SYSTEM AND METHOD FOR DETERMINING STATOR WINDING
RESISTANCE IN AN AC MOTOR USING MOTOR DRIVES
GOVERNMENT LICENSE RIGHTS
[0001] The present invention was made at least in part with Government support
under Contract No. DE-FC36-04GO14000, awarded by the United States Department of
Energy. The Government may have certain rights in the invention.
BACKGROUND OF THE INVENTION
[0002] The present invention relates generally to alternating current (AC) induction
motors and, more particularly, to a system and method for determining the stator
winding resistance of AC motors by way of a motor drive, for thermal protection of AC
motors, improving motor control performances, and condition monitoring of AC
motors.
[0003] The usage of motor drives in various industries has recently become more
prevalent based on the increasing need for energy savings and control flexibility in
motor operation. Based on these needs, improvements in motor control performance
have become increasingly important. One factor of improved motor control
performance is the accuracy of motor parameter estimation, which is of great
importance to the overall control performance of motor drives. Among the plurality of
motor parameters that might be estimated, such as stator and rotor resistances, stator and
rotor leakage inductances, magnetic inductance, etc., stator resistance is the most
difficult parameter to be identified because of its small per unit value. However, the
accuracy of stator resistance estimation is essential to accurately determining a plurality
of related motor parameters. For example, an accurate estimation of stator resistance
allows for the further estimation of rotor/stator flux, rotor speed, air-gap torque, stator
copper loss, and other similar parameters. The accurate estimation of stator winding
resistance is thus beneficial for motor controls and is widely used in motor condition
monitoring, fault diagnostics and prognostics, and instantaneous efficiency evaluation.
[0004] Another known use for the estimated stator winding resistance is for
determining stator winding temperature, which can be used for thermal protection of the
motor. Thermal protection is an important aspect in the monitoring of motor conditions,

as the thermal stress on the stator winding is considered to be one of the main reasons
for stator winding insulation failure. It is commonly assumed that the motor's life is
reduced by 50% for every 10° C increase in temperature above an acceptable stator
winding temperature limit. Therefore, accurate monitoring of the stator winding
temperature is beneficial for motor protection purposes.
[0005] Various methods for determining the stator winding temperature have been
proposed to estimate the average winding temperatures from the stator winding
resistances. Over the years, various stator winding resistance estimation methods have
been proposed for different purposes. Generally, they are divided into three major
categories: direct measurement methods, equivalent circuit-based methods, and signal-
injection-based methods. Direct methods, such as the IEEE standard-118, give the most
accurate stator resistance estimates, but have limitations and drawbacks due to the fact
that resistance is only measured at a certain temperature and the resistance variations
due to temperature changes are not considered. A further drawback of direct
measurement methods is that the motor has to be disconnected from service to perform
the required tests.
[0006] The equivalent circuit-based methods of Rs estimation use the motor current
and voltage to calculate the stator resistance based on an AC motor equivalent circuit
(i.e., a model of the AC motor). Such model-based methods are non-intrusive and can
respond to changes in the cooling conditions but are generally too sensitive to motor
parameter variations to provide accurate Rs estimation, due to the fact that the motor
parameters may vary under different conditions, such as operating speed, magnetic
saturation, etc. That is, the estimation error of model-based methods can be larger than
20%. Thermal parameter variation and the difficulty of thermal parameter identification
may lead to further inaccuracy in model-based methods.
[0007] The signal injection-based methods for determining stator resistance inject a
DC bias into the stator supply voltage and use the DC component of the voltage and
current to calculate the stator resistance. In one DC signal injection method, a resistor
in parallel with a transistor is installed in one phase of the motor, which leads to an
equivalent resistance in the induction motor that is different when input current is

positive and negative, thus producing a DC component. Although this approach can be
accurate and robust to the variations in cooling conditions and motor parameters, it
suffers from its intrusive nature, as an extra DC signal injection circuit needs to be
installed in series with one of the motor leads. Additionally, due to the current limits of
semiconductor devices, previous signal injection-based methods cannot generally be
directly applied to motors beyond 100 hp.
[0008] It would therefore be desirable to design an accurate, non-intrusive method
for determining stator winding resistance. It would further be desirable to use an
existing device to inject the DC component for determining stator resistance, and
accordingly, to estimate the stator winding temperature.

