U.S. patent application number 11/644634 was filed with the patent office on 2007-05-24 for motor parameter estimation method and apparatus.
Invention is credited to Yehia El-Ibiary.
Application Number | 20070118307 11/644634 |
Document ID | / |
Family ID | 34377053 |
Filed Date | 2007-05-24 |
United States Patent
Application |
20070118307 |
Kind Code |
A1 |
El-Ibiary; Yehia |
May 24, 2007 |
Motor parameter estimation method and apparatus
Abstract
A system and method for establishing estimated values of
electrical parameters of a motor. The electrical parameters may be
established from motor databases, measured input electrical data,
measured output data, and various estimations to account for
unknown motor parameters. Compensations also may be provided for
stator resistance, cable resistance, and other motor parameters.
Based on the foregoing data, the system and method also may be used
to estimate motor operating parameters, such as torque, efficiency,
output power, output speed, and other performance criteria of the
motor. The system and method also may establish energy and monetary
comparison data between the motor and at least one alternative
motor.
Inventors: |
El-Ibiary; Yehia;
(Simpsonville, SC) |
Correspondence
Address: |
ROCKWELL AUTOMATION, INC./(FY)
ATTENTION: SUSAN M. DONAHUE, E-7F19
1201 SOUTH SECOND STREET
MILWAUKEE
WI
53204
US
|
Family ID: |
34377053 |
Appl. No.: |
11/644634 |
Filed: |
December 22, 2006 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
10675104 |
Sep 30, 2003 |
7184902 |
|
|
11644634 |
Dec 22, 2006 |
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Current U.S.
Class: |
702/60 |
Current CPC
Class: |
H02P 23/14 20130101;
G01R 31/343 20130101 |
Class at
Publication: |
702/060 |
International
Class: |
G01R 21/06 20060101
G01R021/06 |
Claims
1. A system, comprising: a motor estimation module adapted to
establish estimated values of a plurality of electrical parameters
of an electric motor based on electrical input data; and an energy
analysis module adapted to establish energy performance indicia of
the electric motor.
2. The system as recited in claim 1, wherein the motor estimation
module is operable to establish an estimated value of an operating
parameter of the electric motor based on the estimated values of
electrical parameters of the electric motor.
3. The system as recited in claim 2, wherein the operating
parameter is motor torque.
4. The system as recited in claim 2, wherein the operating
parameter is motor efficiency.
5. The system as recited in claim 2, wherein the operating
parameter is output power.
6. The system as recited in claim 2, wherein the operating
parameter is rotor temperature.
7. The system as recited in claim 1, wherein the energy analysis
module comprises an energy usage module adapted to establish energy
usage data of the electric motor.
8. The system as recited in claim 1, wherein the energy analysis
module comprises an energy savings module adapted to establish
energy savings data of an alternative electric motor versus the
electric motor.
9. The system as recited in claim 1, comprising a monetary analysis
module adapted to establish monetary performance indicia of the
electric motor based at least partially on the energy performance
indicia.
10. The system as recited in claim 9, wherein the monetary analysis
module comprises a cost analysis module adapted to establish
operational cost data of the electric motor.
11. The system as recited in claim 9, wherein the monetary analysis
module comprises a monetary savings module adapted to establish
operational savings data of an alternative electric motor versus
the electric motor.
12. The system as recited in claim 1, comprising a database of
customer motors and operational data of the customer motors.
13. The system as recited in claim 1, comprising a database of
alternative motors and operational data of the alternative
motors.
14. The system as recited in claim 1, comprising a database of
motors and power losses of the motors.
15. The system as recited in claim 14, wherein the power losses
comprise friction and windage losses.
16. One or more machine-readable media having application
instructions encoded thereon, the application instructions
comprising: instructions adapted to establish estimated values of a
plurality of electrical parameters of an electric motor based on
electrical input data; and instructions adapted to establish energy
performance indicia of the electric motor.
17. The one or more machine-readable media as recited in claim 16,
wherein the application instructions comprise instructions adapted
to establish energy usage data of the electric motor.
18. The one or more machine-readable media as recited in claim 16,
wherein the application instructions comprise instructions adapted
to establish monetary performance indicia of the electric motor
based at least partially on the energy performance indicia.
19. A method, comprising: providing an instrumentation system with
electrical input data of an electric motor; operating the
instrumentation system to establish estimated values of a plurality
of electrical parameters of the electric motor based on the
electrical input data; and engaging the instrumentation system to
establish energy performance indicia of the electric motor.
20. The method as recited in claim 19, wherein engaging comprises
obtaining energy savings data of an alternative electric motor
versus the electric motor.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application is a divisional of U.S. patent application
Ser. No. 10/675,104, entitled "Motor Parameter Estimation Method
and Apparatus," filed Sep. 30, 2003, which is incorporated by
reference herein.
BACKGROUND
[0002] The present technique relates generally to the field of
electric motors. More particularly, the invention relates to a
novel technique for estimating unknown parameters of an induction
motor based on motor data obtained at one or more operating points
or a no-load operating point.
[0003] A wide variety of induction motors are available and are
currently in use throughout a range of industrial applications. In
general, such motors include a stator provided in a motor housing
and a rotor surrounded at least partially by the stator and
supported for rotation within the housing. The stator and rotor may
be mechanically and electrically configured in a variety of manners
depending upon a number of factors, including: the application, the
power available to drive the motor, and so forth. In general,
however, electric power is applied to the stator to produce a
rotating magnetic field to drive the rotor in rotation. Mechanical
power is transmitted from the motor via an output shaft coupled to
the rotor.
[0004] Motor operating parameters, such as output torque or
efficiency, may only be determined with the motor in operation.
Knowledge of these motor operating parameters can be important for
a number of reasons. However, the devices used to measure motor
operating parameters may interfere with the operation of the motor
or may be relatively expensive. In addition, it may be difficult to
measure the operating parameter. For example, it may be desirable
to maintain the temperature of the rotor below a specific
temperature. However, it is extremely difficult to measure the
rotor temperature. In addition, it may be desirable to establish
the torque and/or efficiency of a given motor to ensure that the
proper motor is used in a given application. However, a typical
torque measuring device requires the motor to be disconnected from
its load each time the torque measurement is desired, interfering
significantly with the operation of the motor. Previous attempts to
develop a device to estimate motor operating parameters, such as
torque and efficiency, have relied on motor nameplate data.
However, these attempts have not yielded accurate results.
Alternatively, a customer may not have the values of the motor
electrical parameters that might be used to develop an estimate of
various motor operating parameters.
[0005] A need exists for a technique for obtaining electric motor
operating parameter data that is less expensive than conventional
methods and which minimizes the disruption to the operation of a
system incorporating the electric motor.
BRIEF DESCRIPTION
[0006] The present technique provides a novel system and method for
establishing estimated values of electrical parameters of a motor.
The electrical parameters may be established from motor databases,
measured input electrical data, measured output data, and various
estimations to account for unknown motor parameters. Compensations
also may be provided for stator resistance, cable resistance, and
other motor parameters. Based on the foregoing data, the system and
method also may be used to estimate motor operating parameters,
such as torque, efficiency, output power, output speed, and other
performance criteria of the motor. The system and method also may
establish energy and monetary comparison data between the motor and
at least one alternative motor.
DRAWINGS
[0007] The foregoing and other advantages and features of the
invention will become apparent upon reading the following detailed
description and upon reference to the drawings in which:
[0008] FIG. 1 is a perspective view of an electric motor
illustrating the various functional components of the motor
including a rotor and a stator, in accordance with certain aspects
of the invention;
[0009] FIG. 2 is the single-phase steady state equivalent schematic
circuit of an induction motor, according to an exemplary embodiment
of the present technique;
[0010] FIG. 3 is a system for providing estimated values of various
motor operating parameters, according to an exemplary embodiment of
the present technique;
[0011] FIG. 4 is a process for providing estimated values of
various motor operating parameters based on data obtained at two
load conditions of the motor, according to an exemplary embodiment
of the present technique;
[0012] FIG. 5 is an alternative equivalent schematic circuit of a
steady state induction motor, according to an exemplary embodiment
of the present technique;
[0013] FIG. 6 is an alternative process for providing estimated
values of various motor operating parameters based on data obtained
with no-load on the motor, according to an exemplary embodiment of
the present technique;
[0014] FIG. 7 is another alternative process for providing
estimated values of various motor operating parameters based on
data obtained at a single load on the motor, according to an
exemplary embodiment of the present technique;
[0015] FIG. 8 is further alternative process for providing
estimated values of various motor operating parameters based on
data obtained at first, second, and third loads on the motor,
according to an exemplary embodiment of the present technique;
[0016] FIG. 9 is another alternative process for providing
estimated values of various motor operating parameters based on
baseline motor parameters and data obtained at a desired operating
load on the motor, according to an exemplary embodiment of the
present technique; and
[0017] FIG. 10 is a system for providing estimated values of
various motor operating parameters, according to an exemplary
embodiment of the present technique.
DETAILED DESCRIPTION
[0018] Turning now to the drawings, and referring first to FIG. 1,
an electric motor is shown and designated generally by the
reference numeral 20. In the embodiment illustrated in FIG. 1,
motor 20 is an induction motor housed in a conventional NEMA
enclosure. Accordingly, motor 20 includes a frame 22 open at front
and rear ends and capped by a front end cap 24 and a rear end cap
26. The frame 22, front end cap 24, and rear end cap 26 form a
protective shell, or housing, for a stator assembly 28 and a rotor
assembly 30. Stator windings are electrically interconnected to
form groups, and the groups are, in turn, interconnected. The
windings are further coupled to terminal leads 32. The terminal
leads 32 are used to electrically connect the stator windings to an
external power cable (not shown) coupled to a source of electrical
power. Energizing the stator windings produces a magnetic field
that induces rotation of the rotor assembly 30. The electrical
connection between the terminal leads and the power cable is housed
within a conduit box 34.
[0019] In the embodiment illustrated, rotor assembly 30 comprises a
cast rotor 36 supported on a rotary shaft 38. As will be
appreciated by those skilled in the art, shaft 38 is configured for
coupling to a driven machine element (not shown), for transmitting
torque to the machine element. Rotor 36 and shaft 38 are supported
for rotation within frame 22 by a front bearing set 40 and a rear
bearing set 42 carried by front end cap 24 and rear end cap 26,
respectively. In the illustrated embodiment of electric motor 20, a
cooling fan 44 is supported for rotation on shaft 38 to promote
convective heat transfer through the frame 22. The frame 22
generally includes features permitting it to be mounted in a
desired application, such as integral mounting feet 46. As will be
appreciated by those skilled in the art, however, a wide variety of
rotor configurations may be envisaged in motors that may employ the
techniques outlined herein, including wound rotors of the type
shown, and so forth. Similarly, the present technique may be
applied to a variety of motor types having different frame designs,
mounting and cooling styles, and so forth.
[0020] Referring generally to FIG. 2, an equivalent circuit for
steady state operation of the induction motor of FIG. 1 is shown
and designated generally by the reference numeral 50. The induction
motor is powered by an AC power source, designated by reference
numeral 52, having a voltage amplitude V.sub.1 and a frequency
.omega.. The stator of the motor has an electrical resistance
R.sub.1, as represented by reference numeral 54, and a leakage
inductance L.sub.1, as represented by reference numeral 56. The
motor also has core loss resistance R.sub.c due to core losses in
the stator and rotor, designated by the reference numeral 58. The
motor also has a magnetizing inductance L.sub.m, designated by
reference numeral 60. The rotor also has an electrical resistance
R.sub.2, designated by reference numeral 62. As illustrated, the
rotor resistance R.sub.2 is modified by dividing the rotor
resistance R.sub.2 by the slip s of the rotor. Finally, the rotor
also has a leakage inductance L.sub.2, as represented by reference
numeral 64. Electric current flows through the stator to produce
the magnetic field. The electric current I.sub.1 through the stator
is represented by arrow 66. In addition, the magnetic field induces
an electric current I.sub.2 in the rotor, as represented by arrow
68. Finally, electric current I.sub.3 flowing through the core loss
resistance R.sub.c and the magnetizing inductance L.sub.m is
represented by arrow 70.
[0021] In a typical AC circuit, the voltage and current vary over
time. In an inductive circuit, such as an induction motor, the
voltage leads the current by an angle, known as the phase angle
.phi.. In addition, some power is alternately stored and released
by the inductance of the circuit. This power is known as the
"reactive power." In addition, the resistance of the circuit
dissipates power as heat and the load utilizes a portion of the
input power, this power is known as the "real power." The "apparent
power" is the product of the total voltage and the total current in
the AC circuit. The ratio between the real power and the apparent
power of a load in an AC circuit is known as the "power factor" of
the load. The cosine of the phase angle is the power factor.
