energies Article
Temperature Estimation of Stator Winding in Permanent Magnet Synchronous Motors Using d-Axis Current Injection Bum-Su Jun 1 , Joon Sung Park 2 1 2
*
ID
, Jun-Hyuk Choi 2 , Ki-Doek Lee 2 and Chung-Yuen Won 1, *
Department of Electrical and Computer Engineering, Sungkyunkwan University, Suwon 16419, Korea;
[email protected] Intelligent Mechatronics Research Center, Korea Electronics Technology Institute (KETI), Bucheon 14502, Korea;
[email protected] (J.S.P.);
[email protected] (J.-H.C.);
[email protected] (K.-D.L.) Correspondence:
[email protected]; Tel.: +82-31-290-4963
Received: 9 July 2018; Accepted: 30 July 2018; Published: 6 August 2018
Abstract: This paper presents a stator winding temperature detection method for permanent magnet synchronous motors (PMSMs) using a motor parameter estimation method. PMSM performance is highly dependent on the motor parameters. However, the motor parameters vary with temperature. It is difficult to measure motor parameters using a voltage equation without additional sensors. Herein, a stator winding temperature estimation method based on a d-axis current injection method is proposed. The proposed estimation method can be used to obtain stator temperatures and to achieve reliable operation. The validity of the proposed method is verified through simulations and experimental results. Keywords: permanent magnet synchronous motor (PMSM); motor parameter estimation; stator winding temperature estimation; d-axis current injection; stator winding resistance
1. Introduction Permanent magnet synchronous motors (PMSMs) are widely employed in industrial drives, electric vehicles, renewable energy systems, etc., owing to their high torque density, high power density, and high efficiency [1]. The motors, primarily applied in drones and fans, are of the outer rotor type, in which the rotor is located outside and the stator is located inside. These motor types are surface-mounted permanent magnet synchronous motors (SPMSMs) with the same d-axis inductance and q-axis inductance. The torque is generated only by the q-axis current. In outer-rotor-type motors, the stator is located inside and temperature rises may occur and, as such, turn faults may occur as well. The life of the motor can be reduced by approximately 50% for every 10 ◦ C increase in the stator winding temperature design limit [2,3]. The motor parameters are dependent on current and temperature. Due to high temperatures, or high currents, turn faults [4–6] in the stator may occur. Current can be easily measured using the current sensors of the inverter. However, it is difficult to obtain the internal temperature of the motor, especially that of the stator winding. Among all temperature monitoring methods, the most accurate is to insulate temperature sensors [3]. However, the insulation of the temperature sensor is not cost-effective and temperature sensor reliability problems may occur. Motor internal temperature estimation methods can be classified into thermal model methods [7–10], and motor parameter estimation methods [11–15]. The lumped-parameter thermal network [7] is the most well-known thermal model method. The thermal model system is an eighth-order dynamic model, with many thermal capacitances and resistances, either directly acquired from various experimental tests, or derived from the dimensions
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and material thermal properties of the motor. However, with some assumptions in place, a few Energies 2018, 11, x FOR PEER REVIEW 2 of 14 simplified thermal models have been proposed [8–10]. The computations are less complicated, but the thermal models are stillproposed significant withThe many model parameters able to be identified from simulations models have been [8–10]. computations are less complicated, but the thermal models are still significant with many model model isparameters able to on be the identified simulations and and experimental tests. The thermal highly dependent coolingfrom system and the geometry Theanalysis thermal model is highly on the cooling system and the These geometry of theexperimental motor, and tests. specific for each motordependent design and application is required. results of the motor, and specific analysis for each motor design and application is required. These results lead to limited applications and require long development times. In the parameter estimation method, to limited applications and require long development times. In the parameter estimation statorlead resistance is used as the indicator of the stator winding temperature. This approach has method, stator resistance is used as the indicator of the stator winding temperature. This approach