Online Rotor and Stator Resistance Estimation Based on Artificial

energies

Article Online Rotor and Stator Resistance Estimation Based on Artiﬁcial Neural Network Applied in Sensorless Induction Motor Drive

Tuan Pham Van 1, Dung Vo Tien 1, Zbigniew Leonowicz 2,* , Michal Jasinski 2 , Tomasz Sikorski 2 and Prasun Chakrabarti 3,4 1 Faculty of Electrical Engineering, Vinh University of Technology Education, 117 Nguyen Viet Xuan Street, Vinh City 890000, Vietnam; [email protected] (T.P.V.); [email protected] (D.V.T.) 2 Faculty of Electrical Engineering, Wroclaw University of Science and Technology, 50-370 Wroclaw, Poland; [email protected] (M.J.); [email protected] (T.S.) 3 Department of Computer Science and Engineering, Techno India NJR Institute of Technology Udaipur, Rajasthan 313003, India; [email protected] 4 Data Analytics and Artiﬁcial Intelligence Laboratory, Engineering-Technology School, Thu Dau Mot University, Thu Dau Mot City 820000, Vietnam * Correspondence: [email protected]; Tel.: +48-71-320-2626

Received: 5 September 2020; Accepted: 18 September 2020; Published: 21 September 2020

Abstract: This paper presents a new approach method for online rotor and stator resistance estimation of induction motors using artiﬁcial neural networks for the sensorless drive. In this method, the rotor resistance is estimated by a feed-forward neural network with the learning rate as a function. The stator resistance is also estimated using the two-layered neural network with learning rate as a function. The speed of the induction motor is also estimated by the neural network. Therefore, the accurate estimation of the rotor and stator resistance improved the quality of the sensorless induction motor drive. The results of simulation and experiment show that the estimated speed tracks the real speed of the induction motor; simultaneously, the error between the estimated rotor and stator resistance using neural network and the normal rotor and stator resistance is very small.

Keywords: rotor resistance estimation; stator resistance estimation; sensorless control; artiﬁcial neural network (ANN); indirect ﬁeld-oriented control (IFOC)

1. Introduction The problem of the sensorless indirect rotor flux control of induction motor (IM) is an important aspect in the study of induction motor drive systems [1]. In the sensorless control of a vector controlled three-phase induction motor drive, the rotor flux angle depends on the rotor resistance [2–5]. On the other hand, the rotor flux estimation is sensitive to the changes in the rotor and the stator resistance, especially in the case of the low rotational speed; the speed estimation of an induction motor again depends on the estimated rotor flux [6]. Therefore, the accuracy of the estimated rotor and stator resistance will improve the accuracy of the estimated speed and the estimated rotor flux, thereby improving the quality of the sensorless drive control [7]. In the operation of induction motor drives, the rotor resistance can vary up to 100% due to changes in temperature and rotor speed, so obtaining this information through a thermal model or temperature sensors is very difficult, especially for induction motors [8]. The rotor resistance estimation algorithms have been widely studied in the literature. The well-known approaches in recent studies are based on the following: Model Reference Adaptive System (MRAS) [9–11], •

Energies 2020, 13, 4946; doi:10.3390/en13184946 www.mdpi.com/journal/energies Energies 2020, 13, 4946 2 of 16

Extended Kalman Filters [12–14]; • Sliding Mode Control [15,16]; • Fuzzy Logic Technique [17,18]. • However, recently, different combinations and modifications have also been proposed. Interesting examples include the following: One article [19] concerns a sensorless control approach for a five-phase induction motor drive. • The sensorless scheme uses the sliding mode theory, which applies a sliding mode observer to estimate rotor resistance. The operation methodology of the proposed control technique is formulated using the mathematical model of the machine and the two-time-scale approach. The author of [20] proposes the combination of parameter estimation-based observers with the • dynamic regression extension and mixing parameter adaptation. The first framework is used to recast the flux observation task as a parameter estimation problem, for which the dynamic regressor extension and mixing method (DREM) technique is applied. One article [21] proposes using carrier signal injection with minimized torque ripple for rotor • resistance estimation. The proposed approach is based on the injection of a relatively low-frequency carrier signal into the reference of the rotor flux linkage magnitude as well as extraction of the induction machine’s response to the carrier signal, which is then used in a model reference adaptive system. The author of [22] proposes the verification of rotor resistance identification in the field-oriented • control-based drive system using the slip ring machine-based test bench. The paper proposes the torque calculations using the current stator and flux to propose the model reference adaptive system for online estimation of rotor resistance (without injection of the signal). Other articles [23,24] propose an online estimated rotor resistance method using a neural network. • However, the proposed method is still limited by the learning rate that is pre-selected and does not change during the rotor resistance estimation process. Therefore, if the learning rate is selected inappropriately, it will lead to a slow network training process and large network output errors. The choice of appropriate learning rate is mainly based on the experience of the researchers. The literature also proposes several approaches to stator resistance estimation. The well-known approaches in recent studies are based on the following: MRAS [25–27]; • Luenberger Observer [28–31]; • Fuzzy Logic Technique [32–34]; • However, recently, different combinations and modifications have also been proposed. Interesting examples include the following: One article [35] proposes a novel Power Quality Model Reference Adaptive System (PQ-MRAS) • concept for stator resistance. It uses the active and reactive power of the machine, which is calculated using measurable signals, (e.g., stator voltage and current). The paper includes a detailed description of the proposed estimator. The author of [36] proposes online identification of stator resistance based on the model reference • adaptive system. In the article, the backpropagation is used to define the error between the measured and estimated value of stator current to adjust the weights of the neural network. The author of [37] presents the IM model that is transformable into the adaptive observer • form. In this method, stator resistance estimation leads to the overparameterization problem. The proposed solution uses the first-order approximation of the error dynamics to the adaptive observer. The online stator resistance estimation methods using a neural network were studied and • performed in [38]. However, in the proposed method, the learning rate must be selected and not changed during the estimation process. Consequently, this reduces its accuracy. Energies 2020, 13, x FOR PEER REVIEW 3 of 16

• The online stator resistance estimation methods using a neural network were studied and performed in [38]. However, in the proposed method, the learning rate must be selected and not changed during the estimation process. Consequently, this reduces its accuracy. In this article, the authors propose a novel method to estimate rotor resistance and stator resistance using artificial neural networks with the learning rate as a function. This is an extension of previous research seeking to improve the control quality of the sensorless induction motor drive. This paper is arranged as follows. Section 2 presents the method to estimate rotor resistance using a two-layered neural network with the learning rate as a function. In Section 3, the rotor and stator resistance estimation method by using a two-layered neural network in which the learning rate is also a function is proposed. The experimental results in Section 4 have been proven with the proposed algorithm. The rotor and the stator resistance are accurately estimated, leading to the estimated speed of the motor being very close to the real speed, thus having the potential to improve the quality of the induction motor sensorless drive system. Finally, conclusions are given in Section 5.

