Temperature Estimation in Inverter-Fed Machines Using ... - IEEE Xplore

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 44, NO. 3, MAY/JUNE 2008

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Temperature Estimation in Inverter-Fed Machines Using High-Frequency Carrier Signal Injection Fernando Briz, Senior Member, IEEE, Michael W. Degner, Senior Member, IEEE, Juan M. Guerrero, Member, IEEE, and Alberto B. Diez, Member, IEEE

Abstract—Temperature monitoring using the injection of a high-frequency carrier signal voltage is proposed in this paper. The carrier signal voltage is used to estimate the transient impedance of the system, which is a function of the stator transient resistance and, therefore, the windings’ temperature. The variation of the stator transient impedance’s phase angle is used to track the temperature of the stator windings. The method can be implemented in standard inverter-fed drives with no additional hardware, with minimal computational requirements, and with practically no interference with the regular operation of the drive. Index Terms—Carrier signal injection, temperature estimation, temperature monitoring, thermal protection.

I. I NTRODUCTION

S

INCE thermal overloading is one of the major causes of motor failures [1], [2], thermal protection and monitoring are standard features found in most electric machine drives. Discrete thermal sensors, mounted directly on the stator windings, are often used for this purpose. Using such devices increases the cost and reduces the reliability of the drive due to the additional components and manufacturing steps that are required. As an alternative, estimation of the temperature using electromechanical variables (currents/voltages/speed) has been developed, which can be grouped into two major categories [3]: 1) methods that are based on thermal models [4]–[7] and 2) methods that estimate the temperature from the resistance [3], [8]–[12]. Thermal models usually calculate power loss inside the machine using terminal measurements and then estimate the temperature at specific locations in the machine using a model to represent the heat flow. One important limitation of thermal models is that they generally assume a fixed thermal system and, therefore, provide inaccurate results if the system changes Paper IPCSD-07-099, presented at the 2007 Industry Applications Society Annual Meeting, New Orleans, LA, September 23–27, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Industrial Drives Committee of the IEEE Industry Applications Society. Manuscript submitted for review September 28, 2007 and released for publication October 22, 2007. This work was supported in part by the Research, Technological Development and Innovation Programs of the Spanish Ministry of Science and Education-ERDF under Grants MEC-04-DPI2004-00527 and MEC-ENE2007-67842-C03-01. F. Briz, J. M. Guerrero, and A. B. Diez are with the Department of Electrical, Computer and Systems Engineering, University of Oviedo, 33204 Gijón, Spain (e-mail: [email protected]; [email protected]; alberto@isa. uniovi.es). M. W. Degner is with Research and Advanced Engineering, Ford Motor Company, Dearborn, MI 48121-2053 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2008.921380

due to the failure of a component that provides the basis for the thermal system performance (e.g., fan, blower, pump, or blockage of a cooling passage) [3]. An alternative to the use of thermal models is to estimate the stator and/or rotor resistance(s), from which the temperature of the windings can be estimated by using the linear relationship between the temperature and the resistance of conductors in the machines [3], [8]–[11]. Two basic approaches exist for resistance estimation: 1) methods that inject a test signal [8], [9] and 2) methods that use the fundamental excitation in combination with a machine model to estimate the resistance [3], [10], [11]. In [8], a device is developed to inject a small dc signal into a line-connected machine for the purpose of estimating the stator resistance. This method, however, requires additional hardware and creates torque pulsations when the dc current is injected. In [9], the stator and rotor resistances are estimated using an ac signal injection, which limits its application to inverter-fed machines. The injected signals are superimposed on the fundamental excitation; their frequencies are chosen to maximize the sensitivity to temperature variations of the stator and rotor resistances. Temperature estimation based on the stator or rotor resistances obtained from terminal measurements and a model of the machine has the advantages of not requiring additional hardware and not interfering with the regular operation of the machine [3], [10], [11]. However, these models can show significant parameter sensitivity, with their performance dependent on the operating point of the machine (i.e., load level, flux level, and speed) [3]–[10]. The injection of a high-frequency carrier signal voltage for temperature monitoring purposes is proposed in this paper. This injected signal is used to measure the high-frequency impedance of the machine (i.e., the stator transient impedance) from which the temperature of the stator windings can be estimated. This measurement shows a reduced sensitivity to the operating point of the machine (i.e., torque level and speed) and can be accomplished with no additional hardware, minimal computational requirements, and minimal interference with the operation of the machine, thereby making the method suitable for implementation in standard, low-cost inverter-fed ac drives. In contrast to the method described in [9], which is based on the fundamental (low-frequency) model of the machine, the method described in this paper is based on the machine’s high-frequency model. This results in two major differences. First, the frequency for the injected signal can be made independent of the machine’s operating point or parameters. The

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selection of the injected signal’s frequency in [9] requires precise knowledge of the machine’s parameters, which makes it sensitive to the accuracy of the parameter estimates. In contrast, the selection of the carrier signal frequency for the proposed method does not depend on the machine’s parameters. Second, spectral separation between the fundamental excitation and injected signal simplifies the signal processing and minimizes the impact of the injected signal on the torque-producing behavior of the machine. In [9], the frequencies used for the injection were spectrally close to the fundamental excitation frequency (the difference in the range of a few tens of hertz). This produces currents in the range of 8% to 22% of the rated current, with significant torque pulsations and additional losses. The carrier signal currents resulting from the proposed method are spectrally far from the fundamental excitation and, as will be shown, are significantly smaller in magnitude.

