Evaluation of Direct Torque Control with a Constant-Frequency Torque Regulator Under Various Discrete Interleaving Carriers

electronics

Article Evaluation of Direct Torque Control with a Constant-Frequency Torque Regulator under Various Discrete Interleaving Carriers

Ibrahim Mohd Alsofyani and Kyo-Beum Lee *

Department of Electrical and Computer Engineering, Ajou University, 206, World cup-ro, Yeongtong-gu Suwon 16499, Korea * Correspondence: [email protected]; Tel.: +82-31-219-2376

Received: 25 June 2019; Accepted: 20 July 2019; Published: 23 July 2019

Abstract: Constant-frequency torque regulator–based direct torque control (CFTR-DTC) provides an attractive and powerful control strategy for induction and permanent-magnet motors. However, this scheme has two major issues: A sector-flux droop at low speed and poor torque dynamic performance. To improve the performance of this control method, interleaving triangular carriers are used to replace the single carrier in the CFTR controller to increase the duty voltage cycles and reduce the flux droop. However, this method causes an increase in the motor torque ripple. Hence, in this work, different discrete steps when generating the interleaving carriers in CFTR-DTC of an induction machine are compared. The comparison involves the investigation of the torque dynamic performance and torque and stator flux ripples. The effectiveness of the proposed CFTR-DTC with various discrete interleaving-carriers is validated through simulation and experimental results.

Keywords: constant-frequency torque regulator; direct torque control; ﬂux regulation; induction motor; interleaving carriers; low-speed operation

1. Introduction There are two well-established control strategies for high-performance motor drives: Field orientation control (FOC) and direct torque control (DTC) [1–3]. The FOC method has received wide acceptance in industry [4]. Nevertheless, it is complex because of the requirement for two proportional-integral (PI) regulators, space-vector modulation (SVM), and frame transformation, which also needs the installation of a high-resolution speed encoder. Alternatively, to ensure the quickest torque dynamic of the induction motor drive, the DTC has become the alternative popular control scheme because of its simple structure and excellent torque response [1]. The most common problems linked with the classical DTC are flux droop in the low-speed region, variable switching frequency, large increase in the flux, and torque ripples. Variouscontrol methods have been applied to tackle the issues in classical DTC drives. The common method used to enhance the DTC performance is adopting SVM (known as DTC-SVM). In this scheme, an appropriate voltage reference should be well estimated for the complete utilization of SVM, and, hence, it contains extra control methods, such as PI torque and flux regulators, dead-beat control, and sliding-mode control [4–6]. Although this scheme has the merits of obtaining a constant-switching frequency and fewer torque ripples, the torque dynamics and simplicity of the classical DTC are lost. The second popular control method is model predictive control (MPC), which is generally classified into conventional MPC and finite-set predictive torque control (FS-PTC) [7–17]. The choice of voltage vectors for FS-PTC is attained through a predefined cost function instead of using a look-up table. This method has intuitive features, straightforward implementation, and simple inclusion of nonlinearities