BRIEF DESCRIPTION OF THE INVENTION
[0009] The present invention provides a system and method for determining the
stator winding resistance of AC motors by way of a motor drive. Determination of the
stator winding resistance provides for thermal protection of AC motors, improved motor
control performance, and condition monitoring of AC motors.
[0010] In accordance with one aspect of the invention, a system to estimate
resistance of a stator winding of an AC motor includes an AC motor drive having an
input connectable to an AC source and an output connectable to an input terminal of an
AC motor. The AC motor drive further includes a pulse width modulation (PWM)
converter having a plurality of switches therein to control current flow and terminal
voltages in the AC motor and a control system connected to the PWM converter. The
control system is configured to generate a command signal to cause the PWM converter
to control an output of the AC motor drive corresponding to an input to the AC motor,
selectively generate a modified command signal to cause the PWM converter to inject a
DC signal into the output of the AC motor drive, and determine a stator winding
resistance of the AC motor based on the DC signal of at least one of the voltage and
current.
[0011] In accordance with another aspect of the invention, a method for determining
resistance of a stator winding of an AC motor includes the step of providing an AC
motor drive in series between an AC power source and the AC motor, the AC motor
drive including a pulse width modulation (PWM) converter to condition voltage and
current to the AC motor. The method also includes the step of selectively operating the
AC motor drive in a standard mode and a DC injection mode, wherein operating the AC
motor drive in the DC injection mode includes the steps of adding a DC command to at
least one of an AC voltage command and an AC current command to form a composite
command, generating a switching pattern for the PWM converter based on the
composite command, and operating the PWM converter according to the switching
pattern to introduce a DC signal into the AC motor voltage and current. Operating the
AC motor drive in the DC injection mode further includes the steps of measuring the

DC signal in at least one of the voltage and current provided to the AC motor and
determining the resistance of the stator winding based on the measured DC signal.
[0012] In accordance with yet another aspect of the invention, an AC motor drive
configured to control transmission of voltage and current from an AC power source to
an AC motor having a stator winding is provided. The AC motor drive includes a pulse
width modulation (PWM) converter to condition an AC motor line voltage and phase
current to the induction motor, the PWM converter comprising a plurality of switches
and being configured to operate according to a space vector modulation (SVM) control
scheme to control the plurality of switches. The AC motor drive/also includes a control
system configured to selectively modify the SVM control scheme for the PWM
converter to inject a DC signal into the AC motor line voltage and phase current and
determine the resistance of the stator winding based on the DC signal.
[0013] Various other features and advantages of the present invention will be made
apparent from the following detailed description and the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS
[0014] The drawings illustrate preferred embodiments presently contemplated for
carrying out the invention.
[0015] In the drawings:
[0016] FIG.. 1 a schematic of an AC motor drive according to one aspect of the
invention.
[0017] FIG. 2 is a schematic view of a closed-loop control scheme for DC injection
for the motor drive of FIG. 1 according to an embodiment of the invention.
[0018] FIG. 3 is a schematic view of a field-oriented closed-loop control scheme for
DC injection for the motor drive of FIG. 1 according to an embodiment of the invention.
[0019] FIG. 4 is a diagram of a DC command injected into a control vector of a
space vector modulation (SVM) control scheme for controlling switching in a pulse
width modulation (PWM) converter according to an embodiment of the invention.
[0020] FIG. 5 is a graph of a generated stator current with and without an injected
DC component for the closed-loop control scheme of FIGS. 2 and 3.
[0021] FIG. 6 is a schematic view of an open-loop control scheme for DC injection
for the motor drive of FIG. 1 according to an embodiment of the invention.
[0022] FIG. 7 is a graph of a generated stator current with and without an injected
DC component for the open-loop control scheme of FIG. 6.
[0023] FIG. 8 is a schematic view of the DC equivalent circuit of the AC motor
system of FIG. 1 when operated in DC injection mode.
[0024] FIG. 9 is a flow chart illustrating a technique for estimating a stator winding
temperature according to an embodiment of the invention.

[0025] FIG. 10 is a flow chart illustrating a technique for estimating a stator winding
temperature in a motor drive open-loop control scheme according to an embodiment of
the invention.
[0026] FIG. 11 is a block schematic of a controller configured to generate a DC
command for transmission to a motor drive according to an embodiment of the
invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
[0027] The embodiments of the invention set forth herein relate to a system and
method for remote stator winding resistance estimation for thermal protection of
induction motors. An AC motor drive is controlled to inject a DC signal into an AC
motor line voltage and phase current to the induction motor. A reference voltage and/or
reference current command generated by a control system in the AC motor drive is
modified to include a DC command therein, thereby modifying a control scheme for a
pulse width modulation (PWM) converter in the AC motor drive to inject the DC signal
into the AC motor line voltage and phase current. This DC signal is analyzed to
determine a stator winding resistance.
[0028] Embodiments of the invention are directed to AC motor drives encompassing
a plurality of structures and control schemes. The general structure of an AC motor
drive 10 is shown in FIG. 1. The motor drive 10 may be configured, for example, as an
adjustable speed drive (ASD) designed to receive a three AC power input, rectify the
AC input, and perform a DC/AC conversion of the rectified segment into a three-phase
alternating voltage of variable frequency and amplitude that is supplied to a load. In a
preferred embodiment, the ASD operates according to an exemplary volts-per-hertz
characteristic. In this regard, the motor drive provides voltage regulation of ±1% in
steady state with less than 3% total harmonic distortion, ±0.1 Hz in output frequency,
and fast dynamic step load response over a full load range.
[0029] In an exemplary embodiment, a three-phase AC input 12a-12c is fed to a
three-phase rectifier bridge 14. The input line impedances are equal in all three phases.
The rectifier bridge 14 converts the AC power input to a DC power such that a DC bus
voltage is present between the rectifier bridge 14 and a switch array 16. The bus voltage
is smoothed by a DC bus capacitor bank 18. The switch array 16 is comprised of a
series of IGBT switches 20 and anti-parallel diodes 22 that collectively form a PWM
inverter 24. The PWM inverter 24 synthesizes AC voltage waveforms with a fixed
frequency and amplitude for delivery to a load, such as an induction motor 26.
Operation of the inverter 24 is via a control system 28, which may further be comprised
of a plurality of PID controllers each having a system layer and a programmable