significant advantages over the thermal model method. The accuracy of the stator temperature has significant advantages over the thermal model method. The accuracy of the stator temperature estimation is not affected by the motor specifications, cooling method, or operating conditions [11,12], estimation is not affected by the motor specifications, cooling method, or operating conditions [11,12], and the stator resistance cancan bebe estimated electricalequivalent equivalent model of the motor and the stator resistance estimatedfrom from the the electrical model of the motor [13]. [13]. However, the stator resistance is significantly small and performance of the temperature estimation However, the stator resistance is significantly smallthe and the performance of the temperature is tooestimation sensitive is totoo motor inductance To improve accuracy of the stator sensitive to motorvariations inductance[2]. variations [2]. To the improve the accuracy of the resistance stator resistance estimation, map an inductance and back electromotive map are required. estimation, an inductance and backmap electromotive force (BEMF)force map(BEMF) are required. The inductance The BEMF inductance and BEMF from map are fromand the experimental simulations and experimental results. lead map and mapmap are identified theidentified simulations results. These factors These factors lead to long development times being required. to long development times being required. This paper presents a stator winding temperature estimation method for motor systems without This paper presents a stator winding temperature estimation method for motor systems without additional temperature sensors. To obtain the stator winding temperature, the motor parameters are additional temperature sensors. To obtain the stator winding temperature, the motor parameters estimated. The estimated parameters enable the stator winding temperature to be obtained because are estimated. The vary estimated parameters For enable the stator winding temperature to be obtained the parameters with temperature. the motor parameter estimation, the d-axis current because the parameters vary withThis temperature. For the motor parameter estimation, the d-axis current injection method is proposed. paper is organized as follows: the principles and analysis of the injection method is proposed. This paper is organized as follows: the principles and analysis of the SPMSM operation are presented in Section 2; the proposed estimation method is analyzed in Section SPMSM operationand are experimental presented inresults Section the proposed estimation is analyzed in Section 3; 3; simulation are2;described in Sections 4 and 5method to evaluate the performance of the temperature estimation; andare finally, conclusions are presented Section 6. the performance of simulation and experimental results described in Sections 4 and in 5 to evaluate the temperature estimation; and finally, conclusions are presented in Section 6. 2. Operations of PMSMs
2. Operations of PMSMs model of PMSMs in the synchronous reference frame is given by [14–16]: The fundamental The fundamental model of PMSMs synchronous reference frame is given by [14–16]: e in the vd = Rs ide - ωr Lq iqe + pLd ide e e ω L ie + pL ie vd =vqeR=s iRd s− iqe + ωr r Lqd iqde + pLqdiqe d+ ωr ψm (1) veq = Rs ihqe + ωr Ld ide + pLq iqe + ω r ψm i 3 P e T =Te 3=P L − e Ld L- qLqieiideeiqe++ ψ ψm m iiqq ,, e d q 2 2 2 2 d
(
)
(1)
v d,q and d,q are the d-, q-axis stator voltage and current vectors in the synchronous reference wherewhere ve d,q and ie d,qiare the d-, q-axis stator voltage and current vectors in the synchronous reference respectively. Rs and arethe thestator statorresistance resistance and TheThe equivalent frame,frame, respectively. Rs and Ld,qLd,qare and d-, d-,q-axis q-axisinductance. inductance. equivalent circuit of PMSMs is shown in Figure 1. The motor speed and the rotor flux are denoted by ω r and ψm, ψm , circuit of PMSMs is shown in Figure 1. The motor speed and the rotor flux are denoted by ω r and respectively. p and P are differential operatorand andthe the motor motor poles, respectively. p and P are the the differential operator poles,respectively. respectively. e
e
(a)
(b)
Figure 1. Equivalent circuit of permanent magnet synchronous motors (PMSMs): (a) d-axis; (b) q-axis.
Figure 1. Equivalent circuit of permanent magnet synchronous motors (PMSMs): (a) d-axis; (b) q-axis.
Assuming the steady-state condition, voltage Equation (1) can be approximated as Equation (2). It is noteworthy that ωrLd,qied,q are the coupling terms, and that ωrψm is the BEMF voltage. Based on Equation (2), the voltage and current vectors are described in Figure 2 [16].