[0022] Referring generally to FIG. 3, a system for providing
estimated values of various motor electrical parameters and motor
operating parameters is shown and designated generally by reference
numeral 80. The system 80 comprises a data processing module 82
that is electrically coupleable to the motor 20. The data
processing module 82 is operable to utilize data obtained at two
load conditions of the motor 20 to establish values of various
electrical parameters of the motor, such as the electrical
resistance of the rotor and the leakage inductance of the stator
and rotor. The data processing module then uses the values of the
estimated motor electrical parameters to estimate motor operating
parameters, such as the temperature of the rotor, the torque of the
motor, and the efficiency of the motor. The data processing module
82 may be provided as a stand-alone device, as part of a motor, or
in a kit form to be added to an existing installed motor.
[0023] In the illustrated embodiment, the data processing module 82
has a processor module 84. Preferably, the processor module 84
utilizes a processor (not shown) and operates in accordance with
programming instructions to produce estimates of various motor
operating parameters. The processor module 84 may have
analog-to-digital converters for converting analog data into
digital data. In this embodiment, the processor module 84 is
electrically coupled to each phase 86 of the input power to the
motor 28 to enable the module to receive electrical input data,
such as the input voltage, current, frequency, and power. However,
the data also may be entered into the system manually. The input
voltage data may be the line-to-line voltage or the phase voltage.
The average phase voltage for a connection may be established by
averaging the three line-to-line voltages and dividing by the
{square root over (3)}. The average line current is the phase
current. Input power data also may be obtained directly or
calculated from the stator voltage, current, and resistance data. A
speed sensor 88 also is electrically coupled to the processor
module 84. The speed sensor 88 may be integral with the motor or a
separate device coupled to the processor module 84. The speed
sensor 88 may measure the speed of the shaft 38 coupled to-the
rotor 36 in order to establish rotor speed. Alternatively, the
speed sensor 88 may measure the speed of the rotor 36 directly.
[0024] In the illustrated embodiment, the system 80 is operable to
output motor electrical parameter data and motor operating
parameter data to a control module 90. Preferably, the control
module 90 has a visual display 92 to provide visual indications of
the various parameters. Preferably, the control module 90 has a
keypad or keyboard 94 to enable data, such as the electrical input
data, rotor speed data, and any known motor electrical parameters,
to be inputted into the processor module 84. In addition, in the
illustrated embodiment the processor module 84 and the control
module 90 are coupled to a network 96 to enable data to be
transferred to or from remote terminals 98. The remote terminals 98
may be personal computers, or other digital communication
devices.
[0025] The electrical input data may also be measured at the motor
controller, rather than at the motor itself. However, in certain
applications the motor controller may be quite remote from the
motor. To facilitate the measurement of data at the motor, such as
the rotor speed, and at other locations, such as at a motor
controller, a time log of the measured voltages, currents, power
and frequency may be used to record data. The voltages, currents,
power and frequency corresponding to the time of the speed
measurement are retrieved from the time log and matched to the
speed of the rotor at that time. An adjustment also can be provided
for the effect on the electrical input data caused by taking the
measurement at the motor controller. First, the length of the cable
between the motor and the starter may be measured. In addition, the
ambient temperature is measured and the gauge of the cable
identified. The diameter of the conductor may be calculated from
the gauge of the cable. The resistance of the cable may be
estimated based on the operating temperature, the length and
diameter of the cable. The cable resistance is then subtracted from
the total measured resistance to establish the stator resistance.
Furthermore, the power loss in the cable may be established from
the measured current and estimated cable resistance. The cable
power is then subtracted from the measured power to obtain the
power delivered to the motor.
[0026] Referring generally to FIG. 4, a process for establishing
values of various motor electrical parameters and various motor
operating parameters using the system of FIG. 3 is shown and
designated generally by reference numeral 100. The process
comprises obtaining the resistance of the stator, as represented by
block 102. The process also comprises obtaining data at a first
operating load point and providing the data to the processor module
84, as represented by block 104. In a presently contemplated
embodiment, the data obtained at the first load point comprises:
input voltage data, input current data, input power data, and shaft
speed data. It should be noted that the input power can either be
measured or calculated from the other input data. In addition, the
process may measure motor frequency and temperature. Some data may
be provided to the system 80 using the control module 90 or may be
provided from a remote station 98 via the network 96. Preferably,
the motor has a low load at the first operating point.
[0027] The process also comprises obtaining data from the motor at
a second load point and providing the data to the processor module
84, as represented by block 106. The stator resistance R.sub.1 data
need only be obtained once if the stator temperature is obtained at
each load point. Preferably, the motor has a full load at the
second load point.
[0028] The data processing module 82 may then be operated to
establish estimated values of various motor parameters, as
represented by block 108. The programming instructions provided to
the data processing module 82 are adapted to utilize a novel
technique for establishing the values of the various motor
parameters. The equivalent circuit of FIG. 2 provides a starting
point to illustrate the development of the technique for estimating
various motor parameters. Referring generally to FIG. 5, an
equivalent circuit, designated generally by reference numeral 110,
to the circuit of FIG. 2 is illustrated. In FIG. 5, each inductance
illustrated in FIG. 2 is converted into an inductive reactance to
facilitate solving for the unknown motor parameters. In addition,
some of the reactances are combined to simplify the circuit 110.
The stator leakage reactance X.sub.1, designated by reference
numeral 112, is a function of the electrical frequency .omega. of
the power source and the stator leakage inductance L.sub.1. The
equivalent reactance X.sub.e, designated by reference numeral 114,
is a function of the magnetizing reactance X.sub.m, the rotor
resistance R.sub.2, the slip s and the rotor leakage reactance
X.sub.2. The magnetizing reactance X.sub.m, in turn, is a function
of the electrical frequency .omega. and the magnetizing inductance
L.sub.m. The rotor leakage reactance X.sub.2 is a function of the
electrical frequency .omega. and the rotor leakage inductance
L.sub.2. The equivalent resistance R.sub.e, designated by reference
numeral 116, is a function of the rotor resistance R.sub.2, the
leakage reactance X.sub.2, the slip s, and the core loss resistance
R.sub.c. Of the parameters illustrated in FIGS. 2 and 5, the stator
resistance R.sub.1 and the motor slip s can be measured relatively
easily. This leaves the values of five parameters to be
established: X.sub.1, R.sub.2, X.sub.2, R.sub.c, and X.sub.m. These
parameters are more difficult to measure than the stator resistance
R.sub.1 and the motor slip s.
[0029] Several assumptions and an approximation are made to
simplify the process of developing a technique for estimating
X.sub.1, R.sub.2, X.sub.2, R.sub.c, and X.sub.m. Namely, it is
assumed that the frequency of the power is constant, that the speed
of the rotor does not change during the gathering of the load point
data, and that the reading of the data is done quickly so that the
rotor temperature is constant during the gathering of the data.
Additionally, it has been established experimentally that excellent
results are obtained by estimating the stator leakage reactance
X.sub.1 to be 5% of the magnetizing reactance X.sub.m, or:
X.sub.1=0.05X.sub.m. (1) However, this factor may range from 0.02
to 0.07. By making this approximation the number of unknowns is
reduced to four. Thus, only four equations are needed to solve for
the values of the remaining unknown motor parameters. However, the
equations relating these unknowns are highly nonlinear and an
expression for the remaining unknowns by using measurements
obtained at two load points is nontrivial. In the present
technique, this process is facilitated by obtaining an actual value
for the stator leakage reactance X.sub.1. This value is then used
in finding the values of the remaining unknowns.
[0030] In addition, the rotor leakage inductance L.sub.2 and
magnetizing inductance L.sub.m are converted into reactances in
FIG. 5 to assist in solving the various unknown motor parameters.
Reactance is a function of the inductance and the frequency .omega.
of the circuit. The reactances were combined with the rotor
resistance R.sub.2 and the core loss resistance R.sub.c to form an
equivalent reactance X.sub.e and a total resistance R.sub.t. At a
first load point, the total resistance R.sub.t1 is given by the
following equation: 1 R t .times. .times. 1 = 1 R c + 1 ( R 2 s 1 +
s 1 .times. X 2 2 R 2 ) . ( 2 ) ##EQU1##
[0031] The first term on the right side of the equation is the
reciprocal of the core loss resistance R.sub.c and the second term
is the reciprocal of the new modified rotor resistance as a result
of factoring the rotor leakage reactance X.sub.2. At the second
load point, the total resistance R.sub.t2 is given by the following
equation: 1 R t .times. .times. 2 = 1 R c + 1 ( R 2 s 2 + s 2
.times. X 2 2 R 2 ) . ( 3 ) ##EQU2##
[0032] Similarly, the equivalent reactances at the two motor load
points X.sub.e1 and X.sub.e2 are given by the following equations:
1 X e .times. .times. 1 = 1 X m + X 2 ( R 2 2 s 1 2 + X 2 2 ) ; and
( 4 ) 1 X e .times. .times. 2 = 1 X m + X 2 ( R 2 2 s 2 2 + X 2 2 )
. ( 5 ) ##EQU3## The right hand sides of equations (4) and (5) also
have two terms, one resulting from the magnetizing reactance
X.sub.m and the other resulting from factoring the rotor leakage
reactance X.sub.2.
[0033] The following equations for equivalent reactance X.sub.e and
equivalent resistance R.sub.e may be developed using FIG. 5 and
data obtained at the two load points of the motor. The equation for
the equivalent reactance X.sub.e is given as follows: X e = - B 2
.times. A + B 2 - 4 .times. A .times. .times. C 2 .times. A , ( 6 )
##EQU4## where A, B, and C are given by:
A=1.05*0.05*sI.sub.1.sup.2; (7) B=-1.1I.sub.1V.sub.1is; and (8)
C=V.sub.1i.sup.2s+(sR.sub.1I.sub.1-sV.sub.1R)(I.sub.1R.sub.1-V.sub.1R)
(9) V.sub.1i is the imaginary portion of the voltage and is a
function of the amplitude of the power source voltage V.sub.1 and
the sine of the power factor angle. V.sub.1R is the real portion of
the voltage and is a function of the amplitude of the power source
voltage V.sub.1 and the cosine of the phase angle. In addition, the
equivalent resistance R.sub.e is given by the following equation: R
e = sX e .function. ( V 1 .times. j - .05 .times. I 1 .times. X e )
( V 1 .times. R - I 1 .times. R 1 ) . ( 10 ) ##EQU5##
[0034] As discussed above, it was assumed that the stator leakage
reactance is 5%, or 0.05 of the magnetizing reactance X.sub.m. With
no load on the motor, the rotor section of the circuit is
considered open and the value for the slip s is considered to be
zero. The total reactance of the circuit is made of the sum of the
stator leakage reactance X.sub.1 and the magnetizing reactance
X.sub.m. Since X.sub.1 can be expressed as equal to 0.05 X.sub.m,
then the total no-load reactance can be written as 1.05 X.sub.m.
The value of X.sub.e at the two load points is used to extrapolate
the value at no-load to yield X.sub.m. The value of X.sub.e at
zero-load is the magnetizing reactance X.sub.m. In addition, the
slip s is used as a measure of the load. Through experimentation
using different load points and different motors, it has been found
that the following equation yields a very close value for the
magnetizing reactance X.sub.mi to be used for estimating the stator
leakage reactance X.sub.1: X m .times. .times. i = X e .times.
.times. 1 + ( X e .times. .times. 2 - X e .times. .times. 1 )
.times. .times. s 1 1 4 ( s 1 - s 2 ) 1 4 . ( 11 ) ##EQU6##
[0035] In equation (11) above, s.sub.1 is the slip at a high load
and s.sub.2 is the slip at a low load, noting that s.sub.1 is
greater than s.sub.2. The value of X.sub.mi may then be used to
establish the value of X.sub.1, in accordance with equation (1)
provided above.
[0036] Once the value of X.sub.1 is obtained, new values for
R.sub.t and X.sub.e may be obtained. These new values of R.sub.t
and X.sub.e are based on a fixed known value of the stator
reactance X.sub.1, and may be determined in accordance with the
following equations: .alpha. 1 = 1 R t .times. .times. 1 - 1 R t
.times. .times. 2 ; and ( 12 ) .alpha. 2 = 1 X e .times. .times. 1
- 1 X e .times. .times. 2 . ( 13 ) ##EQU7##
[0037] There now are four equations and four unknowns. The unknowns
are R.sub.2, X.sub.2, R.sub.c, and X.sub.m. To eliminate R.sub.c,
equation (3) is subtracted from equation (2) to yield the following
equation: .alpha. 1 = R 2 s 1 .times. ( R 2 2 s 2 2 + X 2 2 ) - R 2
s 2 .times. ( R 2 2 s 1 2 + X 2 2 ) ( R 2 2 s 1 2 + X 2 2 ) .times.