Fig. 1.

Injection of the carrier signal voltage in an inverter-fed machine.

II. M EASUREMENT OF THE S TATOR T RANSIENT I MPEDANCE When a balanced, polyphase, high-frequency carrier signal voltage (1) (ωc in the range of several hundred hertz, ωc
ωr ) is applied to a machine, its dynamic response can be modeled using the stator transient impedance (2) with the resulting current consisting of a positive-sequence component of the form shown in (3) for symmetric machines [13], [14]. Since (1) is a periodic, sinusoidal excitation, the p operator in (2) can be replaced by jωc in the steady state (4), allowing the corresponding magnitude (5) and phase (6) of the equivalent impedance to be obtained, where Lσs and Rs (7) are the stator transient inductance and resistance, respectively, and Zσs (4) is the stator transient impedance s jωc t vqds = Vc ejθc _c = Vc e s s  s vqds _c = Lσs piqds_c + Rs iqds_c

(3)

s vqds _c

(4)

= (Lσs jωc +

=

Zσs isqds_c

Vc Icp s s ∠Zσs = ρ = ∠(jωc Lσs + Rs ) = ∠vqds _c − ∠iqds_c
2 Lm L2 Rs = Rs + Rr ; Lσs = Ls − m . Lr Lr |Zσs | = |jωc Lσs + Rs | =

TABLE I INDUCTION MOTOR PARAMETERS

(1) (2)

isqds_c = Icp ej(ωc t−ρ) = Icp ej(θc −ρ) Rs ) isqds_c

Fig. 2. (a) Measured q- and d-axes components of the stator current with a carrier voltage of ωc = 375 Hz, Vc = 10 V (peak) and (b) frequency spectrum.

(5) (6) (7)

The carrier signal voltage is injected into the machine by adding it to the commanded fundamental voltage. This fundamental voltage can be generated in an open-loop fashion (e.g., V/Hz methods) or be commanded by current regulators (e.g., vector control methods), as shown in Fig. 1. Fig. 2 shows the measured q- and d-axes components of the stator current and their corresponding frequency spectra, including both the fundamental current and the carrier signal current. The parameters of the machine are shown in Table I. Measurement of the current is performed using the current sensors and 12-bit A/D converters already present in the drive for current regulation and protection purposes. 10-bit A/D converters were also tested and found to provide enough resolution for the current measurement.

III. T EMPERATURE E STIMATION U SING THE S TATOR T RANSIENT I MPEDANCE Temperature variations in the induction machine cause the stator resistance Rs and the rotor resistance Rr to vary. This variation is a linear function of the change in temperature that depends on the material properties of each winding Rs = Rs0 + αs Rs0 (Ts − T0 )

(8)

Rr = Rr0 + αr Rr0 (Tr − T0 )

(9)

where αs and αr are the temperature coefficients of the stator and rotor resistances, T0 represents the reference temperature, Rs0 and Rr0 are the stator and rotor resistances at T0 , and Ts and Tr are the stator and rotor temperatures. It can be observed from (5) through (9) that the stator transient impedance depends both on the stator and the rotor

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Fig. 4. Sensitivity of the stator transient impedance magnitude and phase to variations in temperature as a function of the carrier signal frequency. Fig. 3. Schematic of the variation of the stator transient impedance magnitude and phase with temperature.

temperatures as well as on each winding’s temperature coefficient. For simplicity, this paper will first consider the case where the stator and rotor windings are made of the same material (αs = αr ) and are at equal temperatures. The more general case, where these simplified assumptions are not valid, will be discussed in the following section. If it is assumed that the stator and rotor windings are made of the same material and are at equal temperatures, (8) and (9) can be substituted into (7) to form (10). This allows the stator temperature to be readily obtained from the stator transient resistance   + αs Rs0 (Ts − T0 ). Rs = Rs0

(10)

According to (5) and (6), both the magnitude and the phase of the stator transient impedance depend on the stator transient resistance and, therefore, its temperature. Their usefulness for estimating the temperature of the machine’s windings can be determined by analyzing how both are affected by changes in temperature. From (4) and (10), the stator transient impedance can be written as (11). The effect of a temperature variation ∆Ts can be modeled as a change in the stator transient impedance given by (12), with the variation of the overall stator transient impedance’s magnitude and phase being given by (13) and (14), respectively. This is shown schematically in Fig. 3  Zσs = jωc Lσs + Rs0 [1 + αs (Ts − T0 )]  ∆Zσs = Rs0 αs ∆Ts

(11) (12)

∆|Zσs | = |Zσs0 + ∆Zσs | − |Zσs0 |

(13)

∆∠Zσs = ∠(Zσs0 + ∆Zσs ) − ∠Zσs0 .