Electronics 2019, 8, 820; doi:10.3390/electronics8070820 www.mdpi.com/journal/electronics Electronics 2019, 8, 820 2 of 15 and constraints. Generally, PTC strategies, although helping to address the problem, are associated with some issues such as the increase in total harmonic distortion and a high computational burden [11]. Lately, interest has increased in using DTC with a constant-frequency torque regulator (CFTR-DTC) in AC motor drives [18–23]. The DTC-CFTR was initially created for achieving a constant switching frequency of inverters and a reduction of torque and flux ripples [18]. Unlike the DTC-SVM and MPC methods, there is a possibility to solve the stated DTC problems by applying CFTR in the basic configuration of classical DTC while maintaining the simple DTC algorithm. To date, only a handful of studies have been reported to address these problems in the CFTR. Some studies of DTC-CFTR have applied it in multilevel-based DTC (ML-DTC), such as three-level [19] and five-level [20] systems. They can provide a higher degree of freedom in control to obtain smoother torque and flux responses and to lead to a torque ripple reduction. In previous work [21], an over modulation method was proposed to enhance CFTR-DTC by retaining a single active-voltage vector during the torque transient. In other work [22], the digital signal processor (DSP) board was extended using a field programmable gate array controller to generate a higher carrier frequency, thus achieving a further reduction of the torque ripple. Nevertheless, this work requires extending extra software and an external controller to the drive system. In other research [23], CFTR-DTC has been investigated for low-speed operation showing satisfactory performance in terms of flux regulation improvement. Nevertheless, it still suffers from sector-flux droop and poor torque dynamic performance. In [24], CFTR-DTC with interleaving carriers was reported to improve the CFTR at the low-speed range. The configuration of the controller is like the conventional CFTR; yet, the method needs two carrier waveforms with a 90◦ phase shift for the upper and lower sides. However, the CFTR rules in [24] were only limited for the low-speed region because of the large torque ripple. In this study, the interleaving triangular waveforms are also used to replace the conventional single carrier in the CFTR-DTC of an induction machine (IM). Unlike the work in [24], CFTR-DTC with interleaving carriers is investigated in simulation and experimentation for all speed regions by including all the controller rules. Moreover, various frequencies of interleaving carriers were investigated in the experimental implementation considering the discrete nature of DSP. The rest of this work contains the following sections. The induction motor modeling and principles of the conventional CFTR-DTC are presented in Section2. The Ohmic voltage e ﬀect on the ﬂux droop in the-low speed region for CFTR-DTC is illustrated in Section3. The proposed CFTR-DTC with interleaving carriers is also described in Section3. The simulation results are presented in Section4. The description of the experimental setup, implementation of interleaving carriers with various frequencies, and experimental results are presented in Section5. The conclusion is given in Section6.

2. Fundamentals of CFTR-DTC of IM

2.1. Induction Motor Model The induction motor (IM) dynamic modeling can be given in terms of space-vector relations, which are described in the stator stationary-reference frame as follows.

d→ → ψs →v s = Rs i s + (1) · dt

d→ → → ψr 0 = Rr i r jωr ψ + (2) · − · r dt

→ → → ψ = Ls i s + Lm i r (3) s · · → → → ψ = (Lr/Lm) ψ σLs i s (4) r · s − ·

3 → → Te = pψ i s (5) 2 s × Electronics 2019, 8, 820 3 of 15

where →v s is a voltage vector, which is calculated depending on the selected switching states (Sa,Sb, → → → and Sc) attained from the look-up table (Table1). i s and i r are stator and rotor currents, and ψs → and ψr are stator and rotor ﬂux linkages, respectively. Rs and Rr are the stator resistance and rotor 2 resistance, respectively. p is the number of pole pairs, and σ = 1 L /LsLr is a leakage coeﬃcient. Ls − m is a stator inductance, Lr is a rotor self-inductance, and Lm is a magnetizing inductance. ωr is the rotor motor speed in rad/s.

Table 1. Selection of voltage vectors.

ψstat Tstat θs(1) θs(2) θs(3) θs(4) θs(5) θs(6)

1 →v s,2 [100] →v s,3 [110] →v s,4 [010] →v s,5 [011] →v s,6 [001] →v s,1 [101] 1 0 →v s,0 [000] →v s,7 [111] →v s,0 [000] →v s,7 [111] →v s,0 [000] →v s,7 [111] 1 →v [001] →v [101] →v [100] →v [110] →v [010] →v [011] − s,6 s,1 s,2 s,3 s,4 s,5 1 →v s,3 [110] →v s,4 [010] →v s,5 [011] →v s,6 [001] →v s,1 [101] →v s,2 [100] 0 0 →v s,7 [111] →v s,0 [000] →v s,7 [111] →v s,0 [000] →v s,7 [111] →v s,0 [000] 1 →v [011] →v [001] →v [101] →v [100] →v [110] →v [010] − s,5 s,6 s,1 s,2 s,3 s,4