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Assuming the steady-state condition, voltage Equation (1) can be approximated as Equation (2). It is noteworthy that ω r Ld,q ie d,q are the coupling terms, and that ω r ψm is the BEMF voltage. Based on Energies 2018, 11, x FOR PEER REVIEW 3 of 14 Equation (2), the voltage and current vectors are described in Figure 2 [16]. ( Energies 2018, 11, x FOR PEER REVIEW
e e e v=d =RsRisdeid−- ω ved ωrrLLq iqqiqe e veq vq =RsRiqseiqe++ ωrr Lddiidede++ ωrω ψrmψm =
(2)
(2)
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vde = Rside - ωr Lq iqe e e e vq = Rsiq + ωr Ldid + ωr ψm
(2)
(a)
(b)
Figure 2. Voltage and current vectors when: (a) i < 0, i > 0; (b) ied = 0, ieq > 0. ed
eq
Figure 2. Voltage and current vectors when: (a) ie d < 0, ie q > 0; (b) ie d = 0, ie q > 0. As shown in Equation (1), the electrical torque is composed of the magnetic torque and the (a) (b) reluctance The magnetic is from the is Lorentz force, and the magnetic reluctance torque As shown intorque. Equation (1), the torque electrical torque composed of the torqueisand the e e ed = 0, ieq > 0. Figure 2. Voltage and currentBecause vectors when: (a) i d < 0, i q > 0; oriented from the L d, Lq asymmetry [17,18]. the inductances L d(b) , L qi are equal for the SPMSMs, reluctance torque. The magnetic torque is from the Lorentz force, and the reluctance torque is the reluctance torque becomes zero, and the torque equation can be rewritten as
oriented from the Ld , Lqinasymmetry Because the Ldmagnetic , Lq are equal As shown Equation (1),[17,18]. the electrical torque is inductances composed of the torque for andthe the SPMSMs, 3 P reluctance torque. The magnetic torque is from the Lorentz force, and the reluctance torque is e the reluctance torque becomes zero, and the T torque equation can be rewritten as = ψ i . (3) e
m q
oriented from the Ld, Lq asymmetry [17,18]. Because 2 2 the inductances Ld, Lq are equal for the SPMSMs, the reluctance torque becomes zero, and the torque 3 P equation can be rewritten as
The electrical torque for the SPMSMs Tecan = be controlled ψm ie . using the q-axis current. The constant 232P3. Theqe torque of the SPMSMs is generated by the torque curves of the SPMSMs are shown in Figure Te = ψm iq . (3) 22 q-axis current and the d-axis current does not contribute to torque generation.
(3)
The electrical torque for the SPMSMs can be controlled using the q-axis current. The constant The electrical torque for the SPMSMs can be controlled using the q-axis current. The constant torque curves of the SPMSMs are shown in Figure 3. The torque of the SPMSMs is generated by the torque curves of the SPMSMs are shown in Figure 3. The torque of the SPMSMs is generated by the q-axis current and the and d-axis current does notnot contribute totorque torque generation. q-axis current the d-axis current does contribute to generation.
Figure 3. Constant torque curves for surface-mounted permanent magnet synchronous motors (SPMSMs).
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Figure 3. Constant torque curves for surface-mounted permanent magnet synchronous motors (SPMSMs).
Figure 4 shows the conventional control configuration of SPMSMs for speed control. Because the torque of SPMSMs generated by the q-axis current, the d-axis current command is set to zero, and the Figure 4isshows the conventional control configuration of SPMSMs for speed control. Because q-axis current is of used to construct thebyspeed controller. Information position the torque SPMSMs is generated the q-axis current, the d-axis currentabout command is set toand zero,speed is andby thethe q-axis current sensor. is used toThe construct speed controller. Information about position and speed measured position q-axisthe current command is determined by the speed controller, measured by the position sensor. The q-axis command is determined the speed and theisd-, q-axis current controllers generate thecurrent d-, q-axis voltage references.byThe pulse width controller, and the d-, q-axis current controllers generate the d-, q-axis voltage references. The pulse modulation (PWM) duties are determined using the space vector PWM method, based on the voltage width modulation (PWM) duties are determined using the space vector PWM method, based on the reference in the synchronous reference reference frame. Finally, PWMPWM duties are are applied totothe voltage reference in the synchronous frame. Finally, duties applied thepower power switch using the gateusing drivetheofgate thedrive inverter. switch of the inverter.
.