2. Rotor Resistance Estimation Using Artificial Neural Networks The rotor resistance estimator structure of the induction motor is based on MRAS [1,3], presentedEnergies in Figure2020, 13, 49461. 3 of 16 The outputs of the reference model (voltage model) are components of rotor leakage flux in the static frame: In this article, the authors propose a novel method to estimate rotor resistance and stator resistance using artiﬁcial neural networks with theL learning rate as a function. This is an extension of previous ψσvm r −− research seeking to improve the controlαααα=VRidtLi quality() of the sensorless induction motor drive. This paper is  rL  s ss ss arranged as follows. Section2 presents them method to estimate rotor resistance using a two-layered (1) neural network with the learning rateL as a function. In Section3, the rotor and stator resistance ψσvm =VRidtLir ()−− estimation method by using a two-layered rββββ neural s network ss in which ssthe learning rate is also a function  Lm is proposed. The experimental results in Section4 have been proven with the proposed algorithm. The rotor and the stator resistance are accurately estimated, leading to the estimated speed of the motor where σ = (1 − L2m/Ls Lr)—leakage coefficient. Statorbeing leakage very close flux to has the realthe speed,following thus havingequations: the potential to improve the quality of the induction motor sensorless drive system. Finally, conclusions are given in Section5. ψ =−()VRidt 2. Rotor Resistance Estimation Using Artiﬁcialssssααα Neural Networks  (2) ψ =−()VRidt The rotor resistance estimator structure ssssβββ of the induction motor is based on MRAS [1,3], presented in Figure1.

vm vsα ψrα + εα

vsβ Reference Model _

isα [3] ψ rβ vm + εβ isβ _

ψrαim

Z-1 Error- Back Propagation Neural Model -1 Z (Adaptive Model) [4] Z-1

ψrβim

Z-1

Rr_es

Figure Figure1. Rotor 1. Rotorresistance resistance estimator estimator based based on on MRAS MRAS including including aa neural neural network network trained trained by the by the error-backerror-back propagation propagation algorithm. algorithm. The outputs of the reference model (voltage model) are components of rotor leakage flux in the static frame:   vm Lr hR i  ψ = (Vsα Rsisα)dt σLsisα  rα L − −  m (1)  L hR i  vm = r ( )  ψrβ Vsβ Rsisβ dt σLsisβ  Lm − − 2 where σ = (1 L m/Ls Lr)—leakage coefficient. − Stator leakage flux has the following equations:  R  ψsα = (Vsα Rsisα)dt  − (2)  R  ψs = (Vs Rsis )dt β β − β Energies 2020, 13, x FOR PEER REVIEW 4 of 16

EnergiesBecause2020, 13 the, 4946 direct current (DC) voltage applied to the inverter is undulating, the integral4 of stage 16 in Equation (2) causes the stator leakage flux error. Therefore, it is necessary to adjust the stator leakage flux estimation using a multi-level low-pass filter [18]. From Equations (1) and (2), and Because the direct current (DC) voltage applied to the inverter is undulating, the integral stage in throughEquation some (2) causes transformations, the stator leakage we obtain flux error. equations Therefore, used it isto necessaryestimate torotor adjust flux the according stator leakage to the voltageflux estimation model as using follows: a multi-level low-pass filter [18]. From Equations (1) and (2), and through some transformations, we obtain equations used toLLLL estimate rotor flux according− 2 to the voltage model as follows: ψψvm ()=−−−rsrm  rsααk (k)11 i(k) s α   LL2  vm Lr mmLsLr Lm  ψ  (k) = ψsα(k 1) − i2sα(k 1) (3)  rα L LLLL− − L − −  ψψvm ()=−−−m rsrm11m (3)  rsββk(k)i(k)2 s β   Lr LLLsLr Lm  vm ( ) = mm( ) ( )  ψrβ k ψsβ k 1 − isβ k 1 Lm − − Lm − On the other hand, the equations of the adaptive model (current model) are as follows: On the other hand, the equations of the adaptive model (current model) are as follows: ψψim()=−−−+− im () ψ im () ()  rrααkW123 k111 W r β k Wik s α  im im im  ψ (k) = W ψ (k 1) W ψ (k 1) + W isα(k 1) (4)  ψψrαim()=−+−+−1 rα im ()1112 r ψβ im ()3 ()  rrββkW123− k− W r α− k Wik s β− (4)   im im im  ψ (k) = W ψ (k 1) + W ψ (k 1) + W is (k 1) rβ 1 rβ − 2 rα − 3 β − T T W =−1 s WL= s 1 T Ts 3 T Tms wherewhere W1 = 1 r , ,WTW2= ω= ω,r Ts, W3 =r L. m. − Tr 2 rs Tr TsT iss isthe the sampling sampling time time and and Tr == LLr/Rr/Rrr isis the the rotor rotor timetime constant.constant.W W2 2does does not not depend depend on on the the rotor rotor timetime constant. constant. It Itcan can be be seen seen that that the the weights weights WW11 andand WW33 dependdepend on on the the rotor rotor time constant. IfIf thethe Lr rotorLr rotor self-inductance self-inductance is not is not changed, changed, the the weights weights WW1 1andand WW33 will bebe updatedupdated based based on on the the rotor rotor resistanceresistance to to obtain obtain high high efficiency. eﬃciency. TheThe two-layered two-layered neural neural network usedused to to estimate estimate rotor rotor ﬂux flux by by the the current current model model is illustrated is illustrated in inFigure Figure2 .2.