application layer that perform high speed operations such as space-vector modulation,
DC bus voltage decoupling, and protection, for example. The control system 28
interfaces to the PWM inverter 24 via gate drive signals and. sensing' of the DC bus
voltage and pole currents (by way a voltage sensor 34 for example) such that changes in
DC bus voltage can be sensed. These voltage changes can be interpreted as transient
load conditions and are used to control switching of the switch array 16 of PWM
inverter 24 such that near steady-state load conditions are maintained.
[0030] Embodiments of the invention are described below for both closed-loop and
open-loop control of the motor drive 10. Referring first to FIG. 2, a general closed-loop
scheme 30 of motor control for motor drive 10 is shown according to an embodiment of
the invention. In an exemplary embodiment for the closed-loop scheme, the control
system 28 of motor drive 10.includes a speed controller 32 that generates a desired flux
λ* and torque command T* based on a speed command ω* received from an input
device (not shown) and a measured or estimated rotor speed co. A flux/torque estimator
34 is also included in the control system 28 of motor drive 10 and estimates a flux λ and
torque T of the induction motor 26 using measured three-phase voltages Vabc and
currents Iabc. The desired flux λ* and torque command T* and the estimated flux λ and
torque T of the induction motor 26 are output by the speed controller 32 and the
flux/torque estimator 34, respectively, to a flux/torque controller 36, which generates a
stator current command Iabc* based on the estimated λ and T, the flux command λ*, and
torque command T*. A current controller 38 receives the stator current command Iabc*
along with a measured stator current Iabc to generate a stator voltage command Vabc*-
The stator voltage command Vabc* is relayed to a switching signal generator 40 that,
based on the stator voltage command Vabc*, generates a plurality of switching signals
(i.e., a switching pattern) for controlling switching of the array of switches in the PWM
converter 24. Based on the switching pattern generated by the switching signal
generator 40, the PWM inverter 24 synthesizes AC voltage waveforms with a fixed
frequency and amplitude for delivery to induction motor 26.
[0031] Also included in control system 28 of motor drive 10 is a controller 42.
According to an embodiment of the invention, controller 42 is configured to selectively

generate a DC current command signal for transmission to the flux/torque controller 36.
The selective generation of the DC current command signal by controller 42 allows for
motor drive 10 to alternate between operation in a standard mode and a DC injection
mode. During standard operation of AC motor drive 10, controller 42 is in a-
deactivated state such that no DC command signal is generated thereby. The standard
mode thus is considered the "normal" mode of operation for the AC motor drive 10.
Controller 42 is further configured/programmed to selectively operate the motor drive
10 in the DC injection mode to inject a DC signal or component into the motor line
voltages and phase current. During the DC injection mode, controller 42 operates to
generate a DC command in the form of a DC current command that is transmitted to the
flux/torque controller 36. That is, with reference to FIG. 2, for a closed-loop current-
control voltage-fed .motor drive, the DC command is introduced or added to the
flux/torque controller 36 to modify the current command iabc*.
[0032] When a DC current command is generated and added by controller 42 to
flux/torque controller 36, the flux/torque controller 36 generates a modified current
command iabc' (i.e., composite current command), which is described as:
iabc'= iabc*+ iabcdc [Eqn. 1],
where iabc' is the new current command with DC current command injected, iabC dcis the
DC current command as stated, and iabc* is the current command generated by
flux/torque controller 36. Responsive to the modified current command iabc' generated
by flux/torque controller 36, current controller 38 is caused to generate a modified
voltage command Vabc' responsive thereto.
[0033J Based on the DC current command iabcdc generated/added by controller 42, a
modified current command iabc' and resulting modified voltage command Vabc' are
generated by control system 28. The resulting modified voltage command Vabc' causes
a modification to the switching pattern generated by the switching signal generator 40.
That is, the switching pattern generated by the switching signal generator 40 for
controlling of the PWM converter 24 when a DC current command iabcdc is added by
controller 42 (forming a resulting modified voltage command Vabc') is modified as