( R 2 2 s 2 2 + X 2 2 ) . ( 14 ) ##EQU8## To eliminate X.sub.m,
equation (5) is subtracted from equation (4) yielding the following
equation: .alpha. 2 = X 2 ( R 2 2 s 2 2 + X 2 2 ) - X 2 ( R 2 2 s 1
2 + X 2 2 ) ( R 2 2 s 1 2 + X 2 2 ) .times. ( R 2 2 s 2 2 + X 2 2 )
. ( 15 ) ##EQU9##
[0038] From the equations provided above, equations may now be
established for R.sub.2, X.sub.2, R.sub.c, and X.sub.m. By dividing
equation (14) by equation (1 5), the following relationship for the
X.sub.2 and R.sub.2 can be established: X.sub.2=.gamma.R.sub.2.
(16) where .gamma. is given by the following equation: .gamma. = -
.alpha. 1 .function. ( s 1 + s 2 ) 2 .times. .alpha. 2 .times. s 1
.times. s 2 + ( .alpha. 1 .alpha. 2 ) 2 .times. ( s 1 + s 2 ) 2 + 4
.times. s 1 .times. s 2 2 .times. s 1 .times. s 2 . ( 17 )
##EQU10## The rotor resistance R.sub.2 may be established by
substituting .gamma.R.sub.2 for X.sub.2 in equation (15) and using
algebraic manipulation to produce the following equation: R 2 =
.gamma. .alpha. 2 ( 1 s 1 2 + .gamma. 2 ) - .gamma. .alpha. 2 ( 1 s
2 2 + .gamma. 2 ) . ( 18 ) ##EQU11## In addition, the core loss
resistance R.sub.c may be established in terms of R.sub.2 and
X.sub.2 by manipulating equation (2) to produce the following
equation: R c = 1 ( 1 R t .times. .times. 1 - R 2 s 1 ( R 2 2 s 1 2
+ X 2 2 ) ) ( 19 ) ##EQU12## Finally, the magnetizing reactance
X.sub.m may be established in terms of R.sub.2 and X.sub.2 by
manipulating equation (4) to produce the following equation: X m =
1 ( 1 X e .times. .times. 1 - X 2 ( R 2 2 s 1 2 + X 2 2 ) ) . ( 20
) ##EQU13##
[0039] The data processing module 82 is programmed to use the
above-described equations and methodology to establish estimated
values of rotor resistance R.sub.2, leakage reactance X.sub.2, core
loss resistance R.sub.c, and magnetizing reactance X.sub.m. Voltage
and current input data are obtained at the two load points and
provided to the processor module 84. Input power data also may be
obtained at the same two points or calculated from the voltage,
current, and/or resistance data. In addition, motor speed data also
is provided to the data processing module 82. The motor speed data
may be the RPM of the motor or the slip. Ideally, the measurements
at the two load points are made simultaneously to avoid potential
change due to a change in the operating condition of the motor. In
addition, in the illustrated embodiment the line-to-line electrical
resistance of the stator is provided to the processor. The phase
resistance is established by averaging the line-to-line resistance
and dividing by 2. The data processing module 82 is operable to
establish the value of the equivalent reactances X.sub.e1 and
X.sub.e2 using equations (6) through (10) provided above at each
load point. The processor also is operable to establish the initial
magnetizing reactance X.sub.mi using equation (11) provided above.
In addition, the processor is operable to establish the value of
the phase leakage reactance X.sub.1 from the magnetizing reactance
X.sub.mi. Using the value of X.sub.1, the processor is operable to
find new values for the equivalent resistances R.sub.t1, R.sub.t2,
X.sub.e1, and X.sub.e2, where: R t .times. .times. 1 = R e .times.
.times. 1 s 1 ; and ( 21 ) R t .times. .times. 2 = R e .times.
.times. 2 s 2 . ( 22 ) ##EQU14##
[0040] The system may also be operated to estimate motor operating
parameters based on the values of X.sub.1, R.sub.2, X.sub.2,
R.sub.c, and X.sub.m, as represented by block 118. For example, the
system may be adapted to establish the values of the rotor torque
T, the rotor temperature, and the motor efficiency based on the
values of R.sub.2, X.sub.2, R.sub.c, and X.sub.m, electrical input
data and rotor speed data. The rotor current I.sub.2 may be
established using the following equation: I 2 = ( I 1 - ( V 1
.times. R - I 1 .times. R 1 ) R c - ( V 1 .times. i - I 1 .times. X
1 ) X m ) + j .function. ( ( V 1 .times. R - I 1 .times. R 1 ) X m
- ( V 1 .times. i - I 1 .times. X 1 ) R c ) . ( 23 ) ##EQU15## The
shaft torque may be obtained from the rotor resistance R.sub.2 and
the rotor current I.sub.2, as follows: T .times. .times. ( N
.times. - .times. m ) = 3 .times. I 2 .times. .times. rms 2 .times.
R 2 .omega. s .times. s . ( 24 ) ##EQU16## In the above equation,
I.sub.2rms is the RMS value of the rotor current I.sub.2, and
.omega..sub.s is the mechanical synchronous speed in rad/second
given by: .omega. s = 4 .times. .pi. .times. .times. f p . ( 25 )
##EQU17## In this equation, f is the alternating current frequency
in Hz and p is the number of poles of the motor.
[0041] The shaft torque may be converted to foot-pounds by
multiplying the torque in Newton-meters by 0.738. In addition, the
shaft torque is modified by subtracting the friction and windage
loss R.sub.F&W and the stray load loss using published values
and IEEE standards, as shown in the following table: TABLE-US-00001
Motor Power SLL % of output power 1-125 HP 1.8 126-500 HP 1.5
501-2499 HP 1.2
[0042] The motor efficiency is established by dividing the
estimated output mechanical power by the input electrical power.
.eta. = P out P in . ( 26 ) ##EQU18## The estimated output
mechanical power P.sub.out may be established from the torque T and
the rotor speed data.
[0043] The above-described technique was used to estimate the
efficiency of a 10 HP motor and a 600 HP motor using data from a
motor design program and test data. The following are the results
obtained for a 10 HP motor and the discussion of these results.
TABLE-US-00002 Motor Data: HP: 10 Elec. Des.: E9893A A RPM: 1175
Frame: 0256T Enclosure: TEFC Design: B Volts: 575 LR Code: G Amp:
10.1 Rotor: 418138071HE Duty: Cont. Stator: 418126002AJ
INS/AMB/S.F.: F/40/1.15 FAN: 702675001A TYP/PH/HZ: P/3/60
[0044] Using data from the program at full load and at 1/4 load,
the parameters of the motor were identified using the new method.
The following is a summary of the results. TABLE-US-00003 Estimated
Efficiency Program Efficiency % Error Full Load 91.315 91.097
0.239% 3/4 Load 92.154 91.850 0.330% 1/2 Load 92.101 91.661 0.479%
1/4 Load 89.005 88.186 0.928%
[0045] From the above results it can be seen that the error in the
estimated efficiency is less than 1% of the efficiency obtained
from the program results. It can also be observed that the error
increases as the load decreases. By examining the calculated losses
it was noticed that the calculated core loss is less than the
program value by 19 watts. This fixed error becomes a larger
percentage of the total loss at low loads and as a result the
percentage error in efficiency increases as the load decreases.
[0046] The estimated efficiency was also compared to laboratory
test data. The following is a summary of the results for the 10 HP
motor. TABLE-US-00004 Estimated Efficiency Actual Efficiency %
Error Full Load 89.98 90.310 -0.36% 1/4 Load 86.18 86.530
-0.41%
The estimated core loss in this case was more than the measured
value leading to a lower estimated efficiency than the measured
efficiency.
[0047] The procedure was repeated for a 600 HP motor. The following
are the results obtained for a 600 HP motor and the discussion of
these results. TABLE-US-00005 Motor Data: HP: 600 Elec. Des.: RPM:
1195 Frame: 35C5012Z Enclosure: TEFC Design: 139481 Volts: 575 LR
Code: Amp: 532 Rotor: 710623-2-S Duty: Cont. Stator: 710622-2-T
INS/AMB/S.F.: F/ /1.15
[0048] Comparing the design program data to the estimated values
from the above-described process, the following results were
obtained: TABLE-US-00006 Estimated Efficiency Program Efficiency %
Error Full Load 95.794 95.791 0.003% 3/4 Load 95.843 95.855 -0.013%
1/2 Load 95.318 95.352 -0.035% 1/4 Load 92.655 92.710 -0.059%
The difference between the design program data and estimated value
data is less 0.04%. Initially, the resolution selected for use with
the design program data for the speed of the motor was one decimal
point. The results obtained using one decimal point resolution on
speed lead to higher error in estimation. The results provided
above were obtained using a higher resolution on speed. In
addition, this particular motor has a very low slip. The slip in
RPM at full load is less than 5 RPM so that any error in the speed
measurement will lead to a large error in estimation. The following
are the results obtained using four decimal points resolution,
three decimal points resolution, two decimal points and one decimal
point resolution to illustrate the effect of resolution on the
efficiency estimation.
[0049] Four Decimal Points Resolution: TABLE-US-00007 Estimated
Efficiency Program Efficiency % Error Full Load 95.795 95.791
0.0036% 3/4 Load 95.844 95.855 -0.0122% 1/2 Load 95.320 95.352
-0.0338% 1/4 Load 92.658 92.710 -0.0550%
[0050] Three Decimal Points Resolution: TABLE-US-00008 Estimated
Efficiency Program Efficiency % Error Full Load 95.797 95.791
0.0065% 3/4 Load 95.848 95.855 -0.008% 1/2 Load 95.325 95.352
-0.028% 1/4 Load 92.669 92.710 -0.044%
[0051] Two Decimal Points Resolution: TABLE-US-00009 Estimated
Efficiency Program Efficiency % Error Full Load 95.887 95.791
-0.0143% 3/4 Load 95.969 95.855 -0.0364% 1/2 Load 95.509 95.352
-.0705% 1/4 Load 93.031 92.710 -0.1297%
[0052] One Decimal Point Resolution: TABLE-US-00010 Estimated
Efficiency Program Efficiency % Error Full Load 95.008 95.791
-0.817% 3/4 Load 94.776 95.855 -0.840% 1/2 Load 93.708 95.352
-1.200% 1/4 Load 89.494 92.710 -3.486%
[0053] From the above results it can be concluded that to provide a
good estimation of efficiency for low slip motors using this method
it is preferable to have a resolution on speed to at least two
decimal points. The reason for this is that if the resolution is
less than two decimal points the error in slip causes an error in
the estimation of the core loss, yielding a higher overall
error.
[0054] The system was then operated using lab test data for the 600
HP motor. The resolution of the speed that was used was 1 RPM. This
resolution is less than the minimum recommended for obtaining good
results. The results using this coarse resolution are shown below.
TABLE-US-00011 Estimated Efficiency Program Efficiency % Error Full
Load 96.59 96.65 -0.052% 3/4 Load 95.87 96.68 -0.840% 1/2 Load
95.02 96.17 -1.20% 1/4 Load 95.95 93.62 2.480%
From these results, it can be concluded that the method yields
excellent results for regular slip motors. However, for low slip
motors the resolution on the RPM of the motor is preferably at
least two decimal points so as to get a good estimate of the motor
efficiency in the field. One way of obtaining excellent resolution
of the motor speed is by using accelerometers to measure the motor
vibration and find its spectrum.
[0055] A comparison between the losses seen in the design program
and the estimated losses using the above-described method is
provided below. TABLE-US-00012 Design Program New Method Rotor
Loss: Full Load 1.79 KW 1.785 KW 3/4 Load .980 KW .979 KW 1/2 Load
.430 KW .429 KW 1/4 Load .107 KW .107 KW Core Loss: Full Load 5.77
KW 5.756 KW 3/4 Load 5.81 KW 5.852 KW 1/2 Load 5.85 KW 5.924 KW 1/4
Load 5.9 KW 5.975 KW
The results illustrate general agreement between the design program
results and the new method of estimating motor parameters describe
above.