(14)

The sensitivity of these quantities to changes of temperature is given by (15) and (16), respectively. It should be noted that both of these functions depend on the carrier signal frequency ωc since the stator transient impedance varies with frequency (11). In (15) and (16), the quantities are normalized to a per unit basis by dividing by |Zσs0 | and ∠Zσs0 , respectively, Sensitivity|Zσs | =

∆Zσs 1 ∆Ts |Zσs0 |

(15)

Sensitivity∠Zσs =

∆∠Zσs 1 . ∆Ts ∠Zσs0

(16)

Fig. 5. (a) Magnitude and (b) phase of the stator transient impedance, numerically calculated, as a function of the winding temperature and the carrier signal frequency. The magnitude is represented as a per unit relative to its value at 20 ◦ C for better visualization.

Fig. 4 shows the sensitivity functions (15) and (16), numerically calculated, as a function of the carrier signal frequency for the parameters of the test machine. It can be observed that the magnitude sensitivity (15) is positive, meaning that |Zσs | increases with temperature, and the phase sensitivity is negative, meaning that ∠Zσs decreases with temperature. Fig. 5 shows |Zσs | and ∠Zσs as a function of the temperature and the carrier signal frequency. Three facts can be observed from Figs. 4 and 5. 1) The sensitivity decreases as the carrier signal frequency increases. This is due to the fact that the inductive term of (11), which does not depend on the temperature, dominates the characteristics of the overall impedance as the frequency increases. 2) Except for very low frequencies, the sensitivity of the impedance phase angle to temperature variations is greater than that of the impedance magnitude.

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3) Accurate determination of the impedance magnitude, which is obtained by using (5), requires precise knowledge of the carrier signal voltage. Since the inverter output voltage is not commonly measured in industrial drives, measurement of the dc bus voltage, as well as compensation for the effects caused by the non-ideal behavior of the inverter (e.g., dead time, voltage drop), is required. Measurement of the impedance phase angle, on the other hand, does not require precise knowledge of the carrier signal voltage magnitude. From these observations, the stator transient impedance phase angle is determined to be the preferred quantity for estimation of the temperature. A detailed description of the signal processing used to measure the stator transient impedance and to estimate the winding’s temperature is presented in Section VII.

IV. E FFECTS C AUSED BY D IFFERENCES IN THE S TATOR AND R OTOR T EMPERATURES





εT s = Tˆs − Ts
2 Lm = Lr
2 Lm εT s ≈ Lr

Rr0  Rs0




(17)

αr (Tr − T0 ) − αs (Ts − T0 ) αs

Rr0  (Tr − Ts ). Rs0

variations can be a useful predictor of a fault condition or other situations that require action from the machine’s controller. Results presented in Section VI will illustrate this capability. V. S ELECTION OF THE C ARRIER S IGNAL V OLTAGE

Unfortunately, the conditions for which (10) holds true are not typical in most electric machine applications. Small machines commonly use different materials for the stator and rotor windings, and the stator and rotor temperatures can be significantly different in many applications [7], [11]. For these cases, the temperature obtained using (10) Tˆs (17) is not the stator temperature but a weighted average of the stator and rotor temperatures and their material properties. The error εT s between the estimated Tˆs and actual temperatures Ts (18) can be calculated using (8) and (9), respectively. This can be further simplified to (19) if the stator and rotor windings have similar temperature coefficients, as is the case for copper and aluminum (αcu = 0.004/◦ C; αal = 0.0043/◦ C at 20 ◦ C) R −R Tˆ = s  s0 + T0 αs Rs0

Fig. 6. Error in the estimated stator temperature as a function of the difference between stator and rotor temperature and the magnetizing versus rotor inductance relationship.

 (18) (19)

Equation (19) is graphically shown in Fig. 6. According to (19) and Fig. 6, the primary source of error in the estimated stator temperature is a temperature difference between the stator and rotor windings, with the resulting error in the estimated stator temperature being in the range of half of the difference between stator and rotor temperatures. It can be concluded from the previous discussion that if the difference between the stator and rotor temperature varies significantly, then the method can fail to provide an accurate, absolute estimate of the stator temperature. However, even for that case, it allows for the quick and accurate detection of stator transient resistance variation, which can be used to detect abnormal variations in the machine’s temperatures. These