compared to the switching pattern generated by the switching signal generator 40 during
standard operation of the motor drive 10. In the standard mode, the switching pattern
generated by the switching signal generator 40 controls the PWM converter 24 to
generate a controlled AC motor line voltage and phase current for the motor. In the DC
injection mode, the modified switching pattern generated by the switching signal
generator 40 controls the PWM converter 24 to inject a DC signal/component into the
AC motor line voltage and phase current of induction motor 26. The frequency and/or
timing of switching in the PWM converter 24 is controlled according to the modified
switching pattern to cause a disturbance or distortion (i.e., a shift in the phase current
and a notch in the line voltage) of at least one of the phases of the AC motor 26, which
generates or injects a DC component into the motor line voltages and phase currents.
These DC components can be measured and determined for each DC injection mode
period by voltage and/or current sensors 44 included in motor drive 10.
[0034] In the above described closed-loop control scheme, it is recognized that the
effect of the injected DC signal on the speed control must be eliminated. Accordingly,
the motor speed is sampled at a low sampling frequency with a low-pass filter (not
shown), whereby the speed oscillation can be removed by the low-pass filter. The effect
of the injected DC signal on the flux/torque estimator 34 should also be eliminated, to
avoid instability, by removing the DC component of the stator three-phase voltages and
currents fed to the flux/torque estimator 34.
[0035] It is also recognized that the control method in control system 28 and the
flux/torque estimation method may vary for different types of AC motor closed-loop
control. Also, for different types of closed-loop control methods, the estimated flux
may be stator flux, rotor flux, and linkage flux; the three-phase voltages and currents
may also be denoted using different types of transforms in different reference frames,
such as synchronous reference frame, rotor reference frame, stationary reference frame,
etc. The measured stator voltage Vabc can also be replaced by the stator voltage-
command Vabc*, assuming the ideality of the converter, or be calculated using the
switching signals and the DC bus voltage of the PWM converter 24.

[0036] Referring now to FIG. 3, an exemplary closed-loop control scheme for motor
drive 10, a field-oriented control scheme 46, is shown according to an embodiment of
the invention. In the field-oriented control scheme 46, the stator currents and voltages
in the synchronous reference frame (d-q frame) are denoted as iq, id, vq, vd, and the
stator currents and voltages in the stationary reference frame (α-β frame) are denoted as
iα, iβ, vα, vβ. The synchronous reference frame used in this scheme is aligned with the
rotor flux with the angle 9.
[0037] As shown in FIG. 3, a flux estimator 48 in motor drive 10 estimates the rotor
flux using the measured three phase currents and voltages iabc, vabc. Based on the
estimated rotor flux and the motor speed, speed controller 50 and flux controller 52
function to generate stator current commands iq* and id*, which are also respectively
known as a torque command and a speed command. Current controller 38 then
generates the voltage command Vdq* based on the stator current command iq* and id*
and the measured stator current. After reference frame transformation in transformer 56,
the transformed voltage command Vαβ is received by switching signal generator 40,
which generates the switching signals for the PWM converter 24 based on the stator
voltage command.
[0038] Controller 42 is configured to selectively generate a DC current command
signal and introduce the DC current command signal to the current commands in the
control loop. According to one embodiment of the field-oriented control scheme of
motor drive 10, a DC current command is introduced to the current command in the
control loop, (e.g. iq* and id*). In the d-q axis, the updated current commands are:

where iq* & id* are the previous q-d axis current commands; iq**& id** are the
changed q-d axis current commands with DC signal injection; and idc is the magnitude
of the injected DC signal. As applied in the α-β axis, the updated current commands
are:


where iα* & iβ* are the previous α-β axis current commands; iα** & iβ** are the
changed α-β axis current commands with DC signal injection; and idc is the magnitude
of the injected DC signal.
[0039] The resulting modified current command iq**, id** (or iα** & iβ**) causes a
change in the voltage command (from Vdq* to Vdq **) generated by current controller
38, thus further causing a modification to the switching pattern generated by the
switching signal generator 40. According to the field-oriented control scheme 46 of
motor drive 10, switching signal generator 40 modifies a "standard" space vector
modulation (SVM) command scheme or switching pattern in response, to the modified
current command (and resulting modified voltage command). As shown in FIG. 4,
instead of using a normal 6-vector space command scheme for the PWM converter, an
additional DC component 58 is added in the reference vector 60. In this modified space
vector control, an additional q-axis component Vs 60 is added to the original reference
vector Va. For example, if Va=Vq+jVd is the reference vector, the modified vector
would be Vα*=(Vq+Vs)+jVd. In an exemplary embodiment, the magnitude of the
added Vs should be tunable between 0 and 5 volts.
[0040] The modified space vector control generates a modified switching pattern for
controlling the PWM converter 24 to inject a DC signal/component into the AC motor
line voltage and phase current for the motor 26. The frequency and/or timing of
switching in the PWM converter 24 is controlled according to the modified space vector
control to cause a disturbance or distortion (i.e., a shift in the phase current and a notch
in the line voltage) of at least one of the phases of the AC motor, which generates or
injects a DC component 58 into the motor line voltages and/or phase currents, as shown
in FIG. 5. These DC components can be measured and determined for each DC
injection mode period by voltage and/or current sensors 44 included in motor drive 10
to determine resistance in the stator windings, as is explained in greater detail below.