[0056] Referring generally to FIG. 6, an alternative process for
establishing estimated values of various motor electrical
parameters using data obtained at a single operating point with no
load on the motor is shown and designated generally by reference
numeral 120. In addition, the estimated values of the motor
electrical parameters may be used to establish estimated values of
various motor operating parameters. The process comprises obtaining
stator resistance RI data, as represented by block 122. The
line-to-line input resistance may be measured, averaged, and
divided by 2 to determine the phase resistance R.sub.1. The process
also comprises obtaining electrical input data with no load on the
motor and providing the data to the processor module 84, as
represented by block 124. To achieve the no-load condition, the
motor is disconnected from its load. The electrical input data
obtained at the first load points comprises: input voltage data,
input current data. Some data may be provided to the system 80
using the control module 90 or may be provided from a remote
station 98 via the network 96. The current with no-load I.sub.n1
may be measured for each phase and averaged. The three line
voltages may be measured, averaged, and divide by {square root over
(3)} to determine the phase voltage V.sub.1.
[0057] The data processing module 82 may then be operated to
establish estimated values of various motor parameters, as
represented by block 126. The programming instructions are provided
to the data processing module 82 are adapted to utilize a novel
technique for establishing the values of the various motor
parameters using data obtained with no-load on the motor. With no
load on the motor, the rotor portion of the circuit will
effectively be an open circuit and is assumed to be an open circuit
for these purposes. The current I.sub.2 will be sufficiently small
to handle the windage and friction load of the rotor. With no load
on the motor, the stator current I.sub.1 will be the no-load
current I.sub.n1. The stator leakage inductance L.sub.1, the
magnetizing inductance L.sub.m and the core loss resistance R.sub.c
may be established using the following equations. First, the total
resistance R.sub.t may be obtained by the following equation: R t =
P I nl 2 . ( 27 ) ##EQU19##
[0058] The total impedance Z may be found by dividing the input
voltage V.sub.1 by the no-load current I.sub.n1, as follows: Z = V
1 I nl . ( 28 ) ##EQU20##
[0059] The total reactance X.sub.1+X.sub.m may be found from the
total impedance Z and the total resistance R.sub.t, as follows:
X.sub.1+X.sub.m= {square root over (Z.sup.2-R.sub.t.sup.2)}.
(29)
[0060] The individual values for the stator reactance X.sub.1 and
the magnetizing reactance X.sub.m may be found from the assumed
relationship of X.sub.1=0.05 X.sub.m, as follows:
X.sub.1+X.sub.m=1.05X.sub.m. (30)
[0061] Next, the motor friction and windage power P.sub.F&W may
be estimated based on the motor size and construction, if known. If
not, the motor friction and windage power P.sub.F&W is combined
with the core loss. The equivalent resistance R.sub.W&F due to
motor friction and windage power P.sub.F&W may be estimated as
follows: R W & .times. F = P W & .times. F I nl 2 . ( 31 )
##EQU21##
[0062] The series core loss resistance R.sub.m, may be established
as follows: R.sub.m=R.sub.t-R.sub.1-R.sub.W&F. (32)
[0063] The parallel magnetizing inductance L.sub.m, may be
established as follows: L m = X m 2 + R m 2 X m .times. .omega. . (
33 ) ##EQU22##
[0064] The parallel core resistance Rc, may be established as
follows: R c = X m 2 + R m 2 R m . ( 34 ) ##EQU23##
[0065] The stator leakage inductance L.sub.1, may be established as
follows: L 1 = X 1 .omega. . ( 35 ) ##EQU24##
[0066] As with the previous two load point method, the data
processing module 82 may be used to estimate other motor parameters
based on the estimated motor electrical parameter data obtained
above, as represented by block 128. An expression of the rotor
current I.sub.2 may be obtained from the voltage across the rotor
and the rotor impedance. Designating the voltage across the rotor
as V.sub.a and the rotor current as I.sub.2, the following equation
can be written: I 2 = V a R 2 S + j.omega. .times. .times. L 2 . (
36 ) ##EQU25##
[0067] The rotor current can also be expressed using the input
current I.sub.1, the current through the magnetizing inductance
I.sub.m, and the current through the core resistance I.sub.c, as
follows: I.sub.2=I.sub.1-I.sub.c-I.sub.m. (37)
[0068] The above currents can be expressed in terms of the voltage
and the value of the motor parameters as follows: V a = V 1 - I 1
.function. ( R 1 + j .times. .times. .omega. .times. .times. L 1 )
; ( 38 ) I c = V a R c ; .times. and ( 39 ) I m = V a j.omega.
.times. .times. L m . ( 40 ) ##EQU26##
[0069] The following expression for I.sub.2 may be obtained by
manipulating the equations above and substituting the expressions
for I.sub.1, I.sub.c, and I.sub.m from equations (38)-(40) into
equation (37): I 2 = I 1 - ( V 1 - I 1 .function. ( R 1 + j.omega.
.times. .times. L 1 ) ) R c - ( V 1 - I 1 .function. ( R 1 +
j.omega. .times. .times. L 1 ) j.omega. .times. .times. L m . ( 41
) ##EQU27##
[0070] Equations (36) and (41) can now be equated to obtain an
equation relating the input current, the input voltage, and the
motor parameters. Because the resulting equation has a real part
and imaginary part, this will yield two equations. The input
current can be written as a complex quantity:
I.sub.1=I.sub.1R-jI.sub.1i. (42)
[0071] Two equations, one representing the real part and one
representing the imaginary part, may be obtained using equations
(34), (39) and (40). The real part is as follows: ( I 1 .times. R -
V 1 R c + I 1 .times. R .times. R 1 R c + I 1 .times. i .times.
.omega. .times. .times. L 1 R c + I 1 .times. R .times. L 1 L m - R
1 .times. I 1 .times. i .omega. .times. .times. L m ) .times. ( R 2
2 s 2 + .omega. 2 .times. L 2 2 ) = R 2 S .times. ( V 1 - I 1
.times. R .times. R 1 - I 1 .times. i .times. .omega. .times.
.times. L 1 ) - .omega. .times. .times. L 2 .function. ( .omega.
.times. .times. L 1 .times. I 1 .times. R - R 1 .times. I 1 .times.
i ) . ( 43 ) ##EQU28##
[0072] The imaginary part will be given by: ( - I 1 .times. i +
.omega.L 1 .times. L 1 .times. R R c - R 1 .times. I 1 .times. i R
c + V 1 .omega. .times. .times. L m - I 1 .times. R .times. R 1
.omega. .times. .times. L m - I 1 .times. i .times. L 1 L m ) ( R 2
2 s 2 + .omega. 2 .times. L 2 2 ) = .times. - R 2 s .times. (
.omega. .times. .times. L 1 .times. I 1 .times. R - R 1 .times. I 1
.times. i ) - .omega. .times. .times. L 2 .function. ( V 1 - I 1
.times. R .times. R 1 - I 1 .times. i .times. .omega. .times.
.times. L 1 ) . ( 44 ) ##EQU29##
[0073] Equations 43 and 44 can be written as: .alpha. 1 .function.
( R 2 2 S 2 + .omega. 2 .times. L 2 2 ) = .alpha. 2 .times. R 2 +
.alpha. 3 .times. L 2 ; .times. and ( 45 ) .beta. 1 .function. ( R
2 2 S 2 + .omega. 2 .times. L 2 2 ) = .beta. 2 .times. R 2 + .beta.
3 .times. L 2 ; ( 46 ) ##EQU30## where the different variables are
given by: .alpha. 1 = I 1 .times. R - V 1 R c + I 1 .times. R
.times. R 1 R c + I 1 .times. i .times. .omega. .times. .times. L 1
R c + L 1 .times. I 1 .times. R L m - R 1 .times. I 1 .times. i
.omega. .times. .times. L m ; ( 47 ) .alpha. 2 = V 1 - I 1 .times.
R .times. R 1 - I 1 .times. i .times. .omega. .times. .times. L 1 s
; ( 48 ) .alpha. 3 = - .omega. .function. ( .omega. .times. .times.
L 1 .times. I 1 .times. R - R 1 .times. I 1 .times. i ) ; ( 49 )
.beta. 1 = - I 1 .times. i + .omega. .times. .times. L 1 .times. I
1 .times. R R c - R 1 .times. I 1 .times. i R c + V 1 .omega.
.times. .times. L m - I 1 .times. R .times. R 1 .omega. .times.
.times. L m - I 1 .times. i .times. L 1 L m ; ( 50 ) .beta. 2 =
.alpha. 3 .times. S .omega. ; .times. and ( 51 ) .beta. 3 = -
.alpha. 2 .times. .omega. .times. .times. S . ( 52 ) ##EQU31##
[0074] Dividing equations (43) and (44) and solving for the rotor
inductance in terms of the rotor resistance one gets: L 2 = .gamma.
.times. .times. R 2 ; ( 53 ) where .times. : .times. .times.
.gamma. = .alpha. 1 .times. .beta. 2 - .alpha. 2 .times. .beta. 1
.alpha. 3 .times. .beta. 1 - .alpha. 1 .times. .beta. 3 . ( 54 )
##EQU32##
[0075] Solving for the rotor resistance, the following relationship
results: R 2 = .alpha. 2 .alpha. 1 + .alpha. 3 .times. .gamma.
.alpha. 1 .omega. 2 .times. .gamma. 2 + 1 / s 2 . ( 55 )
##EQU33##
[0076] The following process may be used for calculating motor
torque and motor efficiency. First, estimate the slip s from the
shaft speed N and the synchronous speed N.sub.s, as follows: s = N
S - N N S . ( 56 ) ##EQU34## The synchronous speed Ns may be
obtained from the input frequency and the number of poles of the
motor. The power factor may then be computed using the input
current, input voltage, and input power.
[0077] Next, the real and imaginary components of the current
I.sub.1R & I.sub.1i are established using equations (47-54).
The rotor resistance may then be established using the following
equation: R 2 = ( .alpha. 2 .alpha. 1 + .alpha. 3 .alpha. 1 .times.
.gamma. ) ( .omega. 2 .times. .gamma. 2 + 1 s 2 ) . ( 57 )
##EQU35##
[0078] The rotor current and torque can be calculated using the
following equations: I.sub.2= {square root over
(.alpha..sub.1.sup.2+.beta..sub.1.sup.2)}. (58)
[0079] The torque T may be estimated by: T .times. .times. ( in
.times. .times. Newton .times. - .times. meters ) = 3 * I 2 .times.
.times. rms 2 * R 2 .omega. 2 * S ; ( 59 ) ##EQU36## where .omega.
s = 4 .times. .pi. .times. .times. f p ##EQU37## is the synchronous
speed and p is the number of poles. To convert the torque to ft-lbs
multiply the T in Newton-meters by 0.738.
[0080] For the purpose of calculating motor efficiency the output
power needs to be calculated. This can be obtained using the
following equation: Output .times. .times. Power .times. .times. P
out = TN 5252 - P F & .times. W - SLL ; ( 60 ) ##EQU38## where,
T is shaft torque in ft-lb and SLL is the stray load power loss,
which is typically a known percentage motor power depending on
motor size and varies with the square of the torque. The IEEE
standard specifies certain percentage of output power as SLL. This
percentage changes as the motor power changes. For example, for 1
to 125 HP motors, the SLL is equal to 1.8% of maximum power. For
126 to 500 HP motors, the SLL is equal to 1.5% of maximum power.
Finally, for 501 to 2499 HP motors, the SLL is equal to 1.2% of
maximum power.
[0081] As mentioned above, if the friction and windage loss is not
known, its value can be lumped with the core loss. The effect of
lumping the friction and windage loss with core loss is to cause
the rotor loss to be lower than the actual loss, thus raising the
estimated efficiency, since the effect of lumping the friction and
windage loss with the core loss is to reduce the power across the
air gap by the friction and windage loss. In this circumstance, the
rotor loss is the motor slip times the friction and windage loss.
To obtain an estimate of the maximum error using this
approximation, a value of slip equal to 0.025 and a maximum
percentage of friction and windage loss of motor power equal to 3%
may be used. This yields a maximum error in estimating the
efficiency equal to 0.075%, which is within the measurement error.
Tests conducted on different motors indicate the validity of the
assumption. If the value of the friction and windage loss is known,
then that value may be used. The motor efficiency may then be
estimated using the ratio of the estimated output power to the
input power. The above-described method was applied to experimental
data and the results indicate an accuracy of over 99%.
[0082] It is important to note that the core loss is obtained at a
constant frequency. If the motor used at a different frequency,
then the core loss needs to be estimated at the new frequency. In
general the core loss is proportional to the square of frequency
and to the magnitude of the flux density. If the flux density is
constant then a simple equation can be used to estimate the core
loss at a different operating frequency.
Test Results:
[0083] The no-load data from three motors were used to test the
accuracy of the above method. The following is a summary of the
data obtained. TABLE-US-00013 10 HP Motor: Motor Data: HP: 10 Elec.