ψrαim(k-1)

im ψrβ (k-1) ψrαim(k) W1 -W2

W2 isα(k-1) ψrβ im(k) W3

isβ(k-1) W3

FigureFigure 2. 2. Two-layeredTwo-layered neural neural network network used toto estimateestimate rotor rotor ﬂux flux by by the the current current model. model.

TheThesquarefunctionofrotorfluxerrorcalculatedfromthetwomodelsaccordingto square function of rotor flux error calculated from the two models accordingEquations to (3) Equations and (4) is written as follows: (3) and (4) is written as follows: 2 1 2 1 vm im E1 = ε (k) = ψr (k) ψr (k) (5) 2 112 2 − 2 Ek==εψψ(){ vm () kk − im ()} (5) The weights of the networks W1, W223 are obtainedrr from the network training that minimizes the square function E1 [1,9]. W1, W3 are determined as follows: The weights of the networks W1, W3 are obtained from the network training that minimizes the square function E1 [1,9]. W1, W3 areW determined(k) = W ( kas follows:1) + η ∆ W (k) (6) 1 1 − 1 1 W(k)=−+Δ W(k1 )η W(k) W (k)11 = W (k 1) + η ∆ 11W (k) (7)(6) 3 3 − 3 3 =−+Δη W(k)33 W(k1 ) 33 W(k) (7) where

Energies 2020, 13, 4946 5 of 16

where T ∆W (k) = ∂E /∂W = ψvm(k) ψim(k) ψim(k 1) (8) 1 − 1 1 r − r r − T vm im ∆W (k) = ∂E /∂W = ψ (k) ψ (k) is(k 1) (9) 3 − 1 3 r − r − where the learning rates η1 and η3 are pre-selected constants. The problem is to replace the constant learning rate with a function so that after each update of the weight adjustment, the error E value will be reduced with ς (k) = ∆W (k)∆W (k 1), where 1 i i i − the function ς (k) is the error product of the weight adjustment W at times k and (k 1). From this, i i − we build the learning rate function based on the function ςi(k) so that the learning rate changes in the direction of reduction of the error E1 of the neural network. This means that if ςi(k) is positive, the neural network has a slow convergence speed and must increase the learning rate; if ςi(k) is negative, the learning rate must be reduced. Consider the following function: α f (ς ) = sign(ς ) 0 (10) i i ς sign(ς ) 1 + e− i i

ς sign(ς ) ∂ f (ςi) α e i i The derivative of f (ς ) is = 0 − > 0, where α is positively identiﬁed. i 2 0 ∂ςi ς sign(ς ) (1 + e− i i ) Here, f (0) = 0, so ςi(k) f (ςi(k)) > 0 for every ςi(k) , 0. So, the function is f (ςi) congruent and homologous to the error ςi. Therefore, the learning rate function can be updated according to the following rules: η (k) = η (k 1)(1 + f (ς (k 1))) (11) i i − i − where η (k 1) is the learning rate at (k 1), η (k) is the learning rate at k. i − − i The learning rate determined at (11) is diﬀerent from the learning rate mentioned elsewhere [1,9]. The weights of the networks W1, W3 are adjusted by training based on Equation (6) or (7). The rotor resistance is therefore estimated according to Equation (12) or (13) as follows:

Lr(1 W 1) Rr es = − (12) − Ts

LrW3 Rr es = (13) − LmTs Rotor ﬂux estimation from Equation (1) is sensitive to changes in the stator resistance, especially in the low-speed region. Therefore, to minimize the error in the rotor resistance estimation due to the stator resistance variation, an online stator resistance estimator will be analyzed and discussed in Section3.

3. Stator Resistance Estimation Using Artiﬁcial Neural Networks According to [9], we have the following equation, describing components of stator currents in the static frame:

 ( ) = ( ) + im( ) + im( ) + ( )  is∗α k W4is∗α k 1 W5ψrα k 1 W6ψrβ k 1 W7Vsα k 1  − − − − (14)  im im  i (k) = W i (k 1) + W ψ (k 1) W ψ (k 1) + W Vs (k 1) s∗β 4 s∗β − 5 rβ − − 6 rα − 7 β −

" 2 # Ts Lm Ts Ts Lm Ts Lm Ts where W4 = 1 Rs , W5 = , W6 = ωr, W7 = . − σLs LrTr − σLs σLs LrTr σLs Lr σLs The weights W5, W6, W7 are calculated from the motor parameters, motor speed and the sampling time Ts. The weighted W4 depends on the stator resistance. The weight W4 is the adjustment weight. Energies 2020, 13, x FOR PEER REVIEW 6 of 16 Energies 2020, 13, x FOR PEER REVIEW 6 of 16 TL TL T 2 W = smW = smω W = s TL T 5 σTLsm 6 σTLsmr 7 σTs =−sm2 − s W = LLT W = LLω W = L where WR1 , 5 srr, 6 srr , 7 s . 4 TLsm T ss σ LLT σ LL σ L WR=−1 σσLLT − L srr sr s where 4 σσsrr ss , , , . LLTsrr L s The weights W5, W6, W7 are calculated from the motor parameters, motor speed and the The weights W5, W6, W7 are calculated from the motor parameters, motor speed and the sampling time Ts. The weighted W4 depends on the stator resistance. The weight W4 is the samplingadjustmentEnergies time weight.2020 T, 13s., 4946The weighted W4 depends on the stator resistance. The weight6 of 16W4 is the adjustmentEquation weight. (14) can be represented by two layered artificial neural networks as shown in Figures 3 andEquation 4. Equation (14) can (14) be can represented be represented by two by twolayered layered artificial artiﬁcial neural neural networks networks as as shown shown inin Figures 3 and 4. Figures3 and4.