Selection of the carrier signal voltage’s frequency and magnitude involves a tradeoff between the accuracy and robustness of the method and the impact that injection of the carrier signal voltage has on the fundamental operation of the drive. Injection of the carrier signal voltage requires that a voltage margin exists between the fundamental excitation voltage and the maximum voltage available from the dc bus. For the case of induction machines, this margin may not exist once the machine goes above rated speed (i.e., in the field weakening region), unless increased field-weakening is applied to artificially create the necessary voltage margin. Because of this, the implementation and discussion of the proposed method will be limited to fundamental excitation frequencies less than the rated frequency (usually 50–60 Hz) in this paper. Other potential impacts of carrier signal injection include increased losses and vibration. Both of these are a strong function of the carrier signal frequency and carrier signal magnitude, with high frequency and low magnitude being preferred. Unfortunately, high-frequency, small-magnitude carrier signals have reduced sensitivity to temperature variations as well as a reduced signal-to-noise ratio. From the experimental work carried out during this research, it was found that carrier signal frequencies in the range of 200–400 Hz (see Figs. 4 and 5) and carrier signal voltage magnitudes in the range of 2% of rated voltage provide the ability to accurately estimate temperature, while having little effect on the fundamental operation of the machine with the resulting acoustic noise being almost imperceptible. This is illustrated in Fig. 7, which shows the standard deviation of the error of the measured impedance phase angle and the resulting standard deviation of the error in the estimated temperature, as a function of the carrier signal voltage magnitude. It can be observed from the figure that carrier signal voltage magnitudes above ∼4 V (peak) (1% of rated voltage) are enough to obtain accurate measurements. The results shown in Fig. 7 were obtained with a carrier signal frequency of ωc equal to 375 Hz. Unless otherwise stated, a carrier signal voltage of 10 V (peak)

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Fig. 7. Experimentally calculated standard deviation of the estimated phase angle of ∠Zσs (in degrees) as a function of the carrier signal voltage magnitude for a carrier signal frequency of ωc = 375 Hz. The second y-axis scale on the left indicates the resulting error in the estimated temperature, in ◦ C, caused by the error in the estimation of the phase angle.

and ωc equal to 375 Hz were used for all the experimental results presented hereafter. This carrier signal offered adequate spectral separation from the fundamental excitation and good accuracy of the temperature estimation, with the resulting carrier signal current being < 4% of rated current. VI. E XPERIMENTAL R ESULTS To confirm the conclusions from the previous discussion, the variation of the stator transient impedance with temperature was measured using the test machine of Table I. The stator winding temperature was measured by placing a type K thermocouple sensor within a stator slot, close to the stator coil end. Fig. 8 shows the magnitude and phase of the stator transient impedance as a function of the temperature measured in the stator windings for two different test sequences, first with the machine being operated at rated flux, 30% of rated load, Fig. 8(a) and then at rated flux, rated load, Fig. 8(b). Experimental results are shown for two carrier signal frequencies ωc equal to 375 Hz and 750 Hz. Fig. 9 shows the rotor versus stator temperatures for the test shown in Fig. 8(b), with the rotor temperature being measured in the end-ring using an infrared thermometer. Some important facts can be observed from Figs. 8 and 9. 1) Variations of the machine’s temperature result in deterministic variations of the stator transient impedance, which are in good agreement with those predicted by the theoretical model (Fig. 5). 2) Although both the magnitude and phase of the stator transient impedance reflect variations caused by temperature changes, the sensitivity (slope) is smaller for the magnitude while being significantly larger for the phase. This is, again, in good agreement with the theoretical predictions. 3) The amount of variation seen in the stator transient impedance’s magnitude and phase due to temperature changes increases as the carrier signal frequency decreases. 4) The load level of the machine has little effect on the variation of the stator transient impedance with temperature. It should be noted that, in all cases, the machine was operated at rated flux, which is common in field-oriented controlled machines below their base speed. 5) It is interesting to note that the test shown in Fig. 8(b) (full load) lasted 45 min, and the test shown in Fig. 8(a)

Fig. 8. Measured magnitude and phase of the stator transient impedance as a function of the stator winding temperature with (a) the machine operated at rated-flux, 30% rated load, and (b) the machine operated at rated-flux, ratedload. A fundamental excitation frequency of 4 Hz was used, the rotor speed (slip) being proportional to the load level for each case. Two carrier signal frequencies of ωc equal to 375 Hz and 750 Hz were used. The stator winding temperature was measured using a thermocouple placed within a stator slot.

(30% load) lasted 85 min. Independent of these differences in the test length and in how the heat was generated in the machine, the results shown in Fig. 8(a) and (b) are very similar, indicating a rather constant temperature difference between stator and rotor for both cases.

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Fig. 9. Measured rotor temperature versus stator temperature during test #2 in Fig. 8(b).