Des.: E9893A A RPM: 1175 Frame: 0256T Enclosure: TEFC Volts: 575
Design: B Amp: 10.1 LR Code: G Duty: Cont. Rotor: 418138071HE
INS/AMB/S.F.: F/40/1.15 Stator: 418126002AJ TYP/PH/HZ: P/3/60 FAN:
702675001A No load Current: 4.41 ampere No Load Voltage: 574.9
volts No Load Power: 261.73 watts Stator Resistance: 0.8765 ohm
F&W power: 57 watts Stray Load Loss: 1.13% obtained from
experimental data
The results obtained are as follows:
[0084] Actual Motor Efficiency at full load=90.2434%
[0085] Estimated Motor Efficiency=90.8452%
[0086] Estimation Error=0.6357% TABLE-US-00014 150 HP Motor: Motor
Data: HP: 150 Elec. Des.: W00868-A-A001 RPM: 1180 Frame: EC360
Enclosure: TENV Volts: 460 Amp: 10.1 Duty: 15 Min INS/AMB/S.F.:
F//1.15 No Load Current: 66.09 ampere No Load Voltage: 460 volts No
Load Power: 2261 watts Stator resistance: 0.03509 ohm F & W
power: 896 watts Stray Load Loss: 0.85% from test data
The results obtained are as follows:
[0087] Actual Motor Efficiency at full load=93.106%
[0088] Estimated Motor Efficiency=93.413%
[0089] Estimation Error=0.3303% TABLE-US-00015 600 HP Motor: Motor
Data: HP: 600 Elec. Des.: RPM: 1195 Frame: 35C5012Z Enclosure: TEFC
Volts: 575 Design: 139481 Amp: 532 LR Code: Duty: Cont. Rotor:
710623-2-S INS/AMB/S.F.: F//1.15 Stator: 710622-2-T No Load Current
= 148.45 ampere No Load Voltage = 575 volts No Load Power = 6860
watts Stator resistance = .0091 ohm F & W power = 1725 watts
Stray Load Loss = 1.3% from Test data
The results obtained are as follows:
[0090] Actual Motor Efficiency at full load=96.025%
[0091] Estimated Motor Efficiency=95.976%
[0092] Estimation Error=-0.0500%
[0093] To make the estimation of the motor efficiency less
sensitive to slight errors in measured frequency, the following
process may be performed. First, the stator loss is calculated
using the input current and the estimated stator resistance
R.sub.1. The friction and windage loss is estimated based on the
motor size, type, and speed. The rotor loss may be estimated by
subtracting the stator loss from the Input power P and multiplying
the remainder by the slip. The stray load loss SLL is estimated
based on the IEEE standard, as described above, with the exception
that the core loss is neglected. The modified input power is then
calculated at the two measurement points by subtracting the above
losses from the input power P.
[0094] A plot of the modified input power versus measured speed may
then be performed to determine the core loss. The core loss is the
modified input power at the synchronous speed n.sub.s. This can be
determined mathematically using the following equation: CoreLoss =
( P 1 - n 1 .function. ( P 2 - P 1 n 2 - n 1 ) ) + ( P 2 - P 1 n 2
- n 1 ) .times. n S ; ( 61 ) ##EQU39## where:
[0095] P.sub.1 Modified Input power at point 1 "low load"
[0096] P.sub.2 Modified Input power at point 2 "high load"
[0097] n.sub.1 Motor speed at point 1
[0098] n.sub.2 Motor speed at point 2
[0099] n.sub.s Synchronous speed using the measured frequency at
low load.
[0100] The rotor loss and the stray load loss SLL may then be
recalculated using the new core loss value. The magnetizing
inductance L.sub.m, rotor resistance R.sub.2, and rotor leakage
inductance L.sub.2 are calculated as provided previously. This
method was found to be less sensitive to error in frequency
measurements.
[0101] The temperature of the rotor during motor operation may be
estimated using the estimated value of the rotor resistance R.sub.2
and the following equation relating changes in electrical
resistance of the rotor to changes in temperature: R.sub.2
hot=R.sub.2 cold(1+.alpha.(T.sub.hot-T.sub.cold)); (62) where:
R.sub.2 cold is the rotor resistance at a first temperature;
R.sub.2 hot is the rotor resistance at a second temperature;
T.sub.cold is the rotor temperature at a first temperature;
T.sub.hot is the rotor temperature at a second temperature; and
.alpha. is the temperature coefficient of electrical resistance of
the rotor in .OMEGA./unit of temperature.
[0102] As an example, the above equation may be manipulated
algebraically to obtain the following equation for an aluminum
rotor: T hot = R 2 .times. .times. hot R 2 .times. .times. cold * (
225 + T cold ) - 225. ( 63 ) ##EQU40##
[0103] The value used for R.sub.2 hot is the estimated value for
the rotor resistance R.sub.2 at the second temperature T.sub.hot.
The control module 90 may be used to input the rotor temperature at
the first temperature T.sub.cold and the rotor resistance at the
first temperature R.sub.2 cold. In addition, the data may be
provided by the remote stations 98 via the network 96.
[0104] Referring generally to FIG. 7, a process for establishing
values of various motor electrical parameters and various motor
operating parameters using the system of FIG. 3 is shown and
designated generally by reference numeral 130. The process
comprises obtaining the resistance of the stator, as represented by
block 132. The process also comprises obtaining data at a single
operating load point and providing the data to the processor module
84, as represented by block 134. In a presently contemplated
embodiment, the data obtained at the first load point comprises:
input voltage data, input current data, input power data, shaft
speed data, and stator temperature data. It should be noted that
the input power can either be measured or calculated from the other
input data. Some data may be provided to the system 80 using the
control module 90 or may be provided from a remote station 98 via
the network 96.
[0105] As represented by block 136, the data processing module 82
then operates to establish estimated values of various motor
parameters. As discussed above, these estimated motor parameters
may comprise one or more of the circuit parameters in the motor
equivalent circuits 50 and 110 illustrated in FIGS. 2 and 5.
Accordingly, the various motor parameters may comprise the stator
resistance R.sub.1, the slip s, the stator leakage reactance
X.sub.1, the rotor resistance R.sub.2, the rotor leakage reactance
X.sub.2, the core loss resistance R.sub.c, and the magnetizing
reactance X.sub.m. The stator resistance R.sub.1 and the motor slip
s can be measured relatively easily, while the remaining parameters
(i.e., X.sub.1, R.sub.2, X.sub.2, R.sub.c, and X.sub.m) are
estimated by the processor module 84 in accordance with unique
aspects of the process 130 illustrated in FIG. 7.
[0106] As represented by block 138, the data processing module 82
then operates to establish estimated values of other unknown motor
parameters based on the one or more parameters estimated in block
136. For example, the data processing module 82 may estimate output
power, efficiency, torque, and other characteristics of the motor
20. Accordingly, in certain embodiments, the data processing module
82 operates in accordance with the process 130 to obtain various
losses associated with the motor 20. For example, the losses may
comprise stator loss, rotor loss, core loss, friction and windage,
and stray load loss. The stator loss can be estimated accurately by
measuring the stator resistance R.sub.1 and the stator current
I.sub.1. The friction and windage loss can be estimated using
simulated data on different motor sizes. For example, the data
processing module 82 can access a database of motors to obtain the
appropriate friction and windage loss. An exemplary motor database
may list the motor frame size, number of poles, fan diameter, and
the loss associated with the motor. The stray load loss can be
estimated using the IEEE standard. Finally, data processing module
82 estimates the rotor loss and the core loss, as described in
further detail below.
[0107] The rotor loss can be estimated approximately by multiplying
the input power minus the stator loss by the slip, as follows:
RotorLoss=(P.sub.in-3I.sub.1.sup.2R.sub.1)s (64) P.sub.in is the
input power in watts, I.sub.1 is the input current, R.sub.1 is the
stator phase resistance, and s is the slip of the rotor. As
discussed above with reference to FIG. 7, these parameters are
obtained in blocks 132 and 134 of the process 130. Accordingly, the
data processing module 82 readily estimates the rotor loss
according to equation (64). The error in estimating the rotor loss
using this method is equal to the slip s multiplied by the core
loss. In view of the equivalent circuit 50 of FIG. 2, the core loss
can be expressed as follows: CoreLoss = 3 .times. V a 2 R c ( 65 )
##EQU41## V.sub.a is the voltage across the rotor and R.sub.c is
the core loss resistance. Accordingly, the error associated with
the rotor loss calculated above in equation (64) can be expressed
as follows: Rotor .times. .times. Loss .times. .times. Error = 3
.times. V a 2 R c .times. s ( 66 ) ##EQU42## The foregoing
calculation provides an accurate estimation of rotor loss for
motors having low to moderate core loss (e.g., less than 50% of the
total losses). For example, if the core loss (65) is roughly 20% of
the losses, then a motor having 85% efficiency will have a core
loss of approximately the 3% of the input power. If the motor has
four poles and a 40-rpm slip at full load, then the slip s will be
approximately 0.0227. Applying these values to equation (66), the
percentage error in rotor loss is equal to 0.068% of input power.
Accordingly, the rotor loss error (66) has a negligible effect on
the calculation of rotor loss (64) and motor efficiency, as
discussed in further detail below.
[0108] The only loss left to be estimated is the core loss. For
this estimated motor parameter, the data processing module 82
operates to calculate the various parameters of the equivalent
circuits 50 and 110, as illustrated in FIGS. 2 and 5. In the
illustrated embodiment of FIG. 7, the data processing module 82
operates to obtain or estimate the various parameters: R.sub.1, s,
X.sub.1, R.sub.2, X.sub.2, R.sub.c, and X.sub.m. The calculation of
the stator resistance R.sub.1 and the motor slip s can be obtained
relatively easily. However, the data processing module 82 estimates
the remaining parameters (i.e., X.sub.1, R.sub.2, X.sub.2, R.sub.c,
and X.sub.m) using unique aspects of the process 130, as set forth
below. Once all circuit parameters are obtained, the data
processing module 82 estimates the core loss. In turn, the data
processing module 82 can estimate other operating parameters of the
motor, such as motor efficiency, torque, and so forth.
[0109] As discussed above, the process 130 comprises several
assumptions and approximations to simplify the process of
estimating X.sub.1, R.sub.2, X.sub.2, R.sub.c, and X.sub.m. For
example, the frequency of the power is assumed to be constant, the
speed of the rotor is assumed to be constant during the gathering
of the single load point data, and the rotor temperature is assumed
to be constant during the gathering of the data. Additionally, it
has been shown that the stator leakage reactance X.sub.1 can be
expressed as a fraction of the magnetizing reactance X.sub.m using
the following equation: X.sub.1=0.0325X.sub.m (67) As discussed
above, this factor may range from 0.02 to 0.07.
[0110] According to the IEEE standard, the rotor leakage reactance
X.sub.2 can be expressed as a function of the stator leakage
reactance X.sub.1 as follows: For design A motors: X.sub.2=X.sub.1
(68) For design B motors: X.sub.2=1.492X.sub.1 (69) For design C
motors: X.sub.2=2.325X.sub.1 (70) For design D motors:
X.sub.2=X.sub.1 (71) Accordingly, the calculation of rotor leakage
reactance X.sub.2 provided by equations (68) through (71) depends
on the calculation of stator leakage reactance X.sub.1 provided by
equation (67), which in turn depends on the calculation of
magnetizing reactance X.sub.m. The magnetizing reactance X.sub.m is
estimated by the data processing module 82, as set forth below.
[0111] In view of the simplified motor equivalent circuit 110
illustrated in FIG. 5, the data processing module 82 estimates an
approximate value of equivalent resistance X.sub.e using the
following equations relating the measured input current, voltage
and power: Real .times. .times. Part .times. .times. of .times.
.times. Input .times. .times. Impedance .times. .times. Z inR = V
inR I 1 ( 72 ) Imaginary .times. .times. Part .times. .times. of
.times. .times. input .times. .times. Impedance .times. .times. Z
inI = V inI I 1 ( 73 ) X e = ( Z inI - X 1 ) + ( Z inR - R 1 ) 2 (
Z inI - X 1 ) ( 74 ) ##EQU43## V.sub.inR is the real portion of the
input voltage, V.sub.inI is the imaginary portion of the input
voltage, I.sub.1 is the electric current through the stator,
R.sub.1 is the stator resistance, and X.sub.1 is the stator leakage
reactance. The data processing module 82 also defines the parallel
resistive element or total resistance R.sub.t, as set forth in the
following equation: R t = ( Z inR - R 1 ) + ( Z inI - X 1 ) 2 ( Z
inR - R 1 ) ( 75 ) ##EQU44## In this exemplary embodiment, the data
processing module 82 initially assumes the stator leakage reactance
X.sub.1 equal to zero to estimate a first approximation of the
equivalent resistance X.sub.e, as set forth below: X e .times.