Z-1 Z-1

i*sα(k-1) W4 * i sα(k-1) W4 + im ψ rα(k-1) W5 + im ψ rα(k-1) W5 + i*sα(k) *sα im + i (k) ψ rβ(k-1) W6 im + ψ rβ(k-1) W6 + Vsα(k-1) W7 + Vsα(k-1) W7 +

Figure 3. α-axis stator current estimation using artificial neural network. FigureFigure 3. α-axis 3. α-axis stator stator current current estimation estimation using using artiﬁcial artificial neural neural network. network.

Z-1 Z-1

i*sβ(k-1) W4 i*sβ(k-1) W4 + im ψ rβ (k-1) W5 + im ψ rβ (k-1) * W5 + i sβ(k) + i*sβ(k) im ψ rα(k-1) W6 im ψ rα(k-1) W6 - -

Vsβ(k-1) W7 + Vsβ(k-1) W7 +

FigureFigure 4. β-axis 4. β-axis stator stator current current estimation estimation using using artiﬁcial artificial neural neural network. network. Figure 4. β-axis stator current estimation using artificial neural network. The error square function of the stator current measured against the estimated stator current Theaccording error square to Equation function (14) is of written the stator as follows: current measured against the estimated stator current accordingThe error to Equation square function(14) is written of the as stator follows: current measured against the estimated stator current 1 1n o2 according to Equation (14) is writtenE as= follows:ε 2(k) = i (k) i (k) (15) 2 2 s s∗ 2 2112 2 − * ==−ε 2 E22112 (k){ iss (k) i (k)} (15) The weight of the network W is derived==−ε from the training of* the neural network so that the error 4 E2222(k){ iss (k) i (k)} (15) square function E2 is minimal [9]. W4 is determined22 as follows: The weight of the network W4 is derived from the training of the neural network so that the The weight of the network W4 Wis derived(k) = W (kfrom1) +theη ∆ trainingW (k) of the neural network(16) so that the error square function E2 is minimal [9].4 W4 is determined4 − 4 as 4follows: error square function E2 is minimal [9]. W4 is determined as follows: =−+Δη where W(k)44 W(k1 ) 44 W(k) (16) ∂E=−+Δh η iT W(k)442 W(k1 ) 44 W(k) (16) ∆W4(k) = = is(k) is∗(k) is∗(k 1) (17) where −∂W4 − − where Similarly to the method of constructing the learning rate function to estimate rotor resistance in ∂E T Section2, the learning rate isΔ=−=− updated as follows:2 ** − W4 (k)∂E iss (k) i (k)T i s (k1 ) (17) Δ=−=−W (k)∂W2  i (k) i** (k) i (k −1 ) 4 ∂ 4 ss s (17) η (k) =Wη4 (k 1)(1 + f (ς )) (18) 4 4 − 4 Similarly to the method of constructing the learning rate function to estimate rotor resistance in SectionSimilarly 2, the learning to the method rate is ofupdated constructing as follows: the learning rate function to estimate rotor resistance in Section 2, the learning rate is updated as follows: η =−+η ς 44(k) (k11 )( f ( 4 )) (18) η =−+η ς 44(k) (k11 )( f ( 4 )) (18)

Energies 2020, 13, x FOR PEER REVIEW 7 of 16 whereEnergies 2020, 13, 4946 7 of 16 ς =Δ Δ − 444(k) W (k) W (k1 ) (19) where The learning rate determined in ςEquation(k) = ∆ W(18)(k )is∆ Wdifferent(k 1) from the learning rate mentioned(19) in 4 4 4 − [6,9]. Afterward, the stator resistance can be estimated as follows: The learning rate determined in Equation (18) is diﬀerent from the learning rate mentioned in [6,9]. Afterward, the stator resistance=− can be estimated − σ as follows:22 σ Rs−−es{1 W(T/L)(LR/L)(L/T)4 s s m r es r} s s (20)

n 2 2 o Rs es = 1 W4 (Ts/σLs)(LmRr es/Lr ) (σLs/Ts) (20) The speed estimation used− in sensorless− − drive in this− paper is shown after [19], according to Expression (21) below: The speed estimation used in sensorless drive in this paper is shown after [19], according to Expression (21) below: η ψψψvm()−− im () im (1 ) rrrββαkkk ωω()kk=−+ (1 ) w  (21) r_es r_es −−ψψψvm im im − Ts vm ααβ()kkkim ()im (1 ) η ψrrr(k) ψ (k) ψrα (k 1)  w  rβ − rβ −  ωr_es(k) = ωr_es(k 1) +  h i  (21) − Ts  vm im im  where η is the learning rate for estimating rotor speed.ψrα (k ) ψrα (k) ψ (k 1) w − − rβ − where η is the learning rate for estimating rotor speed. 4. Results w 4. Results 4.1. Analysis 4.1. Analysis At the low-speed region, the rotor flux estimation from Equations (3) and (4) is very sensitive to stator andAt therotor low-speed resistance region, [9]. Therefore, the rotor ﬂux online estimation rotor and from stator Equations resistance (3) and estimation (4) is very in sensitive Sections to 2 andstator 3 will and improve rotor resistance the quality [9]. Therefore,of the sensorless online rotor drive and control, stator resistance especially estimation for low inspeeds.Sections A2 diagram and3 of thewill IFOC improve (indirect the quality field-oriented of the sensorless control) drive sensorless control, drive especially with foronline low rotor speeds. and A stator diagram resistance of the estimationIFOC (indirect is shown ﬁeld-oriented in Figure control)5. sensorless drive with online rotor and stator resistance estimation is shown in Figure5.

_ + Vdc

ω*r

ψ*r IFOC Inverter IM

Rr-es vc va ia

ic Rotor resistance estimation Rs-es using ANN Rotor flux Stator resistance estimation estimation (Voltage Model) using ANN

ψvmrα ψvmrβ

Rotor speed estimation (21)

ωr-es FigureFigure 5. 5.DiagramDiagram of of indirect indirect ﬁeld-orientedfield-oriented control control (IFOC) (IFOC) sensorless sensorless drive drive with onlinewith online rotor and rotor stator and statorresistance resistance estimation. estimation.