[0041] According to another embodiment of the invention, motor drive 10 is
operated according to an open-loop control scheme. Referring now to FIG. 6, an open-
loop control scheme 60 for AC motor drive 10 is shown that, according to an exemplary
embodiment, is a scalar open-loop control scheme. According to the open loop control
scheme 60, control system 28 of the motor drive 10 is configured to receive a speed (or
frequency) command from an input device (not shown) in order to generate a voltage
magnitude command V1. The voltage magnitude command V1 is given by a function
K(co) of the speed command, typically referred to as a V/Hz curve. A boost voltage V0,
which is used to operate the motor 26 under low-speed condition, is combined with the
voltage magnitude command V1 to produce a voltage magnitude V*.
[0042] The voltage magnitude V* and the speed command ω* are then transmitted to
a voltage controller 62 and are used to generate a three phase voltage command Vabc*,
which may be represented as:

[0043] The three phase voltage command Vabc* is given by the voltage controller 62
based on speed or frequency commands. The stator voltage command Vabc* is used to
control switching of an array of switches in PWM converter 24. Based on a switching
pattern of the switches, as determined by the stator voltage command Vabc*, the PWM
converter 24 synthesizes AC voltage waveforms with a fixed frequency and amplitude
for delivery to induction motor 26.
[0044] As further shown in FIG. 6, controller 42 is configured to selectively generate
a DC voltage command signal Vabcdc for transmission to the voltage controller 62, so as
to switch operation of the motor drive 10 from a standard mode to DC injection mode.
Upon addition of the DC voltage command signal Vabcdc by controller 42, the modified
voltage command Vabc' generated by voltage controller, described for each phase, is:



wherein Vas, Vbs, Vcs are the previous voltage command without the DC bias of phase A,
B. and C respectively, Vas, Vbs , Vcs are the new voltage command with the DC bias of
phase A, B and C respectively, and Vdc is the injected DC bias.
[0045] Alternatively, the modified voltage command Vabc' generated by voltage
controller can also be described with respect to the q-d reference frame as:

wherein Vq, Vd are the previous voltage command without the DC bias in stationary q-d
reference frame; Vq', Vd' are the new voltage command with the DC bias in stationary q-
d reference frame; Vdc is the injected DC bias.
[0046] Based on the DC voltage command signal Vabcdc generated/added by
controller 42, a modified voltage command Vabc' as set forth in Eqn. 5 is generated by
control system 28. The modified voltage command causes a modification to the
switching pattern of switches in the PWM converter 24 that injects a DC
signal/component into the AC motor line voltage and phase current for the motor 26.
According to an exemplary embodiment of the invention, the modified switching
pattern is generated by way of a modified SVM control scheme as shown in FIG. 4, in
which an additional DC command/component is added in a reference vector of the SVM
control scheme. The frequency and/or timing of switching in the PWM converter is
controlled according to the modified switching pattern to cause a disturbance or
distortion (i.e., a shift in the phase current 63 and a notch in the line voltage, as shown
in FIG. 7) of at least one of the phases of the AC motor, which generates or injects a DC
component into the motor line voltages and phase currents. These DC components can
be measured and determined for each DC injection mode period by voltage and/or
current sensors 44 (FIG. 6) included in motor drive 10.

[0047] Referring now to FIG. 8, an equivalent DC model of the AC motor 26 with
motor drive 10 is illustrated upon injection of DC components, through either the
closed-loop or open-loop control scheme thereof. Because the DC components injected
in the input voltages and currents do not "pass through" the air-gap of the AC motor
(i.e., the rotor/stator air-gap), they have no impact on the rotor circuit of the AC motor
10. With the DC signal injected in one of the three-phase stator currents, e.g. ia, the
stator resistance Rs can be estimated from the DC components of the stator terminal
voltages and currents as:

where and are the DC components of the motor line voltage vab and phase
current ia , respectively. While Eqn. 7 shows, that the phase current is measured for
phase a, and that line-to-line voltage is measured between phases a and b, it is also
envisioned that the phase current could be measured for a different phase and that the
line-to-line voltage could be measured between phase a and a different phase. That is,
the DC components of the motor line voltage and phase current are present in all phases
of the AC motor.
[0048] Based on the estimated Rs from DC signal injection, the stator winding
temperature Ts of motor 26 can be monitored. The Rs variation is linearly proportional
to the Ts variation, as:

where Ts0 and Rs0 represents Ts and Rs at room temperature; and are the
estimated Ts and Rs from DC signal injection; and a is the temperature coefficient of
resistivity.

[0049] Having determined the DC components of the voltage and current, and
, the stator resistance Rs can be estimated according to Eqn. 7 and, accordingly, the
stator winding temperature Ts can then be monitored based on the determined Rs
according to Eqn. 8 in real-time while the AC motor is in operation. In one embodiment
of the invention, controller 42 is configured to generate an alert (e.g., audible or visual
alert) if the stator winding temperature exceeds a pre-determined threshold value. This
alert allows an operator to take a desired action, such as shutting down the AC motor
26.
[0050] According to another embodiment of the invention, it is recognized that stator
winding temperature can be estimated using only current measurements for open-loop
AC drives, such as that shown in FIG. 6. Under steady state conditions (constant load
and constant DC voltage command), assuming that the actually injected DC voltage is
constant, the ratio of the DC current can be derived as:

where Idc and Idc0 is the measured DC current when the stator resistance is Rs and Rs0 ,
respectively.
[0051] In the case of load variation (i.e., non-steady state conditions), assuming that
the change of stator winding temperature before and after load variation can be
neglected, the reference DC current Idc0 can be rescaled as,

where Idc,before and dc,afier are the measured dc current before and after load
variation, respectively; I'dc0 is the new re-scaled reference point after load variation;