Figure 4. Conventional configuration SPMSMs. Figure 4. Conventionalcontrol control configuration forfor SPMSMs. 3. Stator Winding Temperature Estimation Using d-Axis Current Injection
3. Stator Winding Temperature Estimation Using d-Axis Current Injection A temperature increase can cause several adverse effects [18,19]. For example, a temperature rise
A temperature increase canstator cause severalvariation adverseand effects [18,19].the For example, a insulation. temperature rise in the stator winding causes resistance can degrade stator winding in the stator winding causes stator resistance variation and can degrade the stator winding insulation. The stator winding temperature can be detected through estimation of the stator resistance. Under thetemperature steady-state condition, the voltage equationestimation of PMSMs can be expressed as a variable The stator winding can be detected through of the stator resistance. depending on the temperature and current as Under the steady-state condition, the voltage equation of PMSMs can be expressed as a variable depending on the temperature and current vde =as Rside - ωr Lqiqe (4) ( e vq R = Riesiqe−+ ω ωr LLdidie e+ ωr ψm ved = s d r q q (4) e = R ie + ω L ie + ω ψ s qof the stator r d d and magnet r m q In Equation (4), Rs and ψm are v functions temperatures, respectively. Ld,q are the functions of the magnet temperature and the stator current. Equation (4) can be rewritten as
In Equation Equation Rs and ψm are functions of zero the for stator and magnet temperatures, (5),(4), because the d-axis current becomes the torque maximization of SPMSMs:respectively. Ld,q are the functions of the magnet temperature and the stator current. Equation (4) can be rewritten as Equation (5), because the d-axis current becomes zero for the torque maximization of SPMSMs: (
ved = −ωr Lq iqe veq = Rs iqe + ωr ψm
(5)
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vde = -ωr Lqiqe e e vq = Rsiq +ωr ψm
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(5)
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From Equation (5), the q-axis inductance can be expressed as Equation (6). From Equation (5), the q-axis inductance can be expressed as Equation (6).
vede Lq = - vd e Lq = − ωr iqe ωi
(6) (6)
r q
s = RR s =
e ve q
v −- ω ωr ψ ψm q
r m
e
iiqeq
(7) (7)
The The stator stator temperature temperature can be be estimated estimated through through the calculation calculation of the the stator stator resistance, resistance, as as in in Equation (7). However, as the rotor flux can vary with the rotor temperature, the stator winding Equation (7). with the rotor temperature, the stator winding temperature temperature estimation may exhibit low accuracy. accuracy. This may cause a large large error error in in the the temperature temperature estimation estimation of the the stator stator winding. winding. Therefore, an additional equation is required to obtain obtain the the stator stator winding temperature. winding temperature. As As mentioned mentioned in in the the previous previous section, section, the the constant constant torque torque for for the the SPMSMs SPMSMs is is maintained maintained even even if if the the d-axis d-axis current current is is applied applied while while the the constant constant q-axis q-axis current current is is generated. generated. Under Under the constant constant torque torque operation, operation, the the motor motor speed speed is is maintained, maintained, and and Equation Equation (4) (4) can can be be expressed. expressed. Figure Figure 55 shows shows voltage voltage and and current current vectors vectors for for temperature temperature estimation. estimation. The d-axis d-axis current current injection injection can can be be performed performed while while the q-axis current is constant. When the d-axis current i is injected, the voltages and currents can the q-axis current is constant. is injected, the voltages and currents can be be e e e e e e e e expressed (i), and i dd(i), (i), ii q(i), respectively. When When ieedd==0,0,the thevoltage voltage and and the the current can be expressedas asvv dd(i), vv q(i), be q (i),respectively. e e (0), and ee (0), ie e (0), respectively. The voltage equation expressed expressed as asvvedd(0), v eqq(0), and i dd(0), i q(0), respectively. The voltage equation for generating the same same q torque torque can can be be summarized summarized as as Equations Equations (8) (8) and and(9). (9).