6) In Fig. 9, the linear relationship between the rotor and stator temperatures suggests that the rotor temperature for this machine can be estimated using a simple scaling of the stator temperature [11]. It is noted, however, that further verification of this relationship is needed to ensure that it is valid over all expected operating conditions. From the experimental data shown in Fig. 8(b), a linear relationship can be established between the stator transient impedance phase angle ∠Zσs and the stator temperature Ts (20), with the units of ∠Zσs and Ts being degrees and ◦ C, respectively. The stator temperature was estimated during the online implementation of the method using (21), with a equal to 74.4 ◦ C degrees and b equal to 0.03076 ◦ C ∠Zσs = a − bTs a − Zσs Tˆs = . b

Fig. 10. Temperature (a) measured using the sensor and (b) estimated from the stator transient impedance. (c) Estimation error. The machine was operated at rated-flux, rated-load, a carrier signal of ωc = 375 Hz, Vc = 10 V, was used. Forced cooling was connected as marked by vertical lines.

(20) (21)

Fig. 10(a) and (b) show the stator temperature directly measured and estimated from the stator transient impedance phase angle, respectively. The machine was operated at rated load, rated flux. No significant natural ventilation existed. Forced ventilation was connected and disconnected, as indicated in the figure. Fig. 10(c) shows the difference in the temperature measured by the sensor and that estimated from ∠Zσs . It can be observed from the figure that a good agreement between the estimated and measured temperatures exists. The difference was limited to about 5 ◦ C. It is important to note that both the thermocouple and the temperature estimation obtained from the stator transient carrier impedance phase angle are lumped measurements of a spatially distributed parameter. The biggest difference being that the thermocouple measures the temperature in a specific point of the windings (or stator lamination) while the stator transient impedance phase angle reflects the average temperature of the winding. The coefficients a and b in (20) and (21) were obtained from the data shown in Fig. 8(b), which was collected with the machine operating at rated flux, rated load, and constant fundamental excitation frequency. It can be observed from Fig. 8 that slight differences exist in the phase of the stator

Fig. 11. Estimated temperature error as a function of the slip (load level). The machine was operated at rated flux.

transient impedance phase angle for the case of 30% of rated load, Fig. 8(a), and rated load, Fig. 8(b). This means that the error in the estimated temperature might increase when the operating point of the machine is different from that used during the commissioning process to tune the parameters a and b in (20) and (21). Fig. 11 shows the error in the estimated temperature as a function of the load level (slip), with the machine operated at rated flux. It can be observed from the figure that the magnitude of the error increases slightly for load levels significantly smaller than that used during the commissioning process. Fig. 12 shows the error in the estimated temperature as a function of the flux level, with the machine working at no-load. Errors of a few degrees Celsius exist when the machine is operated at significantly reduced levels of flux. Finally, the influence of the fundamental excitation frequency on the estimated temperature is shown in Fig. 13. It should be noted that the data used for the commissioning process (Fig. 8) was obtained with ωe equal to 4 Hz. It can be observed from

BRIZ et al.: TEMPERATURE ESTIMATION IN INVERTER-FED MACHINES USING HIGH-FREQUENCY CARRIER SIGNAL INJECTION

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Fig. 12. Estimated temperature error as a function of rotor flux level. The machine was operated at no load.

Fig. 14. (a) Schematic representation of the carrier signal voltage injection. (b) Timing of the carrier signal voltage injection and signal processing.

Fig. 13. Estimated temperature error as a function of the fundamental excitation frequency ωe . The machine was operated at rated flux, rated load.

the figure that the magnitude of the estimation error slightly increases as the fundamental excitation frequency increases. It can be concluded from the experimental results shown in Figs. 11–13 that the operating point of the machine (load level, flux level, and fundamental excitation frequency) influence that stator transient impedance phase angle and can result in an increased error in the estimated temperature when it varies significantly with respect to that used for the commissioning process. However, this error has been found to be limited to a few degrees Celsius from the experiments performed during this research. Finally, it is noted that compensation of these errors would be possible by making coefficients of (21) adaptive as a function of the operating condition of the machine. However, this would require a more complicated commissioning process, as data for different operation conditions would need to be collected. VII. I MPLEMENTATION OF THE M ETHOD It has been shown that the stator transient impedance allows reliable estimation of the temperature of the machine windings. This section describes the implementation of a method based on this observation. A. Intermittent Carrier Signal Voltage Injection All the analyses presented in the previous sections assumed that the carrier signal voltage was continuously injected, allowing for continuous estimation of the stator transient impedance and, consequently, of the temperature. Continuous injection of the carrier signal voltage has, however, unwanted effects, as it produces vibration and additional losses. Since the quantities to be estimated change relatively slowly, intermittent, instead of continuous, injection of the carrier signal voltage is feasible. This implementation is shown schematically in Fig. 14, with

Fig. 15. Measured q- and d-axes components of the stator current with a carrier signal voltage of ωc = 375 Hz, Vc = 10 V (peak) injected for a time t1 = 0.45 s.

