temperature 54 (Figure 2).
The estimated transient bimetal temperature rise 52 and the internal ambient
temperature 54 are employed to estimate the absolute bimetal temperature 55 (Figure
2) and to determine the bimetal resistance 10, which is then employed to estimate the
actual circuit breaker current 16.
Example 3
The uP 46 preferably discrete-time samples the bimetal voltage 14
(Figure 2) at a suitable sampling frequency that is equal to or greater than the Nyquist
rate (i.e., rapid enough that the entire spectral content of the voltage waveform is
captured). See, for example, the sampling period, Tx, of Equation 4, below.
Example 4
Although a processor-based current sensing mechanism is disclosed,
discrete digital electronic components and/or a continuous-time system (e.g., without
limitation, employing analog electronics) and/or combinations thereof may be
employed. Alternatively, other suitable current sensing mechanisms may be
employed. One example includes analog/digital hybrid bimetal voltage sensing, in
which the half-cycle integral or peak of the bimetal voltage is first determined with an
analog circuit and then is digitally sampled.
Example 5
Figure 2 shows a linked first-order continuous-time electrical model 56
and the thermal model 51 of the bimetal 8 and the associated circuit breaker 2 (Figure
1). This model may be replaced by a more detailed model (Example 6, below) if

increased accuracy is desired. The thermal resistance of the bimetal 8, R (8C/W), to
the circuit breaker internal ambient temperature (8C) 54 models transient and steady
state heat loss from the bimetal 8 including conduction, convection and radiation.
The thermal capacitance of the bimetal, C (J/8C), models transient and steady state
temperature rise in the bimetal 8 due to power dissipation. The estimated
instantaneous power dissipated by the bimetal 8 is given by Qbim etal(t) (W). T(t) is
the estimated temperature rise 52 of the bimetal 8 over the circuit breaker internal
ambient temperature 54 versus time, t. T(t) is determined by solving the
continuous-time expression of Equation 1.


Equation 4 provides a substitution for Equation 3 to derive a discrete-
time version of the above continuous-time model through backward rectangular
integration.

wherein:
Ts is sampling period (seconds) (e.g., without limitation, about 1 ms
for a 60 Hz line cycle; a suitable period such that the sampling frequency is equal to
or greater than the Nyquist rate);
z is the discrete-time system equivalent of the Laplace operator 5 found
in continuous-time systems, and is defined from Z-1 {AT(z)} = T(n);
Z-1 is the Inverse Z Transform Operator; and
T = 0) = 0.
Equation 5 represents the discrete-time equivalent of the thermal
model 51.

wherein:
n is an integer, which is greater than or equal to zero;
T(n) is the estimated temperature rise of the bimetal 8 over the
circuit breaker internal ambient temperature (8C) for sample n;
Qbim etal is estimated instantaneous power (W) dissipated by the
bimetal 8 for sample «; and
T(n - 1) is the estimated temperature rise (8C) of the bimetal 8 over
the circuit breaker internal ambient temperature for sample n-1.

Example 6
Relatively better performance in the discrete-time model 51 is
achieved by employing a better integration method, such as trapezoidal integration.
Equation 6 provides a suitable substitution for Equation 3.

Equation 7 represents a relatively more accurate discrete-time
equivalent of the thermal model 51.

wherein:
Qbim etal (n-1) estimated instantaneous power (W) dissipated by
the bimetal 8 for sample n-1.
Example 7
Figure 3 shows the algorithm 58 employing the thermal model of
Example 6. First, at 60, integer n, which represents a sample number, is set to zero.
Next, at 62, a suitable initial bimetal temperature rise above ambient, T(0), is set to
value u for sample 0, which value is a predetermined value (8C) (e.g., without
limitation, zero; about zero; any suitable value). Then, at 64, a suitable initial
estimated instantaneous power dissipated by the bimetal, Qbimetal (0), is set to value v
for sample 0, which value is a predetermined value (W) (e.g., without limitation, zero;
about zero; any suitable value). Then, at 66, the integer, n, is incremented. Next, at
68 and 70, the voltage of the bimetal 8, Vbimetal (n) (V), and the circuit breaker internal
ambient temperature, Tambient(n) (8C), are respectively measured through the ADC 48
(Figure 1). Next, at 72, the estimated absolute temperature 50 of the bimetal (8C) for
sample n is determined from Equation 8.