Idc0 is the previous reference point. With the re-scaled reference point, the update
formulae can be kept un-changed.
[0052] Based on the above determination of the ratio of the DC current (for steady
state or non-steady state loads), the stator winding temperature can be estimated.
Initially, the stator resistance can be represented as:

[0053] Ts can then be estimated, again, as,

where Ts0 and Rs0 represents Ts and Rs at room temperature; and are the
estimated Ts and Rs from DC signal injection; and is the temperature coefficient of
resistivity. Therefore, with the cable resistance, anddrive internal resistance measured
or estimated, the stator winding temperature can be monitored using only the current
sensor for open-loop AC drives.
[0054] According to one embodiment, when the cable resistance Rcable is not
measurable, it can be estimated. That is, given the cable number in the American Wire
Gauge (AWG) standard, Rcable can be estimated based on the resistivity p given by the
AWG standard, the approximate length / of the cable and the ambient temperature TA as:

where µ is the temperature coefficient of resistivity and T0 is the room temperature,
assuming that the cable temperature is the same as ambient temperature.
[0055] According to the above technique for obtaining a more accurate Rs estimate
(via use of stator terminal voltage and current, or current only), it is desired that larger
DC voltage command signals and/or DC current command signals be introduced to
increase the percentage of DC components in the motor voltages and currents.

However, it is recognized that injection of the DC component causes torque pulsations
in the AC motor 26. Therefore, according to an embodiment of the invention, controller
42 is programmed to inject maximal DC components into the voltage and current by
introducing a maximal DC voltage/current command signal, while keeping the resulting
torque pulsations under a preset tolerance range.
[0056] To determine an acceptable DC voltage/current command signal, the torque
pulsations in the AC motor are analyzed. That is; the dominant components in the
torque pulsations and their correlations to the injected DC components are analyzed
using sequence analysis theory in a d-q reference frame. These torque pulsations are
decomposed into components at multiples of the fundamental frequency, each of which
can be separately monitored by observing the sequence components of the motor
currents. Thus, the stator voltage, stator current, and total flux linkage are described as
space vectors in the d-q stationary reference frame, and are defined as
respectively.
[0057] Based on these variables, an air-gap torque, Tag, can be calculated as the cross
product of and according to:

where, P is the number of poles.
[0058] The flux and current space vectors can be decomposed into vectors at
different frequencies using a Fourier Transform, as:

where, the superscript of each decomposed vector/indicates its rotating direction and
rotating frequency in the vector space.

[0059J Assuming that the main input frequency is ωe, the major component in the
total flux linkage is then Neglecting the other harmonics in the flux linkage, the
resultant torque distortion caused by the injected DC current can be evaluated as:

which is oscillating at frequency ωe. The oscillating torque caused by the injected DC
current leads to an oscillation of the rotor speed, approximated as:

where represents the speed oscillation, and J represents the total rotation inertia of
the motor system. Thus, according to the analysis of the torque pulsations in the AC
motor provided by Eqns. 14-17, an acceptable DC voltage/current command signal can
be determined.
[0060] It is noted that the system and method set forth above for injecting a DC
component into an AC motor power supply enables online Rs estimation using only the
motor terminal voltages and currents (or the currents only), without the need of any
other sensors, such as speed and torque transducers. Such an arrangement allows for a
nonintrusive, sensorless, and low-cost technique for determining stator winding
resistance in real-time while the AC motor is in operation.
[0061] Referring now to FIG. 9, a technique 64 for estimating stator winding
temperature in the motor is set forth. The technique begins at STEP 66 with a
determination of whether an estimation of the stator winding temperature is desired at
that particular time. This determination can be made, for example, based on a timed
interval between temperature estimations (e.g., every 5 minutes). If it is determined that
no temperature estimation is desired at that time 68, then the technique moves to STEP
70 where the motor drive continues to operate in a standard mode. If, however, it is

determined that a temperature estimation is desired 72, then the technique moves to
STEP 74 where the motor drive is switched over to a DC injection mode, where a DC
command is introduced to cause the motor drive to inject a DC signal into the motor
drive output, according to one of the closed-loop and open-loop control schemes set
forth in detail above.
[0062] At STEP 76, the DC components Vab, Ia in the AC motor line voltage and
phase current to the induction motor are calculated. Based on the calculated motor, line
voltage and phase current, the resistance and the temperature of the stator winding are
then determined at STEPS 78 and 80, respectively, such as setforth above in Eqns. 7
and 8. The calculated stator winding resistance and temperature can then be
transmitted/reported at STEP 82 to, for example, a controller in the motor drive. The
determined stator winding resistance and temperature can then be analyzed to determine
if, for example, a temperature threshold for the motor has been crossed.
[0063] Referring now to FIG. 10, a current-based technique 84 for estimating stator
winding temperature in the motor is set forth, whereby only the phase current of the
induction motor need be analyzed. The technique is applicable to the open-loop control
technique illustrated in FIG. 6 and begins with injection of a DC signal (i.e., DC
current) at STEP 86. The DC current present in the phase current of the induction motor
is then measured at STEP 88, such as set forth in Eqn. 9. A compensation for the
resistance of the motor drive and of the cable connecting the motor drive and motor is
made at STEP 90, such as set forth in Eqn. 13 for example (based on known or
estimated values for the motor drive resistance Rdrive and the cable resistance Rcable).
The technique 84 then continues at STEP 92 with a determination of whether the motor
load has changed. If the load has not changed 94, then the stator winding temperature is
estimated at STEP 96, according to Eqns. 11 and 12. If the load has changed 98, then
the reference current is re-scaled at STEP 100 (as compared to the current measured at
STEP 88) as set forth in Eqn. 10. Upon this re-scaling, the stator winding temperature
is then estimated at STEP 96.
[0064] While the motor drives described above are set forth as including controller
42 therein, it is also recognized that controller 42 can be set apart in a module/device