the resulting current being shown in Fig. 15. The carrier signal voltage is injected during a time t1 and the resulting carrier signal current is measured during a subset of this time t2 . A delay in the range of at least three stator transient time constants Lσs /Rs needs to be added between the start of injection of the carrier signal voltage (start of t1 ) and the measurement of the carrier signal current (start of t2 ) in order to allow the carrier signal current to reach steady state before the signal processing begins. While small values of t1 and t2 would be preferred to limit the adverse effects of the carrier signal, excessively small values may cause increased sensitivity to noise, reducing the accuracy of the method. Fig. 16 shows the standard deviation of error in the estimated temperature as a function of t2 . It can be observed from the figure that times in the range of a few tenths of a second provide accurate results and that increasing t2 beyond these values does not have any noticeable effect on improving the accuracy of the method. It should be noted that the experimental results shown in Fig. 10 were obtained using intermittent injection with t1 = 0.45 s and t2 = 0.4 s. The intervals between successive carrier signal injections (i.e., temperature measurements) can be set to be constant or dynamically adapted as a function of operating conditions. Intervals in the range of a few minutes would commonly be adequate, as the temperature has slow dynamics, but can be reduced if the machine is continuously

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Fig. 16. Standard deviation of the estimated temperature error as a function of the duration of time for the carrier signal current processing t2 .

Fig. 18. q- and d-axes components of the stator current after the fundamental band rejection filter.

controlled drives, since the stator currents are usually transformed and processed in that reference frame. Fig. 18 shows the resulting signal after removing the fundamental current. An alternative option for removing the fundamental current, when implementing the method in current regulated drives, is to use the fundamental current command as an estimate of the fundamental current and then decoupling it from the measured current (24), as shown in Fig. 17(b). This method relies on the fact that zero error should exist in the steady state for a properly designed current regulator ˆısqds_c = isqds − is∗ qds_f .

Fig. 17. (a) Signal processing to estimate the stator transient carrier signal impedance. The fundamental current is filtered off using a band-stop filter. Alternatively, the fundamental current command can be used for this purpose, as shown in (b).

heavily loaded or if significant temperature variations are observed from measurement to measurement. This last condition is of particular interest since it would be indicative of abnormal operation. B. Separation of the Positive-Sequence Carrier Signal Current Prior to calculating the stator transient impedance, the positive-sequence carrier signal current needs to be isolated from the overall stator current. The stator current can be modeled as consisting of the fundamental component, the positivesequence carrier signal component, and additional components of relatively small magnitude, including switching harmonics, that can be considered as noise (22). Special care is required in removing the fundamental current, as it is significantly larger than the carrier signal current of interest. This can be achieved using a bandstop filter of the form (23), where ωe is the fundamental excitation frequency and bwbrf is the filter bandwidth (Fig. 17) isqds = isqds_f + isqds_c + noise ˆısqds_c s − jωe = . s iqds (s − jωe )2 + bwbrf

(22) (23)

A filter bandwidth of 20 Hz was used for the experimental results presented in this paper. The filter (23) can be implemented as a high-pass filter in the fundamental excitation synchronous frame. This implementation is especially suitable for vector

(24)

Other options for separating the positive-sequence carrier signal current were investigated and found to be more complicated or to provide inferior results. A bandpass filter at the carrier signal frequency is one such example that could be used to isolate the positive-sequence carrier signal current. However, accurate isolation of this component would require very narrow bandwidths, resulting in very slow dynamics and requiring the carrier signal voltage to be injected for a significantly longer time. Separation of the positive-sequence carrier signal current can also be accomplished using fast Fourier transform (FFT) based methods. However, these methods generally require significant computational as well as memory resources and are, therefore, not recommended. C. Calculation of the Stator Transient Impedance Once the positive-sequence carrier signal current has been separated from the overall stator current, it needs to be processed to obtain the angle of the stator transient impedance. This can be done by transforming the positive-sequence carrier signal current to a positive-sequence carrier signal reference frame. In this reference frame, the positive-sequence carrier signal current becomes a dc signal, as shown in Fig. 19. icqds_c = isqds_c ej(θct−ρ) e−jθct = Icp e−jρ .

(25)

Implementation of this solution is particularly suitable if the carrier signal frequency is chosen to be a submultiple of the switching frequency ωs ωs =k ωc

(26)

with k being an integer. In that case, a lookup table containing sin(θc ) and cos(θc ) can be used both to create the carrier signal voltage and to

BRIZ et al.: TEMPERATURE ESTIMATION IN INVERTER-FED MACHINES USING HIGH-FREQUENCY CARRIER SIGNAL INJECTION

Fig. 19. q- and d-axes components of the positive-sequence carrier signal current in a positive-sequence carrier synchronous reference frame.