and current current vectors vectors for for temperature temperature estimation. estimation. Figure 5. Voltage Voltage and
(
ved (i ) = Rs ide (i ) − ωr Lq iqe (i ) veq (i ) = Rs iqe (i ) + ωr Ld ide (i ) + ωr ψm ( ved (0) = −ωr Lq iqe (0) veq (0) = Rs iqe (0) + ωr ψm
(8)
(9)
Because the currents, motor speed, and voltage can be measured or calculated by the current sensor, position sensor, and current controller output, the q-axis inductance can be calculated as Equation (10)
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from Equation (9). We can assume Equation (10) because the difference between the d-axis inductance and the q-axis inductance is sufficiently small. Ld = Lq = −
ved (0) ωr iqe (0)
(10)
Equation (10) can be substituted into Equation (8) and arranged as Equation (11). The phase resistance Rs can be derived by using Equations (11) and (12). ved (i ) = Rs ide (i ) + ved (0)
Rs =
iqe (i ) iqe (0)
ved (i ) ved (0) iqe (i ) − e ide (i ) id (i ) iqe (0)
(11)
(12)
Based on finite element analysis (FEA), the SPMSMs can be modeled and analyzed. The Rs map according to the stator winding temperature can be obtained from the FEA results. The stator winding temperature can be estimated by comparing the calculated Rs with the temperature map. Analysis is not required regarding the inductance and the rotor flux variation according to the current vectors and the magnet temperature using FEA, because the d-, q-axis inductances can be calculated as shown in Equation (10) and the rotor flux is not required to calculate the stator resistance. Figure 6 shows the control block-diagram of the proposed stator winding temperature estimation method using the motor parameter estimation for the SPMSMs. As described above, two equations, depending on whether the d-axis current is injected or not, are required for estimating the stator temperature. To detect the stator temperature, the output d-, q-axis currents, the applied d-, q-axis voltages, and the motor speed are stored when ie d = 0. Subsequently, the d-axis current is applied in the same q-axis current to measure the output d-, q-axis currents, the applied d-, q-axis voltages, and the motor speed. The d-axis current should be applied considering the current limit. After the detection of variables for the temperature estimation, the d-axis current is again applied at zero. The stator resistance is estimated using Equation (12). The stator winding temperature is estimated using the look-up table obtained from FEA. An averaging filter can be used in consideration of inverter noise during data acquisition. The estimation time is determined by the response performance of the current controller and filtering. The stator winding temperature estimation procedure does not need to be continuously operated, and the stator winding temperature can be estimated by applying the d-axis current only when the stator winding temperature is required. A rectangular d-axis current, can be used to estimate the stator winding temperature.
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Figure 6. Proposed control block-diagram for stator winding temperature estimation. Figure 6. Proposed control block-diagram Figure 6. Proposed control block-diagram for for stator stator winding winding temperature temperature estimation. estimation.
4. Simulation Results
4. Simulation Results 4. Simulation Results
Finite element modeling (FEM) was used for the verification of motor parameter variation. The
Finite element modeling (FEM) wasused used the verification of motor variation. Finite element modeling (FEM) was forfor thesimulation verification motor parameter The motor design used for the motor parameter variation withoftemperature isparameter shownvariation. in Figure The motor design used for the motor parameter variation simulation with temperature is shown in motor7,design the motoratparameter variation simulation with temperature is shown in Figure and theused motorfor parameters 20 °C are shown in Table 1. ◦ C are shown in Table 1. Figure 7, and the motor parameters at 20 7, and the motor parameters at 20 °C are shown in Table 1.
Figure 7. SPMSM design. Table 1. Motor parameters at 20 °C.
Figure 7. 7. SPMSM SPMSM design. design. Figure Poles 26
Turns 19
Coil Diameter 0.6mm
Poles Diameter PolesTurns Turns Coil Coil Diameter 26 26
19 19
0.6mm 0.6mm
Irated
Vdc
Slots
Connection
Rs
Table 1.52 Motor parameters at 20 20 ◦°C. Table Motor parameters C.0.0777 Ω 11 A 1. V 24 Yat IIrated rated
Vdc Vdc Slots Slots Connection Connection
1111AA 5252VV
24 24
YY
RsRs
Ld/Lq
ψm
0.08 mH
0.00335 Wb
Ld L /Ldq/Lq
ψm ψm
0.0777 Ω Ω 0.08 mH Wb Wb 0.0777 0.08 mH 0.00335 0.00335
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Figure 8 shows the stator resistance as a function of temperature. As the temperature 8increases, Energies 2018, 11, x FOR PEER REVIEW of 14 the stator resistance increases. The stator resistance can be calculated from Equation (12). The stator winding temperature can bestator estimated using the resistance table as shown in Figure 8. increases, Figure 8 shows the resistance function of AsAs thethe temperature Figure 8 shows the stator resistance asasaafunction of temperature. temperature. temperature increases,
the stator resistance increases. The statorresistance resistance can can be Equation (12).(12). The The stator the stator resistance increases. The stator be calculated calculatedfrom from Equation stator winding temperature can be estimated using the resistance table as shown in Figure 8. winding temperature can be estimated using the resistance table as shown in Figure 8.