.times. ( approximate ) = Z inI + ( Z inR - R 1 ) 2 Z inI ( 76 )
##EQU45##
[0112] In view of the relationships set forth above in equations
(67) through (76), the data processing module 82 estimates an
approximate value for the stator leakage reactance X.sub.1 as a
fraction of the first approximation of the equivalent resistance
X.sub.e, as follows:
X.sub.1(approximate)=0.0325X.sub.e(approximate) (77) Again, this
factor may range from 0.02 to 0.07. After calculating an
approximate value for the stator leakage reactance X.sub.1 as set
forth by equation (77), the data processing module 82 can estimate
the rotor leakage reactance X.sub.2 using the appropriate one of
equations (68) through (71). Accordingly, only the rotor resistance
R.sub.2, the core loss resistance R.sub.c, and the magnetizing
reactance X.sub.m remain to be estimated by the data processing
module 82.
[0113] In the illustrated embodiment of FIG. 7, data processing
module 82 estimates the rotor resistance R.sub.2 using the
following relationships: R 2 = 3 .times. V a 2 .times. s 2
RotorLoss ( 78 ) ##EQU46## Again, V.sub.a is the voltage across the
rotor, s is the slip of the rotor, and the rotor loss is estimated
according to equation (64). The rotor voltage V.sub.a can be
calculated from the real and imaginary parts V.sub.aR and V.sub.aI
of the rotor voltage V.sub.a, as set forth in the following
equations: V.sub.aR=V.sub.1R-I.sub.1R.sub.1 (79)
V.sub.aI=V.sub.1l-I.sub.1X.sub.1 (80)
V.sub.a=(V.sub.aR.sup.2+V.sub.aI.sup.2).sup.1/2 (81) After
calculating the rotor voltage V.sub.a, the data processing module
82 proceeds to calculate the rotor resistance defined by equation
(77). Accordingly, only the core loss resistance R.sub.c and the
magnetizing reactance X.sub.m remain to be estimated by the data
processing module 82.
[0114] The data processing module 82 can calculate the magnetizing
reactance X.sub.m and that core loss resistance R.sub.c from the
following relationships: 1 X e = 1 X m + 1 X 2 + R 2 2 X 2 ( 82 ) 1
R t = 1 R c + 1 R 2 S + X 2 2 R 2 S ( 83 ) ##EQU47## Finally, using
the core loss resistance R.sub.c calculated from equation (83), the
processing module 82 can calculate the core loss defined by
equation (65).
[0115] At this point, the data processing module 82 has estimated
values for all of the motor parameters (e.g., X.sub.1, R.sub.2,
X.sub.2, R.sub.c, and X.sub.m) and all the motor losses (e.g.,
stator loss, rotor loss, core loss, friction and windage loss, and
stray load loss). If desired, after calculating the magnetizing
reactance X.sub.m as set forth in equation (82), the data
processing module 82 can recalculate the stator leakage reactance
X.sub.1 according to equation (67). In turn, the data processing
module 82 can recalculate the other motor parameters (e.g.,
R.sub.2, X.sub.2, R.sub.c, and X.sub.m) and the core loss using the
newly estimated value of stator leakage reactance X.sub.1.
Accordingly, the data processing module 82 can reiterate the
calculations set forth in equations (67) through (83) any number of
times to improve the accuracy of the estimated motor
parameters.
[0116] After obtaining final estimations of these motor parameters
and losses, the data processing module 82 can proceed to estimate
motor operating parameters, such as motor efficiency, torque, and
so forth (block 138). For example, the system may be adapted to
calculate the rotor torque, the rotor temperature, and the motor
efficiency based on the values of R.sub.2, X.sub.2, R.sub.c, and
X.sub.m, electrical input data, and rotor speed data. As discussed
above, the shaft torque may be obtained from the rotor resistance
R.sub.2 and the rotor current I.sub.2 as set forth in equation
(24). In addition, the motor efficiency can be estimated from the
following equation: .eta. = P out P i .times. .times. n = P i
.times. .times. n - SL - RL - CL - FWL - SLL P i .times. .times. n
( 84 ) ##EQU48## SL is the stator loss, RL is the rotor loss
estimated above in equation (64), CL is the core loss estimated
above in equation (65), FWL is the friction and windage loss, and
SLL is the stray load loss.
[0117] The process 130 described above with reference to FIG. 7
provides an exceptional estimation of the motor parameters, motor
losses, and the motor efficiency. These estimations are
particularly accurate if the core loss moderate to low, e.g., less
than 50% of the total motor losses. The reason for this correlation
between accuracy and core loss is due to the assumption of zero
core loss in the estimation of rotor loss, rotor resistance
R.sub.2, and core loss resistance R.sub.C. In the illustrated
embodiment of FIG. 7, the magnitude of the core loss resistance
R.sub.C relates to the addition of the rotor leakage reactance
X.sub.2. Accordingly, the value of the rotor leakage reactance
X.sub.2 results in a different core loss resistance R.sub.C.
[0118] As an example of the accuracy of the single load point
techniques described above, the process 130 was used to estimate
the efficiency of a 60 HP motor. The actual efficiency of the motor
is 94.4%, whereas the process 130 estimated the motor efficiency as
94% using a single load point. In addition, a TENV 75 HP motor
(design B) was evaluated using both the two load points and single
load point techniques described with reference to FIGS. 4 and 7.
The motor efficiency estimated according to the two load points
technique was 90.6%, while the single load point technique yielded
a motor efficiency of 91.6%. The single load point technique of
FIG. 7 estimated motor efficiencies based on the high load point
and different reactance ratios X.sub.2/X.sub.1, i.e., 1.5, 2, 2.5,
and 3, as tabulated below: TABLE-US-00016 Reactance Ratio Core
Resistance Ohm Efficiency 1.5 316 91.6 2 158 90.7 2.5 90.6 89.26 3
56.1 87.25 Zero Core Loss Max Eff. Infinity 92.6
At a reactance ratio of 1.5, the motor efficiency estimated by the
single point technique of FIG. 7 is approximately 1% higher than
the motor efficiency estimated by the two point technique of FIG.
4. Accordingly, it can be concluded that the single point technique
of FIG. 7 estimates the motor efficiency at an accuracy of 98%,
because the accuracy of the two point technique of FIG. 4 has been
established at approximately 99%. As a result, the single point
technique of FIG. 7 can provide a range of motor efficiencies by
estimating the maximum efficiency based on zero core loss and a
lower bound using a leakage reactance ratio of 2.5.
[0119] Referring generally to FIG. 8, a process for establishing
values of various motor electrical parameters and various motor
operating parameters using the system of FIG. 3 is shown and
designated generally by reference numeral 140. The process
comprises obtaining data at a first operating load point and
providing the data to the processor module 84, as represented by
block 142. The process also comprises obtaining data at a second
operating load point and providing the data to the processor module
84, as represented by block 144. The process further comprises
obtaining data at a third operating load point and providing the
data to the processor module 84, as represented by block 146. In a
presently contemplated embodiment, the data obtained at the first,
second, and third load points comprises: input voltage data, input
current data, input power data, shaft speed data, and frequency of
the motor 20. It should be noted that the input power can either be
measured or calculated from the other input data. In addition, the
process may measure motor temperature. However, the data obtained
at these three points generally does not include the stator
resistance of the motor 20. Some data may be provided to the system
80 using the control module 90 or may be provided from a remote
station 98 via the network 96.
[0120] As represented by block 148, the data processing module 82
then operates to establish estimated values of various motor
parameters without the need to measure the stator resistance. As
discussed above, these estimated motor parameters may comprise one
or more of the circuit parameters in the motor equivalent circuits
50 and 110 illustrated in FIGS. 2 and 5. Accordingly, the various
motor parameters may comprise the stator resistance R.sub.1, the
slip s, the stator leakage reactance X.sub.1, the rotor resistance
R.sub.2, the rotor leakage reactance X.sub.2, the core loss
resistance R.sub.c, and the magnetizing reactance X.sub.m. These
seven parameters determine the motor equivalent circuit 50.
Accordingly, the motor equivalent circuit 50 can be fully analyzed
by measuring and/or estimating these parameters. The motor slip s
can be calculated based on the speed of the motor, which is
obtained in blocks 142, 144, and 146. The remaining parameters
(i.e., R.sub.1, X.sub.1, R.sub.2, X.sub.2, R.sub.c, and X.sub.m)
are estimated by the processor module 84 in accordance with unique
aspects of the process 140 illustrated in FIG. 8.
[0121] As represented by block 150, the data processing module 82
then operates to establish estimated values of other unknown motor
parameters based on the one or more parameters estimated in block
148. For example, the data processing module 82 may estimate output
power, efficiency, torque, and other characteristics of the motor
20. In addition, in certain embodiments, the data processing module
82 operates in accordance with the process 140 to obtain various
losses associated with the motor 20. For example, the losses may
comprise stator loss, rotor loss, core loss, friction and windage,
and stray load loss. Based on these losses, the data processing
module 82 can then estimate the motor efficiency.
[0122] To estimate the six unknown motor parameters, the process
140 of FIG. 8 proceeds to solve six equations relating to
measurements of the input voltage, current, power, and output speed
at the three load points. In view of the motor equivalent circuit
50 of FIG. 2, the input impedance at three load points may be
defined by the following equations: Z i .times. .times. n .times.
.times. 1 = Z s + Z c .times. Z r .times. .times. 1 Z c + Z r
.times. .times. 1 ( 85 ) Z i .times. .times. n .times. .times. 2 =
Z s + Z c .times. Z r .times. .times. 2 Z c + Z r .times. .times. 2
( 86 ) Z i .times. .times. n .times. .times. 3 = Z s + Z c .times.
Z r .times. .times. 3 Z c + Z r .times. .times. 3 ( 87 ) ##EQU49##
Z.sub.s is the stator impedance, Z.sub.c is of the core impedance,
and Z.sub.r is the rotor impedance. These three input impedance
equations can be combined by subtracting equation (86) from
equation (85), subtracting equation (87) from equation (85), and
dividing the resulting two equations to obtain the following: ( Z i
.times. .times. n .times. .times. 1 - Z i .times. .times. n .times.
.times. 2 ) .times. ( Z c + Z r .times. .times. 2 ) ( Z i .times.
.times. n .times. .times. 1 - Z i .times. .times. n .times. .times.
3 ) .times. ( Z c + Z r .times. .times. 3 ) = ( Z r .times. .times.
1 - Z r .times. .times. 2 ) ( Z r .times. .times. 1 - Z r .times.
.times. 3 ) ( 88 ) ##EQU50## In addition, given that the rotor
leakage inductance L.sub.2 and the rotor resistance R.sub.2 are the
same at each of the three load points, the right hand side of
equation (88) can be simplified to the following equation: .lamda.
= ( 1 S 1 - 1 S 2 ) ( 1 S 1 - 1 S 3 ) ( 89 ) ##EQU51## S.sub.1,
S.sub.2, and S.sub.3 are the motor slips at the three load points.
As discussed above, these motor slips S.sub.1, S.sub.2, and S.sub.3
can be calculated from speed measurements obtained in blocks 142,
144, and 146 of the process 140. Denoting the quantity in equation
(89) by .lamda., the foregoing equation (88) can be solved for core
impedance Z.sub.c in terms of the rotor impedance Z.sub.r at load
points 2 and 3 as set forth in the following equation: Z c = ( Z i
.times. .times. n .times. .times. 1 - Z i .times. .times. n .times.
.times. 2 ) .times. Z r .times. .times. 2 - .lamda. .function. ( Z
i .times. .times. n .times. .times. 1 - Z i .times. .times. n
.times. .times. 3 ) .times. Z r .times. .times. 3 [ .lamda.
.function. ( Z i .times. .times. n .times. .times. 1 - Z i .times.
.times. n .times. .times. 3 ) - ( Z i .times. .times. n .times.
.times. 1 - Z i .times. .times. n .times. .times. 2 ) ] ( 90 )
##EQU52##
[0123] The core impedance Z.sub.c defined by equation (90) can then
be substituted into equation (88) to obtain an equation in the
rotor input impedances Z.sub.r1, Z.sub.r2 and Z.sub.r3 at the
first, second, and third load points. These rotor input impedances
Z.sub.r1, Z.sub.r2 and Z.sub.r3 are functions of the rotor leakage
reactance X.sub.2 and the motor resistance R.sub.2. The resulting
equation can be decomposed into a real part and an imaginary part
yielding two equations in the two rotor unknowns. The rotor
impedance Z.sub.r can be expressed as: Z r = R 2 S + j .times.