separate from the motor drive and its associated controls. Referring now to FIG. 11,
according to another embodiment of the invention, a controller 102 is shown as a device
separate from a motor drive 104. Controller 102 may be integrated into a remote
control or computing device configured to transmit the DC command signal to motor
drive 104, such as via a wired or wireless connection. As set forth in the embodiments
described in detail above, motor drive 104 may be operated according to an open-loop
or closed loop control technique, and thus, according to embodiments of the invention,
controller 102 may be configured to generate and transmit a DC current command
signal or a DC voltage command signal, as determined by the type of control scheme
used for operating motor drive 104. A DC signal is thus caused to be injected into the
AC motor line voltage and phase current sent to load 26, and this DC signal is analyzed
to determine a stator winding resistance.
[0065] A technical contribution for the disclosed method and apparatus is that it
provides for a computer implemented technique for determining stator winding
resistance for thermal protection of AC motors. The technique controls switching in a
PWM converter in an AC motor drive to generate a DC component in an output of the
motor drive corresponding to an input to the AC motor and determines a stator winding
resistance from the DC component. A temperature of the stator windings can also be
determined in the technique based on the stator winding resistance.
[0066] Therefore, according to one embodiment of the present invention, a system to
estimate resistance of a stator winding of an AC motor includes an AC motor drive
having an input connectable to an AC source and an output connectable to an input
terminal of an AC motor. The AC motor drive further includes a pulse width
modulation (PWM) converter having a plurality of switches therein to control current
flow and terminal voltages in the AC motor and a control system connected to the PWM
converter. The control system is configured to generate a command signal to cause the
PWM converter to control an output of the AC motor drive corresponding to an input to
the AC motor, selectively generate a modified command signal to cause the PWM
converter to inject a DC signal into the output of the AC motor drive, and determine a

stator winding resistance of the AC motor based on the DC signal of at least one of the
voltage and current.
[0067] According to another embodiment of present invention, a method for
determining resistance of a stator winding of an AC motor includes the step of
providing an AC motor drive in series between an AC power source and the AC motor,
the AC motor drive including a pulse width modulation (PWM) converter to condition
voltage and current to the AC motor. The method also includes the step of selectively
operating the AC motor drive in a standard mode and a DC injection mode, wherein
operating the AC motor drive in the DC injection mode includes the steps of adding a
DC command to at least one of an AC voltage command and an AC current command
to form a composite command, generating a switching pattern for the PWM converter
based on the composite command, and operating the PWM converter according to the
switching pattern to introduce a DC signal into the AC motor voltage and current.
Operating the AC motor drive in the DC injection mode further includes the steps of
measuring the DC signal in at least one of the voltage and current provided to the AC
motor and determining the resistance of the stator winding based on the measured DC
signal.
[0068] According to yet another embodiment of the present invention, an AC motor
drive configured to control transmission of voltage and current from an AC power
source to an AC motor having a stator winding is provided. The AC motor drive
includes a pulse width modulation (PWM) converter to condition an AC motor line
voltage and phase current to the induction motor, the PWM converter comprising a
plurality of switches and being configured to operate according to a space vector
modulation (SVM) control scheme to control the plurality of switches. The AC motor
drive also includes a control system configured to selectively modify the SVM control
scheme for the PWM converter to inject a DC signal into the AC motor line voltage and
phase current and determine the resistance of the stator winding based on the DC signal.
[0069] The present invention has been described in terms of the preferred
embodiment, and it is recognized that equivalents, alternatives, and modifications, aside
from those expressly stated, are possible and within the scope of the appending claims.