wherein:
Tambient(n) is the absolute temperature of the circuit breaker internal
ambient (8C), for example, as measured by the thermistor 20 (Figure 1); and
T(n -1) is the previously estimated temperature rise of the bimetal 8
over the circuit breaker internal ambient temperature (8C) for sample n-1.
Then, at 74, the estimated electrical resistance 36 of the bimetal 8,
Rbimetal(n) (), is determined for sample n from Equation 9.

wherein:
fr(T) is a function (e.g., without limitation, derived from data
obtained from the bimetal manufacturer; nearly a linear function; approximated by a
linear function; a hash function) that represents or approximates the variation of
bimetal resistance (q) with bimetal temperature (8C). This provides the corrected
temperature dependent bimetal resistance as a predetermined function of the absolute
temperature of the bimetal 8.
Next, at 76, the estimated instantaneous electric current 86 flowing
through the bimetal, ibimelal (n) (A), is determined for sample n from Equation 10.

Then, at 78, the estimated instantaneous power dissipated by the
bimetal, Qbimetal(n) (W), is determined from one of Equations 11 and 12.

Next, at 80, AT(n) is determined based on the thermal model from
Equation 7, above.
Finally, at 82 and 84 T(n) and Qbimetal(n) axe respectively saved for
use in the next iteration (sample n+1), which is repeated beginning at step 66.
Hence, the P 46 determines the following on an initial iteration of the
iterative algorithm 58: (a) an initial absolute temperature of the bimetal 8 from the
ambient temperature plus a predetermined value, u, at step 62, (b) an instantaneous
power dissipated by the bimetal 8 at step 78, and (c) a temperature rise of the bimetal
8 over the ambient temperature at step 80. Then, on the subsequent iteration of the
iterative algorithm 58, the uP 46 determines: (d) a subsequent absolute temperature of
the bimetal 8 from a subsequent input of the ambient temperature plus the temperature
rise of the bimetal over the ambient temperature at step 72, (e) a subsequent
instantaneous power dissipated by the bimetal at step 78, and (f) a subsequent
temperature rise of the bimetal over the subsequent inputted ambient temperature at
step 80. This process continues on a subsequent iteration of the iterative algorithm 58
to refine the absolute temperature of the bimetal 8 from another input of the ambient
temperature plus the subsequent temperature rise of the bimetal 8, another
instantaneous power dissipated by the bimetal 8, and another temperature rise of the
bimetal 8 over the last input of the ambient temperature.
Example 8
Figure 4 shows the algorithm 58' employing the thermal model of
Example 5. This algorithm 58' is similar to the algorithm 58 of Figure 3 except that
step 64, Qbimetal(0) = v, and step 84, save Qbimetal (n) for use in the next iteration, are
not employed, and except that Equation 5 is used in place of Equation 7 at step 80'.
Example 9
A transient error in the estimated current 86 may arise if T(0) (the
assumed initial temperature rise of the bimetal 8 over ambient temperature at step 62
of Figures 3 and 4) is different than the actual initial temperature rise of the bimetal 8
over ambient temperature. This error may be no worse than that of a conventional
circuit breaker trip unit (which has no compensation for bimetal resistance variation
with temperature). Furthermore, given time, the error will decay to zero. One way to

address this error is to initially set T(0) equal to zero, in order that the estimated
bimetal resistance 36, Rbimetal(n), is minimized and, thus, ibimetal(n) 86 must be equal
to or greater than the actual bimetal current 16 (Figure 2). This approach offers a way
to err on the safe side, but could potentially cause circuit breaker nuisance trips in
some instances.
Example 10
If the thermal models of Examples 5 and 6 are not parameterized
precisely, they may still yield useful information as long as the estimated bimetal
electrical resistance 36 approximates, but does not exceed, the actual bimetal
electrical resistance 10 (Figure 2). In this case, the temperature-related error in the
current measurement will be nonzero, but will be less than that of a circuit breaker
with no temperature compensation.
Example 11
If the estimated bimetal electrical resistance 36 (as calculated by the
algorithms 58,58') becomes greater than the actual bimetal electrical resistance 10
(Figure 2), then the estimated circuit breaker current 86 is less than the actual circuit
breaker current 16 (Figure 2). Hence, the circuit breaker 2 and bimetal thermal model
parameters (R and C) must be suitably chosen to ensure that this case does not
occur.
Example 12
The example trip circuit 26 includes an armature 88, which is attracted
by the large magnetic force generated by very high overcurrents to also actuate the
operating mechanism 18 and provide an instantaneous trip function.
A trip signal 90 is generated at the AFD output 44 in order to turn on a
suitable switch, such as the silicon controlled rectifier (SCR) 92, to energize a trip
solenoid 94. The trip solenoid 94, when energized, actuates the operating mechanism
18 to trip open the separable contacts 6. A resistor 96 in series with the coil of the
solenoid 94 (or the resistance of the coil if the resistor 96 is not used) limits the coil
current and a capacitor 98 protects the gate of the SCR 92 from voltage spikes and
false tripping due to noise.