.times. X 2 ( 91 ) ##EQU53## Using equation (91) at the three load
points yields the rotor impedance Z.sub.r at the three different
slips S.sub.1, S.sub.2, and S.sub.3. After the foregoing
substitution of the core impedance Z.sub.c decomposition into real
and imaginary parts, equation (88) can be redefined as set forth
below: The real part is given by: ( A 22 S 2 2 + A 33 S 3 2 + A 12
S 1 .times. S 2 + A 13 S 1 .times. S 3 + A 23 S 2 .times. S 3 )
.times. R 2 2 - ( A 22 + A 33 + A 12 + A 13 + A 23 ) .times. X 2 2
- [ 2 .times. B 22 S 2 + 2 .times. B 33 S 3 + ( 1 S 1 + 1 S 2 )
.times. B 12 + ( 1 S 1 + 1 S 3 ) .times. B 13 - ( 1 S 2 + 1 S 3 )
.times. B 23 ] .times. R 2 .times. X 2 = 0 ( 92 ) ##EQU54## The
imaginary part is given by: ( B 22 S 2 2 + B 33 S 3 2 + B 12 S 1
.times. S 2 + B 13 S 1 .times. S 3 + B 23 S 2 .times. S 3 ) .times.
R 2 2 - ( B 22 + B 33 + B 12 + B 13 + B 23 ) .times. X 2 2 + [ 2
.times. A 22 S 2 + 2 .times. A 33 S 3 + ( 1 S 1 + 1 S 2 ) .times. A
12 + ( 1 S 1 + 1 S 3 ) .times. A 13 + ( 1 S 2 + 1 S 3 ) .times. A
23 ] .times. R 2 .times. X 2 = 0 ( 93 ) ##EQU55## The A's and the
B's in equations (92) and (93) are functions of the measured input
impedance at the three load points and, also, the rotor resistance
R.sub.2.
[0124] As set forth below in detail below, these two equations (92)
and (93) can be simplified as:
(M.sub.1+M.sub.2R.sub.2)R.sub.2.sup.2+(N.sub.1+N.sub.2R.sub.2)X.sub.2.sup-
.2+(L.sub.1+L.sub.2R.sub.2)R.sub.2X.sub.2=0 (94)
(U.sub.1+U.sub.2R.sub.2)R.sub.2.sup.2+(V.sub.1+V.sub.2R.sub.2)X.sub.2.sup-
.2+(W.sub.1+W.sub.2R.sub.2)R.sub.2X.sub.2=0 (95) Equation (95)
essentially obtains the rotor leakage reactance X.sub.2 in terms of
the rotor resistance R.sub.2. The A's and B's can be defined by the
following equations in which .beta..sub.R and .beta..sub.j are the
real and imaginary parts of the measured differential input
impedance .beta..sub.1 and .beta..sub.2 and the subscripts 1, 2,
and 3 refer to the first, second, and third load points obtained at
blocks 142, 144, and 146 of the process 140 of FIG. 7. A 22 = (
.beta. 1 .times. R 2 - .beta. 1 .times. j 2 ) .times. ( ( 1 S 2 - 1
S 1 ) .times. R 2 + .lamda..beta. 2 .times. R ) - 2 .times. .beta.
1 .times. R .times. .beta. 1 .times. j .times. .beta. 2 .times. j
.times. .lamda. ( 96 ) .beta. 1 = Z i .times. .times. n .times.
.times. 1 - Z i .times. .times. n .times. .times. 2 ( 97 ) .beta. 2
= Z i .times. .times. n .times. .times. 1 - Z i .times. .times. n
.times. .times. 3 ( 98 ) A 33 = .lamda. 2 .function. [ ( .beta. 2
.times. R 2 - .beta. 2 .times. j 2 ) .times. ( ( 1 S 2 - 1 S 1 )
.times. R 2 + .beta. 1 .times. R ) - 2 .times. .beta. 2 .times. R
.times. .beta. 2 .times. j .times. .beta. 1 .times. j ] ( 99 ) A 12
= [ ( .beta. 1 .times. R .times. .beta. 2 .times. R - .beta. 1
.times. j .times. .beta. 2 .times. j ) .times. ( .lamda. 2 .times.
.beta. 2 .times. R - .lamda..beta. 1 .times. R ) - ( .beta. 1
.times. R .times. .beta. 2 .times. j + .beta. 1 .times. j .times.
.beta. 2 .times. R ) .times. ( .lamda. 2 .times. .beta. 2 .times. j
- .lamda..beta. 1 .times. j ) ] ( 100 ) A 13 = - A 12 ( 101 ) A 23
= - [ ( .beta. 1 .times. R .times. .beta. 2 .times. R - .beta. 1
.times. j .times. .beta. 2 .times. j ) .times. ( .lamda..beta. 1
.times. R + .lamda. 2 .times. .beta. 2 .times. R + 2 .times. R 2
.function. ( 1 S 1 - 1 S 2 ) ) - ( .beta. 1 .times. R .times.
.beta. 2 .times. j + .beta. 1 .times. j .times. .beta. 2 .times. R
) .times. ( .lamda..beta. 1 .times. j + .lamda. 2 .times. .beta. 2
.times. j ) ] ( 102 ) B 22 = .lamda..beta. 2 .times. j .function. (
.beta. 1 .times. R 2 - .beta. 1 .times. j 2 ) + 2 .times. .beta. 1
.times. R .times. .beta. 1 .times. j .function. ( ( 1 S 2 - 1 S 1 )
.times. R 2 + .lamda..beta. 2 .times. R ) ( 103 ) B 33 = .lamda. 2
.function. [ .beta. 1 .times. j .function. ( .beta. 2 .times. R 2 -
.beta. 2 .times. j 2 ) + 2 .times. .beta. 2 .times. R .times.
.beta. 2 .times. j .function. ( ( 1 S 2 - 1 S 1 ) .times. R 2 +
.beta. 1 .times. R ) ] ( 104 ) B 12 = [ ( .beta. 1 .times. R
.times. .beta. 2 .times. j + .beta. 1 .times. j .times. .beta. 2
.times. R ) .times. ( .lamda. 2 .times. .beta. 2 .times. R -
.lamda..beta. 1 .times. R ) + ( .beta. 1 .times. R .times. .beta. 2
.times. R - .beta. 1 .times. j .times. .beta. 2 .times. j ) .times.
( .lamda. 2 .times. .beta. 2 .times. j - .lamda..beta. 1 .times. j
) ] ( 105 ) B 13 = - B 12 ( 106 ) B 23 = - [ ( .beta. 1 .times. R
.times. .beta. 2 .times. R - .beta. 1 .times. j .times. .beta. 2
.times. j ) .times. ( .lamda..beta. 1 .times. j + .lamda. 2 .times.
.beta. 2 .times. j ) + ( .beta. 1 .times. R .times. .beta. 2
.times. j + .beta. 1 .times. j .times. .beta. 2 .times. R ) .times.
( .lamda..beta. 1 .times. R + .lamda. 2 .times. .beta. 2 .times. R
+ 2 .times. R 2 .function. ( 1 S 1 - 1 S 2 ) ) ] ( 107 )
##EQU56##
[0125] In turn, an equation (108) can be achieved by dividing
equations (94) and (95) by the square of the rotor leakage
reactance X.sub.2.sup.2 and by defining .alpha.=R.sub.2/X.sub.2
(i.e., the ratio of rotor resistance R.sub.2 to rotor leakage
reactance X.sub.2), as set forth below: .alpha. = ( W 1 + W 2
.times. R 2 ) .times. ( N 1 + N 2 .times. R 2 ) - ( L 1 + L 2
.times. R 2 ) .times. ( V 1 + V 2 .times. R 2 ) ( M 1 + M 2 .times.
R 2 ) .times. ( V 1 + V 2 .times. R 2 ) - ( N 1 + N 2 .times. R 2 )
.times. ( U 1 + U 2 .times. R 2 ) ( 108 ) ##EQU57##
[0126] In view of the equations set forth above, the rotor leakage
reactance X.sub.2 can be obtained in terms of the rotor resistance
R.sub.2 based on equation (95). The rotor leakage reactance X.sub.2
from equation (108) can then be substituted into the equation (94).
This substitution yields a cubic equation in the rotor resistance
R.sub.2. Using a spreadsheet, it was found that the foregoing
equation reduces to a quadratic equation in the rotor resistance
R.sub.2. Accordingly, after solving for the rotor resistance
R.sub.2, the rotor leakage reactance X.sub.2 can be obtained using
equation (108). In turn, the core impedance Z.sub.c can be obtained
using equation (90). Moreover, the stator impedance can then be
obtained using equation (85). If desired, the data processing
module 82 can calculate other parameters based on the foregoing
calculations. For example, the data processing module 82 uses these
estimated parameters to estimate the efficiency of the motor
20.
[0127] The process 140 described above with reference to FIG. 8 was
evaluated with data obtained at three load points on a real motor.
The process 140 provided exceptionally accurate estimations of
motor efficiency. Numerical analysis and the foregoing tests
indicated an estimation error of approximately 1.5% as it pertains
to the estimation of motor efficiency. A portion of this error can
be attributed to inaccuracies encountered in the field due to
instrumentation.
[0128] Referring generally to FIG. 9, a process for establishing
values of various motor electrical parameters and various motor
operating parameters, such as motor torque and speed, is shown and
designated generally by reference numeral 160. The process 160
comprises obtaining baseline motor parameters and providing the
data to the processor module 84, as represented by block 162. For
example, the data processing module 82 may obtain the various
parameters for the motor equivalent circuits 50 and 110 of FIGS. 2
and 5 at a particular baseline condition. In certain embodiments,
as described below, the baseline condition may comprise a motor
frequency (e.g., 60 Hz) for an inverter-driven motor. If desired,
the process 160 may employ any one of the processes 100, 120, 130,
or 140 described above with reference to FIGS. 4, 6, 7, and 8. The
process 160 also comprises obtaining motor data at a desired
operating load point or condition (e.g., a new motor frequency
other than baseline) and providing the data to the processor module
84, as represented by block 164. In a presently contemplated
embodiment, the data obtained at the desired operating load
comprises: input voltage data, input current data, input power
data, shaft temperature data, and frequency data of the motor 20.
It should be noted that the input power can either be measured or
calculated from the other input data. In addition, the data
obtained at these three points generally does not include the speed
and/or torque of the motor 20. Some data may be provided to the
system 80 using the control module 90 or may be provided from a
remote station 98 via the network 96.
[0129] As represented by block 166, the data processing module 82
then operates to establish estimated values of various motor
parameters at the desired operating load based on the baseline
motor parameters and the data obtained at the desired operation
load. Again, this estimation step 166 may be performed without
measurements of the speed and/or torque of the motor 20. As
discussed above, these estimated motor parameters may comprise one
or more of the circuit parameters in the motor equivalent circuits
50 and 110 illustrated in FIGS. 2 and 5. Accordingly, the various
motor parameters may comprise the stator resistance R.sub.1, the
slip s, the stator leakage reactance X.sub.1, the rotor resistance
R.sub.2, the rotor leakage reactance X.sub.2, the core loss
resistance R.sub.c, and the magnetizing reactance X.sub.m. These
seven parameters determine the motor equivalent circuit 50.
Accordingly, the motor equivalent circuit 50 can be fully analyzed
by measuring and/or estimating these parameters. As discussed
below, the data processing model 82 estimates these parameters in
accordance with unique aspects of the process 160 illustrated in
FIG. 9.
[0130] As represented by block 168, the data processing module 82
then operates to establish estimated values of other unknown motor
parameters based on the one or more parameters estimated in block
166. For example, the data processing module 82 may estimate output
power, speed, efficiency, torque, and other characteristics of the
motor 20. In addition, in certain embodiments, the data processing
module 82 operates in accordance with the process 160 to obtain
various losses associated with the motor 20. For example, the
losses may comprise stator loss, rotor loss, core loss, friction
and windage, and stray load loss.
[0131] Returning to block 166, the process 160 estimates the stator
leakage inductance L.sub.1 and the rotor leakage inductance L.sub.2
to be equal to the inductances obtained at the baseline condition.
In this manner, the motor parameters L.sub.1 and L.sub.2 are
assumed constant. Regarding resistances, the process 160 estimates
the stator resistance R.sub.1 and the rotor resistance R.sub.2 as a
function of temperature. For example, the stator resistance R.sub.1
can be calculated based on the baseline temperature T.sub.baseline,
the baseline stator resistance R.sub.baseline, and the current
stator temperature T at the desired operating load, as set forth
below: R = ( 234.5 + T ) ( 234.5 + T baseline ) .times. R baseline
( 109 ) ##EQU58## Accordingly, only three unknown motor parameters
remain to be estimated by the process 160.