Figure 8. Motor parameter map according to stator winding temperature. Figure 8. Motor parametermap mapaccording according to temperature. Figure 8. Motor parameter to stator statorwinding winding temperature.
Figure 9 shows the the d- and q-axis accordingtotoid iand d and iq at 20 °C. Unlike stator Figure 9 shows d- and q-axisinductance inductance maps maps according iq at 20 °C.◦Unlike stator Figuremotor 9 shows the d- and q-axis inductance maps according to id and iq at 20 the C. inductance Unlike stator resistance, inductance varies with rotor temperature and current. Therefore, resistance, motor inductance varies with rotor temperature and current. Therefore, the inductance in in resistance, motor inductance varies with rotor temperature and current. Therefore, the inductance in the simulation should vary according andthe thecurrent. current. The inductance the simulation should vary accordingtotothe thetemperature temperature and The inductance mapmap was was the simulation should vary according to the temperature and the current. The inductance map was derived the FEM analysis and appliedto tomotor motor modeling. modeling. derived fromfrom the FEM analysis and applied derived from the FEM analysis and applied to motor modeling.
(a)
(b)
(a)
(b)
(c)
(d)
(c)
(d) Figure 9. Cont.
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(e) (e)
(f) (f)
Figure 9. 9. dand q-axis inductance maps: (a) LdLatat −40 °C;◦(b) Lq at −40 °C; (c) Ld at 20 °C; (d) Lq (d) at 20 °C; ◦ C; Figure d- and andq-axis q-axisinductance inductancemaps: maps:(a) (a)L −°C; 40 C; (b) at − 40(c) Ld °C; at 20 at dd at (b) Lq atLq−40 °C; Ld(c) at 20 (d)◦ C; Lq at 20Lq°C; d −40 d at 80 °C; (f) L q at 80 °C. (e) L ◦ ◦ ◦ 20 LC; (e)80L°C; 80 LqC;at(f) d at 80L°C. (e) q at 80 C. d at (f)
The basic basic parameters parameters of of the the SPMSM SPMSM are are listed listed in in Table Table 1. 1. The The motor motor parameters parameters with with nonlinear nonlinear The characteristics, as shown in Figures 8 and 9, were applied using a look-up table. The proposed characteristics, Figures 88 and and 9, 9, were were applied applied using using aa look-up look-up table. table. The proposed characteristics, as as shown shown in in Figures The proposed estimation method of of motor parameter parameter Rs was modeled modeled and and simulated simulated in in MATLAB MATLAB Simulink. Simulink. The The estimation estimation method method ofmotor motor parameterRsRwas and simulated in MATLAB Simulink. s was modeled motor model for the simulation is shown in Figure 10. The stator resistance was determined by the motor model for the simulation is shown in in Figure 10.10.The The motor model for the simulation is shown Figure Thestator statorresistance resistancewas wasdetermined determined by by the the stator resistance table according to the stator winding temperature. The inductances were determined stator table according to the stator resistance resistance table according to the stator stator winding winding temperature. temperature. The The inductances inductances were were determined determined by the inductance inductance a three-dimensional three-dimensional table table according according to to current current and and rotor rotor temperature. temperature. by by the the inductance aa three-dimensional table according to current and rotor temperature.
Figure 10. 10. Motor simulation model. Figure Motor simulation simulation model. model. Figure 10. Motor
The SPMSM SPMSM controller controller and and the the motor motor model model were were configured configured as as shown shown in in Figure Figure 11, 11, based based on on The the speed controller. To verify the proposed method, the simulation for the temperature estimation the speed controller. To verify verify the the proposed proposed method, method, the simulation for the temperature estimation method was was performed performed at at 1000 1000 rpm rpm and and 0.2 0.2 Nm. The rotor and the stator temperatures method Nm. The The rotor rotor and and the the stator stator temperatures temperatures were were assumed assumed to be 20 °C and 60 °C, respectively. ◦ ◦ C and 60 °C, C, respectively. to be 20 °C
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Figure 11. Simulationmodel model for winding estimation. Figure 11. Simulation stator winding estimation. Figure 11. Simulation modelfor forstator stator winding estimation.