While specific embodiments of the invention have been described in
detail, it will be appreciated by those skilled in the art that various modifications and
alternatives to those details could be developed in light of the overall teachings of the
disclosure. Accordingly, the particular arrangements disclosed are meant to be
illustrative only and not limiting as to the scope of the invention which is to be given
the full breadth of the claims appended and any and all equivalents thereof.

What is Claimed is:
1. A circuit breaker (2) comprising:
a housing (4);
separable contacts (6);
a bimetal (8) electrically connected in series with said separable
contacts, said bimetal including a temperature dependent resistance (10) and an output
(12) having a voltage (14) representative of current flowing through said separable
contacts;
an operating mechanism (18) structured to open and close said
separable contacts;
a temperature sensor (20) distal from said bimetal, said
temperature sensor including an output (22) having a signal (24) representative of
ambient temperature; and
a trip circuit (26) cooperating with said operating mechanism to
trip open said separable contacts, said trip circuit comprising:
a first circuit (28) including a first input (32) electrically
interconnected with the output of said bimetal to input said voltage representative of
current flowing through said separable contacts, a second input (34) electrically
interconnected with the output of said temperature sensor to input said signal
representative of ambient temperature, a real-time thermal model (29) structured to
provide a corrected temperature dependent resistance (36) of said bimetal as a
function of said voltage representative of current flowing through said separable
contacts and said signal representative of ambient temperature, and an output (38)
including a current value (40) which is a function of said voltage representative of
current flowing through said separable contacts, and said corrected temperature
dependent resistance, and
a second circuit (31) including an input (42) having said
current value and an output (44) structured to actuate said operating mechanism in
response to predetermined current conditions.
2. The circuit breaker (2) of Claim 1 wherein said first circuit
comprises a processor (46) structured to repetitively execute an iterative algorithm
(58;58') as said real-time thermal model.

3. The circuit breaker (2) of Claim 2 wherein said processor is
further structured to periodically input (68,70) said voltage representative of current
flowing through said separable contacts and said signal representative of ambient
temperature.
4. The circuit breaker (2) of Claim 2 wherein said processor is
further structured on an initial iteration of said iterative algorithm to determine
(62,72,78,80;80') (a) an initial absolute temperature of said bimetal from said ambient
temperature plus a predetermined value (68), (b) an instantaneous power dissipated by
said bimetal (78), and (c) a temperature rise of said bimetal over said ambient
temperature (80;80'), and on a subsequent iteration of said iterative algorithm to
determine (72,78,80;80') (d) a subsequent absolute temperature of said bimetal from a
subsequent input of said ambient temperature plus said temperature rise of said
bimetal over said ambient temperature (72), (e) a subsequent instantaneous power
dissipated by said bimetal (78), and (f) a subsequent temperature rise of said bimetal
over said subsequent inputted ambient temperature (80,80').
5. The circuit breaker (2) of Claim 4 wherein said predetermined
value is a constant (u).
6. The circuit breaker (2) of Claim 5 wherein said constant is zero.
7. The circuit breaker (2) of Claim 4 wherein said processor is
further structured to calculate (74) said corrected temperature dependent resistance of
said bimetal as a predetermined function of said subsequent absolute temperature of
said bimetal.
8. The circuit breaker (2) of Claim 7 wherein said processor is
further structured to calculate (76) said current value from said voltage of said bimetal
divided by said corrected temperature dependent resistance of said bimetal.
9. The circuit breaker (2) of Claim 7 wherein said processor is
further structured to calculate (78) said subsequent instantaneous power dissipated by
said bimetal from the square of said voltage of said bimetal divided by said corrected
temperature dependent resistance of said bimetal.
10. The circuit breaker (2) of Claim 7 wherein said processor is
further structured to calculate (80) T(n) as said temperature rise of said bimetal
over said ambient temperature from:

subsequent iteration, and T(n -1) is said temperature rise of said bimetal over said
ambient temperature for said initial iteration.
14. The circuit breaker (2) of Claim 1 wherein said ambient
temperature is within said housing.
15. A method of determining a temperature (50) of a bimetal (8)
electrically connected in series with separable contacts (6), said bimetal including an
output (12) having a voltage (14) representative of current (16) flowing through said
separable contacts, said method comprising:
sensing (20) a temperature representative of ambient
temperature;
inputting (32,48) said voltage representative of current flowing
through said separable contacts; and
employing a real-time thermal model (29) to determine the
temperature of said bimetal from said sensed temperature representative of ambient
temperature and said voltage representative of current flowing through said separable
contacts.
16. The method of Claim 15 further comprising
repetitively executing an iterative algorithm (58;58') as said
real-time thermal model.
17. The method of Claim 16 further comprising
for an initial iteration of said iterative algorithm:
determining (62,72,78,80,80') (a) an initial absolute
temperature of said bimetal from said ambient temperature plus a predetermined value
(62,72), (b) an instantaneous power dissipated by said bimetal (78), and (c) a
temperature rise of said bimetal over said ambient temperature (80,80'); and
for a subsequent iteration of said iterative algorithm:
determining (72,78,80,80') (d) a subsequent absolute
temperature of said bimetal from a subsequently sensed ambient temperature plus said
temperature rise of said bimetal over said ambient temperature (72), (e) a subsequent
instantaneous power dissipated by said bimetal (78), and (f) a subsequent temperature
rise of said bimetal over said subsequently sensed ambient temperature (80,80').

18. The method of Claim 17 further comprising
employing a constant («) as said predetermined value.
19. The method of Claim 17 further comprising
calculating (72) said corrected temperature dependent
resistance of said bimetal as a predetermined function of said subsequent absolute
temperature of said bimetal;
calculating (76) said current value (86) from said voltage of
said bimetal divided by said corrected temperature dependent resistance of said
bimetal; and
calculating (78) said subsequent instantaneous power dissipated
by said bimetal from the square of said voltage of said bimetal divided by said
corrected temperature dependent resistance of said bimetal.
20. The method of Claim 17 further comprising
calculating (80) T(n) as said temperature rise of said bimetal
over said ambient temperature from:

employing R as thermal resistance of said bimetal, C as
thermal capacitance of said bimetal, Ts as a sampling period between said initial
iteration and said subsequent iteration, Qbimetal (n) as said instantaneous power
dissipated by said bimetal for said subsequent iteration, Qbimetal (n-1)) as said
instantaneous power dissipated by said bimetal for said initial iteration, and T(n -1)
as said temperature rise of said bimetal over said ambient temperature for said initial
iteration.
21. The method of Claim 17 further comprising
on another iteration after said subsequent iteration:
determining (72,78,80;80') (g) another absolute temperature of
said bimetal from another input of said ambient temperature plus said subsequent
temperature rise of said bimetal (72), (h) another instantaneous power dissipated by

said bimetal for said another iteration after said subsequent iteration (78), and (i)
another temperature rise of said bimetal over said another inputted ambient
temperature (80;80').
22. The method of Claim 17 further comprising
calculating (80') T(n) as said temperature rise of said bimetal
over said ambient temperature from:

employing R as thermal resistance of said bimetal, C as
thermal capacitance of said bimetal, Tx as a sampling period between said initial
iteration and said subsequent iteration, Qbimetal (n) as said instantaneous power
dissipated by said bimetal for said subsequent iteration, and T(n -1) as said
temperature rise of said bimetal over said ambient temperature for said initial
iteration.

A circuit breaker includes a bimetal electrically connected in series
with separable contacts, and an operating mechanism structured to open and close the
contacts. A temperature sensor distal from the bimetal includes an output having an
ambient temperature signal. A trip circuit includes a first circuit having a first input
electrically interconnected with a bimetal output to input a voltage representative of
current, a second input electrically interconnected with the temperature sensor output
to input the ambient temperature signal, a real-time thermal model structured to
provide a corrected temperature dependent bimetal resistance as a function of the
voltage and the ambient temperature signal, and an output including a current value
which is a function of the ambient temperature signal and the corrected bimetal
resistance. A second circuit includes an input having the current value and an output
structured to actuate the operating mechanism in response to predetermined current
conditions.