4.2. Results of the Simulation 4.2. Results of the Simulation To simulate a sensorless drive system with rotor and stator resistance estimation, the authors used To simulate a sensorless drive system with rotor and stator resistance estimation, the authors MATLAB/Simulink software (2019a, MathWorks, Natick, MA, USA). used MATLAB/Simulink software (2019a, MathWorks, Natick, MA, USA). During the simulation, the rotor and stator resistances differ by 50% from the original values [1,4,9], thus leading to a discrepancy between the actual rotor and stator resistance values and real

Energies 2020, 13, 4946 8 of 16 Energies 2020, 13, x FOR PEER REVIEW 8 of 16

values.During The therotor simulation, resistance the of rotorthe indu andction stator motor resistances varies di fromﬀer by1.84 50% to from2.76 Ω the, the original stator values resistance [1,4,9 of], thusthe motor leading varies to a from discrepancy 1.99 to 2.99 between Ω (simulation the actual process rotor and duration stator 0–9 resistance s); load values TL = 2.0 and Nm real is applied values. Theat time rotor t = resistance 1.5 s. The of induction the induction motor motor parameters varies from are given 1.84 to in 2.76 TableΩ, 1. the stator resistance of the motor varies from 1.99 to 2.99 Ω (simulation process duration 0–9 s); load TL = 2.0 Nm is applied at time Table 1. Induction motor parameters—Siemens (1LA 7096-2AA60-Z). t = 1.5 s. The induction motor parameters are given in Table1. No Parameters Values Table 1. Induction1 motor Rated parameters—Siemens power (1LA 2.2 kW 7096-2AA60-Z). No2 Rated Parameters voltage Values 400 V 3 Rated frequency 50 Hz 1 Rated power 2.2 kW 42 Stator Rated resistance voltage 1.99 400 Ohm V 53 Rotor Rated resistance frequency 1.84 50 HzOhm 64 Magnetizing Stator resistance inductance 1.99 0.37 Ohm H 75 RotorPoles resistance 1.84 Ohm2 86 MagnetizingRated speed inductance 2880 0.37 Rpm H 7 Poles 2 2 98 Rotor moment Rated speed of inertia 0.002159 2880 Rpm kgm 9 Rotor moment of inertia 0.002159 kgm2 4.2.1. Speed of Induction Motor without Rotor and Stator Resistance Estimation 4.2.1.Assuming Speed of Induction that the rotor Motor resistance without increases Rotor and from Stator 1.84 Resistance to 2.76 Ω,Estimation from 0–2 s, it remains 1.84 Ω; in 2–7 s, it increases from 1.84–2.76 Ω; at 7–9 s, the rotor resistance is 2.76 Ω. The stator resistance varies Assuming that the rotor resistance increases from 1.84 to 2.76 Ω, from 0–2 s, it remains 1.84 Ω; from 1.99 to 2.99 Ω for 0–2 s, it remains 1.99 Ω, at 2–7 s and it increases from 1.99–2.99 Ω for 7–9 s in 2–7 s, it increases from 1.84–2.76 Ω; at 7–9 s, the rotor resistance is 2.76 Ω. The stator resistance then stays at 2.99 Ω, but the rotor and stator resistances set for the controller retain their rated varies from 1.99 to 2.99 Ω for 0–2 s, it remains 1.99 Ω, at 2–7 s and it increases from 1.99–2.99 Ω for resistance values. Figure 6a indicates reference speed and estimated speed throughout the 7–9 s then stays at 2.99 Ω, but the rotor and stator resistances set for the controller retain their rated simulation time. In Figure 6b, the stator and rotor resistance values differ by 50% from the initial resistance values. Figure6a indicates reference speed and estimated speed throughout the simulation cold resistance values; the average estimated speed is still 20 rad/s but the pulsation of the speed is time. In Figure6b, the stator and rotor resistance values di ﬀer by 50% from the initial cold resistance nearly 0.3 rad/s. values; the average estimated speed is still 20 rad/s but the pulsation of the speed is nearly 0.3 rad/s.

(a) (b)

FigureFigure 6.6. Speed of induction motor without online rotor (a) andand statorstator resistanceresistance ((bb)) estimation:estimation: referencereference speed,speed, realreal speedspeed andand estimatedestimated speed. speed.

4.2.2.4.2.2. SpeedSpeed ofof InductionInduction MotorMotor withwith OnlineOnline RotorRotor andand StatorStator ResistanceResistance EstimationEstimation TheThe simulationsimulation results results in Figurein Figure7a,b show7a,b show that, with that, the with resistance the resistance estimation estimation algorithms algorithms proposed inproposed Sections in2 and Sections3, the 2 rotor and and3, the stator rotor resistance and stator were resistance accurately were estimated accurately with estimated very small with error very comparedsmall error to compared real resistance to real values. resistance On thevalues. other On hand, the other the accurate hand, the estimation accurate ofestimation rotor and of stator rotor resistancesand stator improvedresistances the improved estimation the of estimation the real speed of the of real the rotorspeed (Figure of the8 ),rotor thereby (Figure improving 8), thereby the qualityimproving of the the sensorless quality of drive the sensorless system. drive system.

Energies 2020, 13, x FOR PEER REVIEW 9 of 16

Energies 2020, 13, 4946 9 of 16 Energies 2020, 13, x FOR PEER REVIEW 9 of 16

(a) (b)

Figure 7. Rotor (a) and stator (b) resistances of induction motor: real resistances and estimated resistances. (a) (b) FigureFigure 7. RotorRotor ( a()a and) and stator stator (b) resistances(b) resistances of induction of induction motor: realmotor: resistances real resistances and estimated and resistances.estimated resistances.