2.2. Fundamentals of CFTR-DTC The CFTR-DTC is a modified variety from the classical DTC [18]. It contains the same parts of the original DTC, except for replacing the torque-hysteresis controller with CFTR, as shown in Figure1. Hence, it still retains the simple configuration of original DTC. The CFTR consists of three key parts: Upper-triangular carrier (Cupper) and lower-triangular carrier (Clower), a PI regulator, and comparators. The torque-error status (Tstat) is the output of CFTR, which is constructed in a similar way to the torque-hysteresis controller in DTC but with constant switching, as   1 , Tc Cupper  ≥ Tstat =  0 , Clower < Tc < Cupper (6)   1 , Tc C − ≤ lower where Tc is the PI-controller output. The basic law of stator-voltage selection is tabulated in Table1. The resultant Tstat is constructed based on three states: 1, 0, and 1, which imply forward-voltage − vector, null-voltage vector, and reverse-voltage vector, respectively. In addition, it preserves the flux comparator, which contains one hysteresis band (∆HBΨ) for regulating the stator flux in a circular path and the look-up table. The output of the flux comparator is the flux-error status (Ψstat). The applications of vs depend on the selection of the optimized switching states (Sa,Sb,Sc) from the look-up table. The switching states are determined by the stator-flux sector (θs) and also depend on whether the torque and stator flux require to be incremented or decremented [2]. Electronics 2019, 8, 820 4 of 15 Electronics 2019, 8, x FOR PEER REVIEW 4 of 16

𝑇𝑒 - 𝑇𝑟𝑒𝑓 + 𝑇𝑒𝑟𝑟 T PI c + 1 C - 0 + p-p Cupper 𝑇𝑠𝑡𝑎𝑡 V + + DC - 0

- + } -Cp-p Clower -1 Switching table Sa Voltage S source 𝜓 𝜓𝑒𝑟𝑟 𝜓𝑠𝑡𝑎𝑡 b IM 𝑠.𝑟𝑒𝑓 + inverter - Sc ΔHB𝜓 |𝜓𝑠| Sector Voltage calculation

𝑣𝑠 Stator and rotor flux 𝑖𝑠 and torque 𝑇𝑒 estimation 𝜔𝑟

FigureFigure 1. 1. ConventionalConventional structure structure of of constant-frequency constant-frequency to torquerque regulator–based regulator–based direct direct torque torque control control (CFTR-DTC).(CFTR-DTC). PI—proportional-integral PI—proportional-integral regulator; regulator; IM—induction motor. 3. Proposed CFTR-DTC with Interleaving Carriers The applications of vs depend on the selection of the optimized switching states (Sa, Sb, Sc) from the look-upOne of table. the main The switching issues normally states ar linkede determined with the by DTCthe stator-flux is the capability sector (𝜃 to) and have also a well-flux depend onregulation whether throughout the torque theand speed stator range, flux requir particularlye to be atincremented very low frequency. or decremented Although [2]. good performance is accomplished in the conventional CFTR-DTC [22], it still suffers from flux droop at low-speed regions 3.during Proposed sector CFTR-DTC transitions. with Figure Interleaving2 illustrates Carriers the flux regulation in the conventional CFTR-DTC where the fluxOne cannot of the entirely main issues fail because normally of regular linked switchingwith the ofDTC triangular is the capability carriers, which to have limit a thewell-flux torque regulationslope variation throughout and stimulate the speed reverse-voltage range, particularly vectors to reduce at very the torquelow frequency. rather than Although the zero-voltage good performancevector [22]. Nevertheless,is accomplished it hasin the flux-sector conventional droop, CFTR-DTC particularly [22], at it the still beginning suffers from of the flux sector droop [25 at]. low-speedConsequently, regions this canduring cause sector non-sinusoidal transitions. current Figure and 2 degradationillustrates the in theflux speed. regulation There arein twothe conventionalinfluences leading CFTR-DTC to this where issue: the The flux voltage cannot drop entirely across fail the because stator of resistance regular switching and the voltage of triangular vector carriers,accountable which for limit incrementing the torque the slope flux [variation25]. and stimulate reverse-voltage vectors to reduce the torqueTo rather simply than analyze the zero-voltage this problem, vector Equation [22]. (1)Nevertheless, can be arranged it has asflux-sector follows: droop, particularly at the beginning of the sector [25]. Consequently, this can cause non-sinusoidal current and degradation dψs → in the speed. There are two influences leading= →vtos thisi sR issue:s. The voltage drop across the stator (7) dt − resistance and the voltage vector accountable for incrementing the flux [25]. ToIf asimply discrete analyze step, Tthiss, is problem, considered Equation and the (1) ohmic can be voltage arranged drop as follows: is neglected, the change in the stator flux during the active voltage vector (∆ψs1) can be given as =𝑣⃗ −𝚤⃗ 𝑅 . (7) ∆ψs1 →v s.∆t (8) If a discrete step, Ts, is considered and the ohmic' voltage drop is neglected, the change in the stator flux during the active voltage vector (∆𝜓) can be given as and the rate of change in stator flux during null-voltage vectors (∆ψs2) can be expressed as ∆𝜓 ≃𝑣⃗.∆𝑡 (8) ∆ψs2 = isRs.∆t. (9) and the rate of change in stator flux during null-voltage− vectors (∆𝜓) can be expressed as