[0132] The series core loss resistance R.sub.m can be calculated
according to the following equation: R m = R m .times. .times. 60
.function. ( .8 .times. ( f 60 ) + .2 .times. ( f 60 ) 2 ) ( 110 )
##EQU59## In the above equation (110), f is the input frequency and
R.sub.m60 is the series core loss resistance, which is known at the
baseline condition of the motor. For example, in this particular
embodiment, the series core loss resistance R.sub.m60 corresponds
to a baseline input frequency of 60 Hz. Accordingly, only two
unknown motor parameters (i.e., L.sub.m and s) remain to be
estimated by the process 160.
[0133] To estimate the two unknown motor parameters, the process
160 of FIG. 9 proceeds to solve two equations using the baseline
motor parameters and the data obtained at the desired operating
load (e.g., input current, voltage, power, and frequency). Based on
the measurement of input current, the input current complex value
can be calculated as set forth below: I.sub.in=I.sub.inR+jI.sub.inI
( 111) Subscripts R and I represent the real and imaginary parts of
the input current I.sub.in. Using the equivalent circuit of the
induction motor, the process 160 can express the input current
I.sub.in in terms of the motor input phase voltage and the
equivalent circuit impedance. First, the input impedance can be
expressed as: Z.sub.in=Z.sub.inR+jZ.sub.inI (112) In real and
imaginary parts, the process 160 can express the input impedance of
equation (112) as follows: Z i .times. .times. n .times. = [ [ R 1
.function. ( R 2 / s + R m ) - X 1 .function. ( X 2 + X m ) ] + j
.function. [ R 1 .function. ( X 2 + X m ) + X 1 .function. ( R 2 /
s + R m ) ] ] ( R 2 / s + R m ) + j .function. ( X 2 + X m ) ( 113
) ##EQU60## Accordingly, in terms of the input phase voltage and
input impedance, the process 160 can express the input current
I.sub.in as set forth below: I i .times. .times. n = V Z i .times.
.times. n .times. .times. R + j .times. .times. Z i .times. .times.
n .times. .times. I ( 114 ) ##EQU61## In turn, the process 100 can
express the foregoing equation (114) as set forth in the following
equation: I inR + j .times. .times. I inI = V ( Z inR Z inR 2 + Z
inI 2 ) - jV ( Z inI Z inR 2 + Z inI 2 ) ( 115 ) ##EQU62##
[0134] In view of the baseline parameters and the data and
parameters at the desired operating load, the process 160 can
equate the real parts and the imaginary parts on both sides of
equation (115) to obtain two equations corresponding to the
baseline and the desired operating load. Given that the only
unknown parameters are the magnetizing reactance X.sub.m and the
slip s, the process 160 can calculate the values of the magnetizing
reactance X.sub.m and the slip s at the desired operating load.
Using the calculated slip s and the measured frequency f the
process 160 can calculate the speed (e.g., rotations per minute) of
the motor. In addition, the process 160 can calculate other motor
operating parameters, such as torque, efficiency, output power, and
so forth. For example, the motor torque can be calculated according
to equation (24), as discussed above. Moreover, given that output
power is related to the output speed times the torque, the process
160 can calculate the output power using the output torque and
speed of the motor. The process 160 can then calculate the new
motor efficiency as set forth in equation (26), as discussed above.
In this manner, the process 160 facilitates the identification of
motor operating parameters without implementing a speed sensor
and/or a torque sensor.
[0135] Referring generally to FIG. 10, a system for establishing
values of various motor electrical parameters and various motor
operating parameters is shown and designated generally by reference
numeral 200. As illustrated, the system 200 comprises the control
module 90 and the data processing module 82, which can be separate
or integral components of a variety of mobile or stationary
systems, electronic devices, instruments, computers, software
programs, circuit boards, and so forth. The illustrated embodiment
of the data processing module 82 comprises a variety of modules or
features to facilitate the estimation of electrical and operating
parameters of the motor 20. Each of these modules may comprise
software programs or components, hardware circuitry, and so forth.
For example, the data processing module 82 may comprise one or more
of the following features: a no-load motor estimation module 202, a
single load point motor estimation module 204, a two load point
motor estimation module 206, a three load point motor estimation
module 208, a baseline-load motor estimation module 210, the data
processor module 84, one or more databases of motor losses 212
(e.g., friction and windage loss database), one or more databases
of new/replacement motors 213, one or more databases of customer
motors 214, a data storage and access module 216, a motor
resistance processing module 218, an energy analysis module 220,
and/or a monetary analysis module 222. Although other features also
may be incorporated into the data processing module 82 of system
200, the foregoing modules may be employed to provide exceptionally
accurate estimations of electrical and operating parameters of the
motor 20, as described below.
[0136] Regarding modules 202 through 210, the no-load motor
estimation module 202 may comprise one or more of the various
features described above with reference to the process 120
illustrated by FIG. 6. Similarly, the single load point motor
estimation module 204 can have one or more of the features
described above with reference to the process 130 illustrated by
FIG. 7. With reference to FIG. 4, the two load point motor
estimation module 206 may incorporate one or more of the features
described above with reference to the process 100. The three load
point motor estimation module 208 can employ one or more of the
features described with reference to the process 140 illustrated by
FIG. 8. Finally, the baseline-load motor estimation module 210 may
comprise one or more of the various features described above with
reference to the process 160 illustrated by FIG. 9.
[0137] Regarding the databases 212 through 214, the system 200 may
store the information locally or remotely on one or more storage
devices, computers, instruments, networks, and so forth.
Accordingly, the databases 212 through 214 may be readily available
on a local storage device or the system 200 may communicate with a
remote device over a network, such as the network 96 illustrated by
FIG. 3. Turning now to the specific databases, the database of
motor losses and parameters 212 may comprise a variety of motor
information, such as motor frame size, number of poles, fan
diameter, and various losses associated with the motor. For
example, the motor losses may comprise the friction and windage
loss for various motors. Accordingly, the database 212 can be
accessed and queried to obtain the desired data, such as the motor
losses. For example, if the system 200 is estimating output power
or operational efficiency, then the motor losses (e.g., friction
and windage loss) can be obtained from the database 214 to
facilitate a more accurate estimation of these operating
parameters.
[0138] As discussed in further detail below, the database of
new/replacement motors 213 can be used by the system 200 to
evaluate and compare existing motors against the benefits of a
new/replacement. For example, the database 213 may comprise a
variety of operational parameters, such as motor efficiency, power
usage, torque, space consumption, and so forth. Accordingly, the
data processing module 82 may compare this motor data against
estimated operational parameters of an old motor, such as the motor
20 being evaluated by the system 200.
[0139] The database have customer motors 214 also may comprise a
variety of electrical and operational parameters for various
motors. For example, each motor at a customer's site can be
recorded in the database 214 according to motor efficiency,
horsepower, application or use, location within the site, and
various other features of the motor. In addition, the database 214
can store performance data taken at various times over the life of
the motor, such that trends or changes in motor performance can be
identified and addressed by customer. The database 214 also can be
organized in various data sheets according to motor type,
application, location, date of test, efficiency, and other
features. Again, the particular data stored in the database 214 may
comprise electrical parameters (e.g., resistances, inductances,
etc.), operational parameters of the motor (e.g., efficiency,
torque, etc.), power usage, time usage, costs, age, specification
information, servicing, maintenance, testing, and so forth.
[0140] In addition to the databases, the illustrated system 200
comprises the data storage and access module 216, which has a data
logging module 224, a data identification module 226, and a data
population module 228. In operation, the data logging module 224
records various motor data and measurements, such as input current,
voltage, frequency, power, time of measurement (e.g., date, clock
time, and duration), speed, and other motor parameters. For
example, the data logging module 224 may store test results
according to a file name, a test time, and/or another identifying
parameter (e.g., a motor speed). In turn, the data identification
module 226 facilitates retrieval of the recorded data according to
one or more identifying parameters. For example, if the system 200
engages one of the motor estimation modules 202 through 210, then
the data storage access module 216 may utilize the data
identification module 226 to identify the appropriate data for use
in estimating motor parameters. In certain embodiments, this may
involve data entry or selection of a filename, a testing time, a
type of measurement, or another identifier. The data storage access
module 216 can then engage the data population module 228, which
retrieves the identified motor data and populates the appropriate
fields with the motor data. For example, the data population module
228 may populate data fields in one of the motor estimation modules
202 through 210 with motor parameters corresponding to input
voltage, current, frequency, power, and/or a variety of other motor
data. The data population module 228 also may populate one or more
visual forms, spreadsheets, formulas, and other functional or
visual objects with the identified data. As a result, the data
storage and access module 216 reduces errors associated with data
logging, retrieval, and use by the system 200, while also improving
the overall efficiency of the system 200 by automating these
functions.
[0141] As illustrated, the motor resistance processing module 218
comprises a temperature compensation module 230, a data entry
module 232, and a resistance calculation module 234. As described
below, these modules 230, 232, and 234 facilitate automatic
calculation of the motor resistance parameters based on various
data input. In this manner, the motor resistance processing module
218 improves the efficiency of the system 200, reduces errors
associated with motor resistance calculations, and improves the
accuracy of the motor resistance values for use by the motor
estimation modules 202 through 210. For example, the illustrated
temperature compensation module 230 uses a baseline measurement of
motor temperature and stator resistance to adjust the stator
resistance as the motor temperature changes. In operation, the
temperature compensation module 230 may employ the following
relationship between stator resistance and temperature for copper:
R t .times. .times. 2 = ( 234.5 + T 2 ) ( 234.5 + T 1 ) .times. R t
.times. .times. 1 ( 116 ) ##EQU63## In this equation (116), T.sub.1
refers to the baseline motor temperature, T.sub.2 refers to the
current motor temperature, R.sub.t1 refers to the baseline
resistance of the stator, and R.sub.t2 refers to the current
temperature-compensated value of the stator resistance. The data
entry module 232 also cooperates with the temperature compensation
module 230 to obtain the baseline motor temperature T.sub.1, the
baseline stator resistance R.sub.t1, and the current motor
temperature T.sub.2 to calculate the current resistance R.sub.t2
according to equation (116). In addition, the resistance
calculation module 234 comprises or more formulas or equations to
facilitate the calculation of resistance (e.g., cable resistance)
based on various motor data or parameters. For example, the
resistance calculation module 234 may cooperate with the data entry
module 232 to obtain a cable gauge, a number of cables for phase, a
cable length, a cable temperature, and other desired parameters to
calculate the desired motor resistance. As a result, the motor
resistance processing module 218 reduces errors associated with
user calculations, improves the overall efficiency of the system
200 by automating these calculations, and improves the accuracy of
resistance values for use by the motor estimation modules 202
through 210.
[0142] Turning now to the energy and monetary analysis modules 220
and 222, the system 200 may engage these modules to evaluate the
performance of the motor 20 and compare this performance against
one or more new/replacement motors, such as those stored in the
database of new/replacement motors 213. As illustrated, the energy
analysis module 220 comprises an energy usage module 236 and an
energy savings module 238. In operation, the energy usage module
236 calculates or estimates the overall energy usage of the motor
20, while the energy savings module 238 calculates or estimates any
energy savings that may be obtained by replacing the existing motor
20 with a new/replacement motor. For example, the energy savings
module 238 may evaluate a variety of motors having different levels
of energy efficiency and other performance criteria. As result, a
customer can make an informed decision whether to replace the motor
20 with a new/replacement motor.
[0143] In addition, the monetary analysis module 222 may function
cooperatively with or separately from the energy analysis module
220. In this exemplary embodiment, the monetary analysis module 222
comprises a cost analysis module 240 and a savings analysis module
242. For example, the cost analysis module 240 may calculate the
monetary cost of the motor 20 based on the output power, the cost
per kilowatt-hour, and the number of hours per week of operation of
the motor 20. Similarly, the savings analysis module 242 may
calculate the monetary cost of a new/replacement motor and then
calculate the monetary difference between the new/replacement motor
and the existing motor 20. As result, a customer can make an
informed decision whether to replace the motor 20 with a
new/replacement motor.
[0144] While the invention may be susceptible to various
modifications and alternative forms, specific embodiments have been
shown by way of example in the drawings and have been described in
detail herein. However, it should be understood that the invention
is not intended to be limited to the particular forms disclosed.
Rather, the invention is to cover all modifications, equivalents,
and alternatives falling within the spirit and scope of the
invention as defined by the following appended claims.
* * * * *