Figure 8. Speed of induction motor with online rotor and stator resistance estimators: reference speed andFigure estimated 8. Speed speed. of induction motor with online rotor and stator resistance estimators: reference speed and estimated speed. 4.3. ResultsFigure 8. of Speed the Experiment of induction motor with online rotor and stator resistance estimators: reference 4.3. Results of the Experiment speedTo re-examine and estimated the proposedspeed. stator and rotor resistance estimation algorithms, an experimental setupTo has re-examine been developed the proposed (Figures 9stator and 10and). Therotor experiment resistance wasestimation performed algorithms, on DS 1104 an connectedexperimental to 4.3. Results of the Experiment thesetup personal has been computer. developed Application (Figures of9 and the controller10). The experiment is known in was the performed literature for on control DS 1104 of connected electronic converters,to theTo personalre-examine as in [computer.39 the,40 ].proposed In thisApplication study, stator we and of use therotor a three-phasecont resistanceroller is inductionestimation known in motor algorithms,the literature 2.2 kW an/400 experimentalfor V—detailed control of setupdataelectronic arehas shown been converters, developed in Table as1. in The(Figures [39,40]. motor 9 In and is this controlled 10). study, The byexperimentwe an use inverter a three-phase was and performed is rigidly induction on connected DS motor 1104 to 2.2connected a 1.5kW/400 kW todcV—detailed the motor—detailed personal data computer. are data shown are Application shown in Table in Table of1. 2theThe. The cont motor DCroller motor is iscontrolled isknown controlled in by the byan literature ainverter 4Q rectifier forand (Mentorcontrol is rigidly II)of electronicinconnected torque converters, control to a 1.5 mode kW as dc (Torquein motor—detailed [39,40]. Control) In this sost dataudy, that are we the shown use load a torquethree-phasein Table can 2. The be induction applied DC motor motor to theis controlled three-phase2.2 kW/400 by V—detailedinductiona 4Q rectifier motor. data (Mentor are shown II) in torquein Table control 1. The mode motor (Torque is controlled Control) byso thatan inverter the load and torque is rigidly can be connectedappliedThe to current to the a 1.5three-phase and kW fluxdc motor—detailed controllers induction motor. were data implemented are shown with in Table a sampling 2. The DC time motor of 0.2 is ms. controlled The speed by aestimator 4Q rectifier using (Mentor the sampling II) in torque time iscontrol 2 ms, themode rotor (Torque resistance Control) estimation so that using the load the samplingtorque can time be appliedis 44 ms, to the three-phase statorTable resistance 2. inductionDC motor estimation parameters—Fuanmotor. using the LiYu samplingan Electric, time Ltd. is (ZD97B-2). 88 ms. An encoder with 5000 pulses/cycle was used to determine position and speed. The load torque is 2 Nm. No Parameters Values Table 2. DC motor parameters—Fuan LiYuan Electric, Ltd. (ZD97B-2). 1 Rated power 1.5 kW Table 2. DC motor parameters—Fuan LiYuan Electric, Ltd. (ZD97B-2). No2 RatedParameters frequency Values 50 Hz No13 Rated Rated Parametersarmature power voltage 1.5 Values200 kW V 124 Rated Rated Rated fieldfrequency power voltage 50 1.5 200 Hz kW V 235 Rated Rated Rated armature field frequency current voltage 200 1.550 Hz VA 346 Rated RatedRated armature field speed voltage voltage 1500 200 200 RpmV V 4 Rated field voltage 200 V 5 Rated field current 1.5 A 5 Rated field current 1.5 A 66 Rated Rated speedspeed 1500 1500 Rpm Rpm

Energies 2020, 13, 4946 10 of 16 EnergiesEnergies 2020 2020, 13, 13x FOR, x FOR PEER PEER REVIEW REVIEW 1010 of of16 16

+ +

RectifierRectifier VdcVdc InverterInverter IM DCDC

_ _ GridGrid MesuremMesurem entent ω ωrr DSDS 1104 1104 MentorMentor II II

PC Grid PC Grid

Figure 9. Experimental setup diagram. FigureFigure 9. ExperimentalExperimental setup setup diagram. diagram.

Figure 10. Experimental table using DS 1104. Figure 10. Experimental table using DS 1104.

In theThe low-speed current and region, flux controllers theFigure sensorless 10. were Experimental implemen drive is table moreted usingwith aﬀ ectedaDS sampling 1104. by the time rotor of 0.2 and ms. stator The speed resistance estimationestimator error using than the in sampling the high-speed time is 2 zone ms, the [9], rotor so in resistance this experiment, estimation a low using speed the sampling 20 rad/s time is set is as the reference44The ms, speed current the stator value and resistance forflux the controllers controller. estimation were After using implemen a numberthe samplingted of with tests, time a sampling the is learning88 ms. time An rate ofencoder to0.2 estimate ms. with The rotor5000speed and statorestimatorpulses/cycle resistance using was the usedsampling chosen to determine as time follows: is 2positi ms,ηr on=the0.015; and rotor speed.η resistances = 0.022.The load estimation The torque motor is using2 runs Nm. the for sampling some time time (around is 6044 min ms, or theIn more) the stator low-speed with resistance a load region,T Lestimation= the2 Nm sensorless (approximately using drive the issampling mo 30%re affected of time the ratedbyis 88the load). ms.rotor An and The encoder stator obtained resistance with results 5000 are presentedpulses/cycleestimation as follows: was error used than to in determine the high-speed positi zoneon and [9], speed. so in this The experiment, load torque a lowis 2 Nm.speed 20 rad/s is set as theIn referencethe low-speed speed region,value for the the sensorless controller. drive After is amo numberre affected of tests, by thethe rotorlearning and rate stator to estimateresistance Inrotor Section and stator 4.3.1 ,resistance the comparison was chosen between as follows: estimation ηr = 0.015; level ηs with= 0.022. and The without motor runs constant for some learning time rate; • estimation error than in the high-speed zone [9], so in this experiment, a low speed 20 rad/s is set as theIn (aroundreference Section 60 4.3.2speedmin or, the valuemore) comparison forwith the a load controller. between TL = 2 Nm After the (approximately speed a number of induction of 30% tests, of the motorthe rated learning with load). and rate The without to obtained estimate online • results are presented as follows: rotorrotor and and stator stator resistance resistance was estimators;chosen as follows: ηr = 0.015; ηs = 0.022. The motor runs for some time