Figure 12 shows the simulation results for the stator winding temperature estimation. In the steady-
Figure12 12 shows shows the results forfor thethe stator winding temperature estimation. In the steadyFigure thesimulation simulation results stator winding temperature estimation. state, where the target speed is reached, the motor parameter estimation method, through the d-axisIn the state, where the target speed is reached, the motor parameter estimation method, through the d-axis steady-state, where the speed reached, the motor parameter estimationthrough method, the current injection, is target operating. Theisstator winding temperature was estimated thethrough motor current injection, is operating. The stator winding temperature was estimated through the motor d-axis current injection, is The stator temperature waswas estimated through the parameter estimation. Asoperating. shown in Figure 12, the winding stator winding temperature estimated almost parameter estimation. As shown in Figure 12, the12, stator winding temperature was estimated almost exactly. motor parameter estimation. As shown in Figure the stator winding temperature was estimated exactly. almost exactly.
(a)
(a)
(b)
(b) Figure 12. Cont.
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(c)
(d)
(e) Figure12. 12.Simulation Simulationresults: results:(a) (a)motor motorspeed; speed;(b) (b)i idand andi i;q;(c) (c)vvd and andvvq;; (d) (d) stator stator resistance resistanceestimation; estimation; Figure q q d d (e)stator statorwinding windingtemperature. temperature. (e)
5. Experimental Results 5. Experimental Results Figure 13 shows an experimental setup for validating the stator winding temperature estimation Figure 13 shows an experimental setup for validating the stator winding temperature estimation method, consisting of a prototype SPMSM and an inverter. The test motor is the outer-rotor-type for method, consisting of a prototype SPMSM and an inverter. The test motor is the outer-rotor-type a drone, and the specifications are shown in Table 1. A 20 kHz PWM frequency was applied to the for a drone, and the specifications are shown in Table 1. A 20 kHz PWM frequency was applied to inverter, and the stator winding estimator was operated synchronously with the PWM frequency. the inverter, and the stator winding estimator was operated synchronously with the PWM frequency. For comparison with the estimation value, the negative temperature coefficient (NTC) thermistor For comparison with the estimation value, the negative temperature coefficient (NTC) thermistor 103NT-4-R025H34G temperature sensor was attached inside the stator winding. A characteristic of 103NT-4-R025H34G temperature sensor was attached inside the stator winding. A characteristic of the the NTC thermistor is that the resistance decreases when the temperature increases. The stator NTC thermistor is that the resistance decreases when the temperature increases. The stator winding winding temperature was obtained from the NTC thermistor, and the accuracy of the estimated stator temperature was obtained from the NTC thermistor, and the accuracy of the estimated stator winding winding temperature was evaluated. For the competitive experiment, the test was carried out with temperature was evaluated. For the competitive experiment, the test was carried out with the actual the actual load fan. The stator winding temperature estimation was compared until temperature load fan. The stator winding temperature estimation was compared until temperature saturation at saturation at 1000 rpm, where the drone fan motor was mainly operated. 1000 rpm, where the drone fan motor was mainly operated. Figure 14 shows the phase current, q-axis current, and d-axis current waveforms for when the dFigure 14 shows the phase current, q-axis current, and d-axis current waveforms for when the axis current was or was not injected at 1000 rpm. For estimating the stator winding temperature, a dd-axis current was or was not injected at 1000 rpm. For estimating the stator winding temperature, axis current of −1 A was injected. The magnitude of the phase current was slightly increased due to a d-axis current of −1 A was injected. The magnitude of the phase current was slightly increased due the d-axis current injection. to the d-axis current injection.
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(a) (a)
(b) Figure motor/ inverter; (b) experimental experimental setup. setup. (b) (b) Figure 13. 13. (a) (a) Test Test motor/inverter; Figure 13. (a) Test motor/ inverter; (b) experimental setup.