According to previous work [22], the∆𝜓 condition =−𝑖 given𝑅.∆𝑡.by Equation (10) cannot be fulﬁlled at(9) low speed because of the small magnitude of ∆ψs1. According to previous work [22], the condition given by Equation (10) cannot be fulfilled at low ∆𝜓 speed because of the small magnitude of ∆ψ. s1 > ∆ψs2. (10)

∆𝜓 >∆𝜓. (10)

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When the rotor speed reduces to a certain low range, the null-voltage vector selection (whenever When the rotor speed reduces to a certain low range, the null-voltage vector selection (whenever torque needs to be reduced) is dominant and critically reduces the magnitude of the stator flux, as torque needs to be reduced) is dominant and critically reduces the magnitude of the stator flux, as shown in Figure 2. shown in Figure2. According to previous research [22], the condition given by Equation (10) cannot be fulfilled at According to previous research [22], the condition given by Equation (10) cannot be fulfilled at low speed because of the long magnitude of null-voltage vectors. Consequently, ∆𝜓 becomes low speed because of the long magnitude of null-voltage vectors. Consequently, ∆ψ becomes highly highly affected by the stator-resistance [20], and, hence, the stator flux, 𝜓 , cannot follows2 its reference affected by the stator-resistance [20], and, hence, the stator flux, ψ , cannot follow its reference value, value, causing the condition in Equation (10) not to be fulfilled, as seens in Figure 2. causing the condition in Equation (10) not to be fulfilled, as seen in Figure2.

𝜓𝑠 𝜓𝑟𝑒𝑓

𝛥𝐻𝐵 𝛥𝜓 𝜓 𝑠1 𝛥𝜓𝑠2

Figure 2. Conventional structure of CFTR-DTC. Figure 2. Conventional structure of CFTR-DTC. The main concept of the proposed controller is to have improved flux regulation at various speed rangesThe andmain to concept minimize of the the proposed flux-sector controller droop is at to low-speed have improved regions. flux Forregu thislation reason, at various interleaving speed T rangescarriers and are to proposed minimize to the increase flux-sector the duty droop cycle at of low-speed the CFTR output,regions. statFor, as this shown reason, in Figure interleaving3. It can be observed that Cupper and Clower are the original carriers, whereas Cupper2 and Clower2 are the added carriers are proposed to increase the duty cycle of the CFTR output, Tstat, as shown in Figure 3. It can second upper and lower carriers, respectively. be observed that Cupper and Clower are the original carriers, whereas Cupper2 and Clower2 are the added secondThe upper calculation and lower for carriers, the torque respectively. error status in Equation (6) cannot be applied for the proposed T torqueThe controller. calculation Hence, for the the torque proposed error rules status for thein Equation new CFTR (6) output, cannot statbe ,applied are given for in the Table proposed2. Unlike work presented elsewhere [25], where only the low-speed range is considered, the proposed torque torque controller. Hence, the proposed rules for the new CFTR output, Tstat, are given in Table 2. Unlikerules coverwork allpresented speed regions. elsewhere From [25], Figure where3, it only is clearly the low-speed observed that range the is time considered, interval for the a proposed shadowed torquesingle rules triangle cover is halfall speed that of regions. the original From carrier, Figure which 3, it is leads clearly to theobserved increase that of thethe switchingtime interval frequency for a shadowedby two times. single Additionally, triangle is thehalf duty that cycleof the becomes original much carrier, larger which than leads that in to the the conventional increase of CFTR. the switchingConsequently, frequency this by can two considerably times. Additionally, reduce the the eff dutyect of cycle the ohmicbecomes drop much and, la hence,rger than improves that in the flux conventionalregulation at CFTR. low-speed Consequently, regions. this can considerably reduce the effect of the ohmic drop and, hence, improves flux regulation at low-speed regions.