(aroundIn Section 60 min 4.3.3 or ,more) the short with discussion a load TL = of2 Nm obtained (approximately results is presented.30% of the rated load). The obtained • results are presented as follows: 4.3.1. Results of Rotor and Stator Resistance Estimation

Figure 11a shows that the estimated rotor resistance with constant learning rate has an average value 2.10 Ω. Figure 11b is an enlarged image of the rotor resistance estimation with constant ≈ learning rate, the estimated rotor resistance with constant learning rate, the pulsation of estimated

EnergiesEnergies 2020 2020, ,13 13, ,x x FOR FOR PEER PEER REVIEW REVIEW 1111 ofof 1616

•• InIn SectionSection 4.3.1,4.3.1, thethe comparisoncomparison betweenbetween estimationestimation levellevel withwith andand withoutwithout constantconstant learninglearning rate;rate; •• InIn SectionSection 4.3.2,4.3.2, thethe comparisoncomparison betweenbetween thethe spspeedeed ofof inductioninduction motormotor withwith andand withoutwithout onlineonline rotorrotor andand statorstator resistanceresistance estimators;estimators; •• InIn SectionSection 4.3.3,4.3.3, thethe shortshort discussiondiscussion ofof obtainedobtained resultsresults isis presented.presented.

4.3.1.4.3.1. ResultsResults ofof RotorRotor andand StatorStator ResistanceResistance EstimationEstimation

EnergiesFigure2020Figure, 13 , 11a11a 4946 showsshows thatthat thethe estimatedestimated rotorrotor resistanceresistance withwith constantconstant learninglearning raterate hashas anan average11average of 16 valuevalue ≈≈ 2.102.10 ΩΩ.. FigureFigure 11b11b isis anan enlargedenlarged imageimage ofof thethe rotorrotor resistanceresistance estimationestimation withwith constantconstant learninglearning rate,rate, thethe estimatedestimated rotorrotor resistanceresistance withwith constantconstant learninglearning rate,rate, thethe pulsationpulsation ofof estimatedestimated resistanceresistance ≈20%. 20%.The The estimated estimated rotor rotor resistance resistance using using the the learning learning rate rate by by function function (11) (11) is is almost almost resistance≈ ≈ 20%. The estimated rotor resistance using the learning rate by function (11) is almost non-pulsating,non-pulsating,non-pulsating, as asas indicated indicatedindicated in in Figurein FigureFigure 11 c. 11c.11c. Figure FigureFigure 12 a 12a12a shows showsshows that thatthat the the estimatedthe estimatedestimated stator statorstator resistance resistanceresistance has an hashas averagean average value value2 Ω .≈ In 2 FigureΩ. In 12Figureb, the estimated12b, the estimated stator resistance stator usingresistance the learning using ratethe accordinglearning rate to an average ≈value ≈ 2 Ω. In Figure 12b, the estimated stator resistance using the learning rate (18)accordingaccording is more accuratetoto (18)(18) isis than moremore using accurateaccurate the constant thanthan usingusing learning thethe constantconstant rate (the learninglearning pulsation raterate of estimated(the(the pulsationpulsation stator ofof resistance estimatedestimated isstator25% resistance when the learningis ≈25% ratewhen is constant,the learning while rate with is theconstant, proposed while method, with the pulsationproposed of method, estimated the stator≈ resistance is ≈25% when the learning rate is constant, while with the proposed method, the statorpulsation resistance of estimated is 3%). stator resistance is ≈3%). pulsation of estimated≈ stator resistance is ≈3%).

((aa)) ((bb))

((cc))

FigureFigureFigure 11. 11.11.( a ()(aa Estimated)) EstimatedEstimated rotor rotorrotor resistance resistanceresistance with withwith learning learninglearning rate raterate is isis constant; constant;constant; (b) ((b)b)zoom zoomzoom of ofof estimated estimatedestimated rotor rotorrotor resistanceresistanceresistance with with with learning learning learning rate rate rate is is constant;is constant; constant; (c ( )(cc estimated)) estimated estimated rotor rotor rotor resistance resistance resistance with with with learning learning learning rate rate rate as as as a a functiona function function fromfromfrom Equation Equation Equation (11). (11). (11).

((aa)) ((bb))

FigureFigureFigure 12. 12. 12.(a ( )(aa Estimated)) Estimated Estimated stator stator stator resistance resistance resistance with with with learning learning learning rate rate rate is is is constant; constant; constant; (b ( ()bb estimated)) estimated estimated stator stator stator resistance resistance resistance withwithwith learning learning learning rate rate rate as as as a functionaa function function from from from Equation Equation Equation (18). (18). (18).

4.3.2. Impact of Online Rotor and Stator Resistance Estimation

Case study 1: Without the online rotor and stator resistance estimation. Figure 13a–d show that the measured speed is pulsating compared to the reference speed: the pulsation of measured speed is 5%; the estimated speed ﬂuctuates around the reference speed; ≈ the pulsation of estimated speed is 6.25%. ≈ Case study 2: With the online rotor and stator resistance estimation. Figure 14a–d show that the measured speed is almost the same as the reference speed, and the pulsation is only 2%; the estimated speed also follows the reference speed, with the same pulsation ≈ of 2%. ≈ Energies 2020, 13, x FOR PEER REVIEW 12 of 16

4.3.2. Impact of Online Rotor and Stator Resistance Estimation Case study 1: Without the online rotor and stator resistance estimation. Figure 13a–d show that the measured speed is pulsating compared to the reference speed: the pulsation of measured speed is ≈5%; the estimated speed fluctuates around the reference speed; the Energies 2020, 13, x FOR PEER REVIEW 12 of 16 pulsation of estimated speed is ≈6.25%. 4.3.2. Impact of Online Rotor and Stator Resistance Estimation Case study 1: Without the online rotor and stator resistance estimation. Figure 13a–d show that the measured speed is pulsating compared to the reference speed: the pulsation of measured speed is ≈5%; the estimated speed fluctuates around the reference speed; the Energiespulsation2020, 13, 4946of estimated speed is ≈6.25%. 12 of 16

(a) (b)

Figure 13. Speed of induction motor without online rotor and stator resistance estimation: (a,b) Reference speed and measurement speed; (c,d) Reference speed and estimated speed.