implement the transformation of the positive-sequence carrier signal current to the positive-sequence carrier signal reference frame (Fig. 17), which avoids the online calculation of trigonometric functions. In addition, the angle of the resulting positivesequence carrier signal current in this reference frame (25) directly corresponds to the phase angle of the positive-sequence carrier impedance ρ. The angle can be obtained using a tan−1 function. Alternatively, a phase-locked loop could also be used for this purpose. For the experiments presented in this paper, a ωs equal to 15 kHz and a ωc equal to 375 Hz were utilized, which results in a k equal to 40 in (26). A lookup table consisting of 20 positions (0 to π) was used to generate both sin(θc ) and cos(θc ). It should be noted from Fig. 19 that a single point of the carrier signal current would be enough to calculate the angle of the stator transient impedance since it is a dc signal. As discussed in Section VII-A, this is not advisable in practice, however, since this signal is contaminated by noise. Instead, the mean value of the positive-sequence carrier signal current (25) during t2 is computed before calculating the tan−1 . This is schematically shown in Fig. 17(a). D. Utilization of the Method During Transients One criteria for the selection of the carrier signal frequency was to have spectral separation with the fundamental excitation. While this can be guaranteed during the steady-state operation of the drive, transients in the fundamental current give rise to additional frequency components, some of which coincide with the carrier signal frequency and interfere with the method. This can be especially important in current regulated drives using high bandwidth current regulators. To avoid this, injection of the carrier signal voltage (and the further signal measurement and processing to estimate the stator temperature) should be performed only when the machine operates in the steady state. It has been shown that a few tenths of a second of carrier signal voltage injection are enough to obtain accurate temperature estimates, allowing the method to be applied in a wide variety of applications, including those that spend minimal amounts of time operating in the steady-state condition. E. Carrier Signal Voltage Injection in Current-Regulated Drives If the method is used in current-regulated drives, then it is important to consider the reaction of the current controller to the

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injection of the carrier signal voltage [15]. If the carrier signal frequency is in the range of the current regulator bandwidth, (which is often the case in high-performance, vector-controlled drives), the current regulator will see the carrier signal current as a disturbance and attempt to compensate for it. This will result in a carrier signal voltage at the inverter input that is different from the commanded carrier signal voltage (both in magnitude and in phase). This can produce a significant reduction in the accuracy of the measurements if not adequately compensated. A solution, which was implemented for the experiments presented in this paper, is to use a band-rejection filter to remove the carrier signal current from the current feedback to the current controller [15] (Fig. 14). This filter will not affect the current regulator performance, provided that it is only implemented when the machine operates in a steadystate condition and that there is adequate spectral separation between the fundamental excitation frequency and the carrier signal frequency. VIII. C ONCLUSION Temperature monitoring using high-frequency carrier signal injection is analyzed in this paper. The stator transient impedance has been shown to provide an accurate estimate of the stator transient resistance, from which the temperature of the stator windings can be estimated. This measurement exhibits a low sensitivity to the operating point of the machine. The method can be implemented in standard drives since it does not require additional hardware and has minimal computational requirements. ACKNOWLEDGMENT The authors wish to acknowledge the support and motivation provided by the University of Oviedo, Spain, and Ford Motor Company, USA. R EFERENCES [1] A. H. Bonnett and G. C. Soukup, “Causes and analysis of stator and rotor failures in three-phase induction motors,” IEEE Trans. Ind. Appl., vol. 28, no. 4, pp. 921–937, Jul./Aug. 1992. [2] R. M. Tallam, S. B. Lee, G. C. Stone, G. B. Kliman, J. Yoo, T. G. Habetler, and R. G. Harley, “A survey of methods for detection of stator-related faults in induction machines,” IEEE Trans. Ind. Appl., vol. 43, no. 4, pp. 920–933, Jul./Aug. 2007. [3] S. B. Lee, T. G. Habetler, R. G. Harley, and D. J. Gritter, “An evaluation of model-based stator resistance estimation for induction motor stator winding temperature monitoring,” IEEE Trans. Energy Convers., vol. 17, no. 1, pp. 7–15, Mar. 2002. [4] Z. Gao, T. G. Habetler, and R. G. Harley, “An online adaptive stator winding temperature estimator based on a hybrid thermal model for induction machines,” in Proc. IEEE Int. Conf. Elect. Mach. Drives, May 2005, pp. 754–761. [5] C. Kral, T. G. Habetler, R. G. Harley, F. Pirker, G. Pascoli, H. Oberguggenberger, and C. M. Fenz, “Rotor temperature estimation of squirrel-cage induction motors by means of a combined scheme of parameter estimation and a thermal equivalent model,” IEEE Trans. Ind. Appl., vol. 40, no. 4, pp. 1049–1057, Jul. 2004. [6] B. K. Bose and N. R. Patel, “Quasi-fuzzy estimation of stator resistance of induction motor,” IEEE Trans. Power Electron., vol. 13, no. 3, pp. 401–408, May 1998. [7] P. H. Mellor, D. Roberts, and D. R. Turner, “Lumped parameter thermal model for electrical machines of TEFC design,” Proc. Inst. Electr. Eng., vol. 138, pt. B, no. 5, pp. 205–218, Sep. 1991.