WE CLAIM
1. A system to estimate resistance of a stator winding of an AC motor, the
system comprising:
an AC motor drive having an input connectable to an AC source and an
output connectable to an input terminal of an AC motor, the AC motor drive
comprising:
a pulse width modulation (PWM) converter having a plurality of
switches therein to control current flow and terminal voltages in the AC motor; and
a control system connected to the PWM converter and configured
to:
generate a command signal to cause the PWM converter
to control an output of the AC motor drive corresponding to an input to the AC motor;
selectively generate a modified command signal to cause
the PWM converter to inject a DC signal into the output of the AC motor drive; and
determine a stator winding resistance of the AC motor
based on the DC signal of at least one of the voltage and current.
2. The system of claim 1 wherein the control system is further configured
to: generate a DC voltage command signal;
combine the DC voltage command signal with an AC voltage command
signal to form the modified command signal.
3. The system of claim 2 wherein the AC motor drive comprises an open-
loop motor drive.
4. The system of claim 1 wherein the control system is further configured
to:
generate a DC current command signal;

combine the DC current command signal with a respective AC current
command signal to form the modified command signal.
5. The system of claim 4 wherein the AC motor drive comprises a closed-
loop motor drive.
6. The system of claim 1 wherein the control system is further configured to
determine a temperature of the stator winding based on the determined stator resistance
in real-time while the AC motor is in operation.
7. The system of claim 6 wherein the control system is further configured to
generate an alert if the stator winding temperature exceeds a pre-determined threshold.
8. The system of claim 1 wherein the control system is configured to
determine a switching pattern for the plurality of switches in the PWM converter based
on the modified command signal, thereby causing injection of the DC signal into at least
one phase of the AC motor.
9. The system of claim 8 wherein the control system is configured to
determine a space vector modulation (SVM) control scheme to provide the switching
pattern for the plurality of switches in the PWM converter.
10. The system of claim 8 further comprising voltage and current sensors
therein, and wherein the control system determines an amplitude of the DC signal from
a line-to-line voltage and a phase current resulting from a disturbance therein caused by
the switching pattern.
11. The system of claim 8 further comprising current sensors therein, and
wherein the control system determines an amplitude of the DC signal from a phase
current resulting from a disturbance therein caused by the switching pattern.
12. The system of claim 1 wherein the control system is configured to:

periodically generate the modified command signal at pre-defined times
during motor operation; and
measure the DC signal injected at each of the plurality of pre-defined
times.
13. A method for determining resistance of a stator winding of an AC motor
comprising:
providing an AC motor drive in series between an AC power source and
the AC motor, the AC motor drive comprising a pulse width modulation (PWM)
converter to condition voltage and current to the AC motor;
selectively operating the AC motor drive in a standard mode and a DC
injection mode, wherein operating the AC motor drive in the DC injection mode
comprises:
adding a DC command to at least one of an AC voltage command
and an AC current command to form a composite command;
generating a switching pattern for the PWM converter based on
the composite command;
operating the PWM converter according to the switching pattern
to introduce a DC signal into the AC motor voltage and current;
measuring the DC signal in at least one of the voltage and current
provided to the AC motor; and
determining the resistance of the stator winding based on the
measured DC signal.
14. The method of claim 13 wherein adding the DC command comprises
adding one of a DC voltage command signal and a DC current command signal.
15. The method of claim 13 wherein generating the switching pattern
comprises generating a space vector control scheme for the PWM converter.

16. The method of claim 13 wherein determining the resistance of the stator
winding comprises determining the resistance of the stator winding based on the
measured DC signal in the current provided to the AC motor.
17. The method of claim 13 wherein determining the resistance of the stator
winding comprises determining the resistance of the stator winding based on the
measured DC signal in each of the voltage and the current provided to the AC motor.
18. The method of claim 13 further comprising determining a temperature of
the stator winding based on the determined resistance of the stator winding.
19. An AC motor drive to control transmission of voltage and current from
an AC power source to an AC motor having a stator winding, the AC motor drive
comprising:
a pulse width modulation (PWM) converter to condition an AC motor
line voltage and phase current to the induction motor, the PWM converter comprising a
plurality of switches and being configured to operate according to a space vector
modulation (SVM) control scheme to control the plurality of switches; and
a control system configured to:
selectively modify the SVM control scheme for the PWM
converter to inject a DC signal into the AC motor line voltage and phase current; and
determine the resistance of the stator winding based on the DC
signal.
20. The AC motor drive of claim 19 wherein the control system is
configured to introduce a DC component into a control vector to modify the SVM
control scheme.
21. The AC motor drive of claim 20 wherein the DC component comprises
one of a DC voltage command signal and a DC current command signal.

22. The AC motor drive of claim 19 wherein the control system is
configured to determine the resistance of the stator winding based on the DC signal in
the phase current.
23. The AC motor drive of claim 19 wherein the control system is
configured to determine the resistance of the stator winding based on the DC signal in
each of the motor line voltage and the phase current.
24. The AC motor drive of claim 19 wherein the control system is further
configured to determine a temperature of the stator winding based on the determined
stator resistance in real-time while the AC motor is in operation.

A system and method for determining the stator winding resistance of AC
motors is provided. The system includes an AC motor drive having an input
connectable to an AC source and an output connectable to an input terminal
of an AC motor, a pulse width modulation (PWM) converter having
switches therein to control current flow and terminal voltages in the AC
motor, and a control system connected to the PWM converter. The control
system generates a command signal to cause the PWM converter to control
an output of the AC motor drive corresponding to an input to the AC motor,
selectively generates a modified command signal to cause the PWM
converter to inject a DC signal into the output of the AC motor drive, and
determines a stator winding resistance of the AC motor based on the DC
signal of at least one of the voltage and current.