Case study 2: With the online rotor and stator resistance estimation Figure 14a–d show that the measured speed is almost the same as the reference speed, and the (c) (d) pulsation is only ≈2%; the estimated speed also follows the reference speed, with the same pulsation Figureof ≈2%.Figure 13. 13.Speed Speed of of inductioninduction motor motor without without online online rotor rotor and stator and statorresistance resistance estimation: estimation: (a,b) (a,b) Reference speed speed and and measurement measurement speed; speed; (c,d () cReference,d) Reference speed speed and estimated and estimated speed. speed.

Case study 2: With the online rotor and stator resistance estimation Figure 14a–d show that the measured speed is almost the same as the reference speed, and the pulsation is only ≈2%; the estimated speed also follows the reference speed, with the same pulsation of ≈2%.

Energies 2020, 13, x FOR PEER REVIEW 13 of 16 (b) (a)

(b) (a)

FigureFigure 14. Speed 14. Speed of induction of induction motor motor withonline with online rotor and rotor stator and resistancestator resistance estimators: estimators: (a,b) Reference (a,b) speedReference and measurement speed and speed;measurement (c,d) Reference speed; (c,d speed) Reference and estimatedspeed and estimated speed. speed.

4.3.3.4.3.3. Discussion Discussion The resultsThe results presented presented in thein the previous previous section section indicate indicate thatthat • Estimated rotor resistance obtained from the proposed methodology ensures that the pulsation Estimated rotor resistance obtained from the proposed methodology ensures that the pulsation is • is 20% lower than with constant learning rate. Additionally, the level of pulsation of the 20% lowerproposed than method with constantis less than learning 1%, which rate. is better Additionally, than results the obtained level of pulsationin, e.g., [16] of (up the to proposed 5%); method• Estimated is less thanstator 1%, resistance which obtained is better from than the results proposed obtained methodology in, e.g., [ensures16] (up that to 5%); the pulsation is 22% lower than with constant learning rate. Additionally, the level of pulsation of the proposed method is less than 3%, which is better than results obtained in, e.g., [35] (not exceeding 10%); • Application of the proposed online rotor and stator resistance estimation ensured a decrease in the value of pulsation of over 4% than with constant learning rate. The indicated results concern the quasi-steady operating state of the drive. Analysis of other operating states is an element for future research.

5. Conclusions This paper proposes a method for estimating the rotor and stator resistance of an induction motor using artificial neural networks with the variable learning rate determined by a function. The results show that online rotor and stator resistance estimation using the proposed method is more accurate when estimating at a constant learning rate and also demonstrate that the online estimation of rotor and stator resistance has contributed to improving the control quality of the sensorless induction motor drive. Future direction of the research will be properties evaluation of the proposed method for various operating states.

Funding: The APC was funded Chair of Electrical Engineering Fundamentals, Wroclaw University of Science and Technology.

Acknowledgments: The authors would like to thank the Electrical Drive Laboratory, Department of Industrial Automation, Hanoi University of Science and Technology for helping us to complete the experiments in this paper.

Conflicts of Interest: The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.

Energies 2020, 13, 4946 13 of 16

Estimated stator resistance obtained from the proposed methodology ensures that the pulsation is • 22% lower than with constant learning rate. Additionally, the level of pulsation of the proposed method is less than 3%, which is better than results obtained in, e.g., [35] (not exceeding 10%); Application of the proposed online rotor and stator resistance estimation ensured a decrease in • the value of pulsation of over 4% than with constant learning rate.

The indicated results concern the quasi-steady operating state of the drive. Analysis of other operating states is an element for future research.

5. Conclusions This paper proposes a method for estimating the rotor and stator resistance of an induction motor using artiﬁcial neural networks with the variable learning rate determined by a function. The results show that online rotor and stator resistance estimation using the proposed method is more accurate when estimating at a constant learning rate and also demonstrate that the online estimation of rotor and stator resistance has contributed to improving the control quality of the sensorless induction motor drive. Future direction of the research will be properties evaluation of the proposed method for various operating states.

Author Contributions: Conceptualization, T.P.V. and D.V.T.; methodology, T.P.V. and D.V.T.; software, T.P.V. and D.V.T.; validation, M.J., T.S. and P.C.; formal analysis, T.P.V. and D.V.T.; investigation, T.P.V. and D.V.T.; resources, T.P.V. and D.V.T.; data curation, T.P.V. and D.V.T.; writing—original draft preparation, T.P.V. and D.V.T.; writing—review and editing, M.J. and P.C.; visualization, T.P.V. and D.V.T.; supervision, Z.L., M.J. and T.S.; project administration, Z.L.; funding acquisition, Z.L. All authors have read and agreed to the published version of the manuscript. Funding: The APC was funded Chair of Electrical Engineering Fundamentals, Wroclaw University of Science and Technology. Acknowledgments: The authors would like to thank the Electrical Drive Laboratory, Department of Industrial Automation, Hanoi University of Science and Technology for helping us to complete the experiments in this paper. Conﬂicts of Interest: The authors declare no conﬂict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.

List of Symbols

α-axis rotor flux linkages estimated by voltage model ψvm rα in the stator reference frame β-axis rotor flux linkages estimated by voltage model ψvm rβ in the stator reference frame ψsα α-axis stator flux linkages in the stator reference frame ψsβ β-axis stator flux linkages in the stator reference frame α-axis rotor flux linkages estimated by current model ψim rα in the stator reference frame β-axis rotor flux linkages estimated by current model ψim rβ in the stator reference frame Vsα α-axis stator voltage in the stator reference frame Vsβ β-axis stator voltage in the stator reference frame isα α-axis stator current in the stator reference frame isβ β-axis stator current in the stator reference frame Lm magnetizing inductance Lr rotor self-inductance Ls stator self-inductance Rs stator resistance Rr rotor resistance Energies 2020, 13, 4946 14 of 16

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