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[8] S. B. Lee and T. G. Habetler, “An online stator winding resistance estimation technique for temperature monitoring of line-connected induction machines,” IEEE Trans. Ind. Appl., vol. 39, no. 3, pp. 684–685, May 2003. [9] Y. Wu and H. Gao, “Induction-motor stator and rotor winding temperature estimation using signal injection method,” IEEE Trans. Ind. Appl., vol. 42, no. 4, pp. 1038–1044, Jul. 2006. [10] S. B. Lee, T. G. Habetler, R. G. Harley, and D. J. Gritter, “A stator and rotor resistance estimation technique for conductor temperature monitoring,” in Conf. Rec. IEEE IAS Annu. Meeting, Rome, Italy, Oct. 2000, pp. 381–387. [11] R. Beguenane and M. E. H. Benbouzid, “Induction motors thermal monitoring by means of rotor resistance identification,” IEEE Trans. Energy Convers., vol. 14, no. 3, pp. 566–570, Sep. 1999. [12] M. Maximini and H. J. Koglin, “Determination of the absolute rotor temperature of squirrel cage induction machines using measurable variables,” IEEE Trans. Energy Convers., vol. 19, no. 1, pp. 34–39, Mar. 2004. [13] D. W. Novotny and T. A. Lipo, Vector Control and Dynamics of AC Drives. New York: Oxford Univ. Press, 1996. [14] P. L. Jansen and R. D. Lorenz, “Transducerless position and velocity estimation in induction and salient AC machines,” IEEE Trans. Ind. Appl., vol. 31, no. 2, pp. 240–247, Mar. 1995. [15] F. Briz, M. W. Degner, and A. B. Diez, “Dynamic operation of carrier signal injection based, sensorless, direct field controlled AC drives,” IEEE Trans. Ind. Appl., vol. 36, no. 5, pp. 1360–1368, Sep./Oct. 2000.

Fernando Briz (A’96–M’99–SM’06) received the M.S. and Ph.D. degrees from the University of Oviedo, Gijón, Spain, in 1990 and 1996, respectively. From June 1996 to March 1997, he was a Visiting Researcher at the University of Wisconsin, Madison. He is currently an Associate Professor in the Department of Electrical, Computer and Systems Engineering, University of Oviedo. His topics of interest include control systems, high-performance ac drives control, sensorless control, diagnostics, and digital signal processing. Dr. Briz received the 2005 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS Third Place Prize Paper Award and was the recipient of two IEEE Industry Applications Society Conference Prize Paper Awards in 1997, 2003, and 2007, respectively.

Michael W. Degner (S’95–A’98–M’99–SM’05) received the B.S., M.S., and Ph.D. degrees in mechanical engineering from the University of Wisconsin, Madison, in 1991, 1993, and 1998, respectively. In 1998, he joined the Ford Research Laboratory, Dearborn, MI, working on the application of electric machines and power electronics in the automotive industry. He is currently the Manager of the Electric Machine Drive Systems Department of the Hybrid Electric Vehicle and Fuel Cell Vehicle Laboratory in Research and Advanced Engineering, Ford Motor Company, where he is responsible for the development of electric machines, power electronics, and their control systems for hybrid and fuel-cell vehicle applications. His interests include control systems, machine drives, electric machines, power electronics, and mechatronics. Dr. Degner received the 2005 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS Third Place Prize Paper Award and has been the recipient of several IEEE Industry Applications Society Conference Paper Awards.

Juan M. Guerrero (S’00–A’01–M’04) received the M.E. degree in industrial engineering and the Ph.D. degree in electrical and electronic engineering from the University of Oviedo, Gijón, Spain, in 1998 and 2003, respectively. Since 1999, he has occupied different teaching and research positions with the Department of Electrical, Computer and Systems Engineering, University of Oviedo, where he is currently a Professor. From February to October 2002, he was a Visiting Scholar at the University of Wisconsin, Madison. From June to December 2007, he was a Visiting Professor at the Tennessee Technological University, Cookeville. His research interests include parallel-connected motors fed by one inverter, sensorless control of induction motors, control systems, and digital signal processing. Dr. Guerrero received an award from the College of Industrial Engineers of Asturias and León, Spain, for his M.E. thesis in 1999, an IEEE Industry Applications Society Conference Prize Paper Award in 2003, and the University of Oviedo Outstanding Ph.D. Thesis Award in 2004.

Alberto B. Diez (M’99) received the M.S. and Ph.D. degrees from the University of Oviedo, Gijón, Spain, in 1983 and 1988, respectively. He is currently an Associate Professor in the Department of Electrical Engineering, University of Oviedo. He was a Member of the Executive Committee D2 “Rolling-Flat Products” of European Commission from 1998 to 2004. His research interests include control systems, high-performance ac drives control, and industrial supervision and control processes.