Figure 14. Phase current waveforms when d-axis current was injected at 1000 rpm. Figure 14. 14. Phase Phase current current waveforms waveforms when when d-axis d-axis current currentwas wasinjected injectedat 1000rpm. rpm. Figure 1000 Figure 15 shows the stator winding temperature estimation results for at no load and fluid load. At no load, stator temperature saturation occurred after approximately 8 min of motor operation, and Figure 15 shows the stator winding temperature estimation results for no load and fluid load. Figure 15 shows the stator winding temperature estimation results for no load and fluid load. the temperature increased to 32 °C. However, the stator temperature saturation occurred after At no load, stator temperature saturation occurred after approximately 8 min of motor operation, and At no load, stator temperature saturation after and approximately 8 minincreased of motortooperation, approximately 2 min of motor operation at occurred the fluid load, the temperature 30 °C. In the temperature increased to 32 °C.◦ However, the stator temperature saturation occurred after and the temperature totemperature 32 C. However, statorand temperature occurred after the fluid load, the fanincreased affects the of thethe motor, the stator saturation temperature saturated at approximately 2 min of motor operation at the fluid load, and the temperature increased to 30 °C.◦ In approximately 2 min of motor operation at the fluid load, and the temperature increased to 30 at C. lower temperatures than at no load. The maximum error of temperature estimation was measured the fluid load, the fan affects the temperature of the motor, and the stator temperature saturated at In the fluid load, temperature of the motor, and the temperature saturated at approximately 2 the °C. fan Theaffects stator the winding temperature estimation wasstator verified for both no load and lower temperatures than at no load. The maximum error of temperature estimation was measured at lower temperatures than at no load. The maximum error of temperature estimation was measured fluid load. approximately 2 °C. The stator winding temperature estimation was verified for both no load and at approximately 2 ◦ C. The stator winding temperature estimation was verified for both no load and fluid load. fluid load.
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(a)
(b) Figure Figure15. 15.Stator Statorwinding windingtemperature temperatureestimation estimationresults resultsatat(a) (a)no noload; load;(b) (b)fluid fluidload. load.
6. Conclusions 6. Conclusions We presented a stator winding temperature estimation method for SPMSMs without additional We presented a stator winding temperature estimation method for SPMSMs without additional temperature sensors. To estimate the stator winding temperature, the stator resistance was estimated temperature sensors. To estimate the stator winding temperature, the stator resistance was estimated using the proposed d-axis current injection. To evaluate the possibilities for the proposed estimation using the proposed d-axis current injection. To evaluate the possibilities for the proposed estimation method, simulations and experimental tests were performed. The test and simulation results showed method, simulations and experimental tests were performed. The test and simulation results showed similar trends. According to both the simulation and the test results, the proposed estimation method similar trends. According to both the simulation and the test results, the proposed estimation method demonstrated potential for winding temperature estimation without additional temperature sensors. demonstrated potential for winding temperature estimation without additional temperature sensors. However, after estimating the stator winding temperature, a control strategy is needed to limit stator However, after estimating the stator winding temperature, a control strategy is needed to limit stator winding temperature in the SPMSM control system. Future work will focus on developing such a winding temperature in the SPMSM control system. Future work will focus on developing such control strategy to limit stator winding temperature. a control strategy to limit stator winding temperature. Author implemented mathematical modeling and performed the experimental test; J.S.P. AuthorContributions: Contributions:B.-S.J. B.-S.J. implemented mathematical modeling and performed the experimental test; designed and performed the control simulation; J.-H.C.J.-H.C. analyzed the simulation and experimental results. K.J.S.P. designed and performed the control simulation; analyzed the simulation and experimental results. K.-D.L. performed the simulation analyzed validated result data through FEM; C.-Y.W. guidedand andrevised revised D.L. performed the simulation andand analyzed thethe validated result data through FEM; C.-Y.W. guided themanuscript. manuscript.All Allauthors authorsdiscussed discussedthe theresults resultsand andcontributed contributedtotowriting writingthe thepaper. paper. the Funding: This research was funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea) under Industrial Funding: This research was funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea) under Technology Innovation Program Grant 10063006, and by the Korea Institute of Energy Technology Evaluation and Industrial Innovation Program and by the(MOTIE) Korea Institute of Energy Planning Technology (KETEP) and the the Ministry of Grant Trade,10063006, Industry & Energy of the Republic of Technology Korea under Evaluation and Planning (KETEP) and the the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Grant 20172010105270. Korea under Grant 20172010105270. Conflicts of Interest: The authors declare no conflicts of interest. Conflicts of Interest: The authors declare no conflicts of interest.
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