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It can be seen that the output of the proposed interleaving-carrier-based CFTR is similar to that of the single-carrier controller [20], which is either of three states: 1, 0, or –1. For better illustration, the active states of 1 and −1 are obtained when PI output lies in the gray area, whereas the zero state is achieved when the PI output signal is located in the white area. It should be noted that for ensuring a proper torque operation of CFTR gains of the PI controller are essential. Hence by adjusting the PI parameters, optimal operation for the motor drive can be achieved. The selection of PI parameters can be carried out using the same procedure in [24], yet the whole peak of the carriers should be taken into account for the selection of PI gains. In principle, the output of the proposed interleaving-carrier-based CFTR is like that of a conventional controller [20], which Electronicscan be 2019either, 8, one 820 of three states: 1, 0, or –1. 6 of 15

Cupper Cupper2

Tc 0 ts

Clower2 Clower

Tsat 1

0 𝜓 𝑠 ts 𝜓𝑟𝑒𝑓

𝛥𝜓𝑠2 v 𝛥𝜓 𝑠1 𝛥𝐻𝐵𝜓

FigureFigure 3. 3. TypicalTypical waveformswaveforms for the the prop proposedosed strategy strategy at at low low speed. speed.

TableTable 2. 2.Rules Rules ofof interleaving-carrier-basedinterleaving-carrier-based CFTR-DTC CFTR-DTC.

Tc Cupper Tc Cupper2 ≥ 𝑇 ≥𝐶k ∥≥ 𝑇 ≥𝐶 1 Teerror > 0 1 Tc < Cupper Tc < Cupper2 𝑇𝑒 >0 𝑇 <𝐶k ∥ 𝑇 <𝐶 Otherwise 0 Otherwise 0 Tc C Tc C ≤ lower k ≤ lower2 1 Teerror 0 𝑇 ≤𝐶 ∥ 𝑇 ≤𝐶 − ≤ Tc > Clower Tc > Clower2 −1 𝑇𝑒 ≤0 𝑇 >𝐶k ∥ 𝑇 >𝐶 Otherwise 0 Otherwise 0

It can be seen that the output of the proposed interleaving-carrier-based CFTR is similar to that of the single-carrier controller [20], which is either of three states: 1, 0, or –1. For better illustration, the active states of 1 and 1 are obtained when PI output lies in the gray area, whereas the zero state is − achieved when the PI output signal is located in the white area. It should be noted that for ensuring a proper torque operation of CFTR gains of the PI controller are essential. Hence by adjusting the PI parameters, optimal operation for the motor drive can be achieved. The selection of PI parameters can be carried out using the same procedure in [24], yet the whole peak of the carriers should be taken into account for the selection of PI gains. In principle, the output of the proposed interleaving-carrier-based CFTR is like that of a conventional controller [20], which can be either one of three states: 1, 0, or –1.

4. Simulation Results To conﬁrm the validity of CFTR-DTC with a single carrier and CFTR-DTC with interleaving carriers, they were simulated using the PSIM simulation tool. The parameters of the induction motor are provided in Table3. Electronics 2019, 8, 820 7 of 15

Table 3. Induction motor parameters.

Rated power 3.7 kW Stator resistance 0.934 Ohm Rated current 8.28 A Rotor resistance 1.225 Ohm Rated speed 1750 r/min Stator inductance 146.2 mH Rated torque 20.36 Nm Rotor inductance 146.2 mH Rated ﬂux 0.6 Wb Mutual inductance 139.5 mH Inertia 0.018 Kg m2 Pole pairs 2 ·

Figure4 shows the steady-state performance of CFTR-DTC with a conventional carrier and CFTR-DTCElectronics 2019 with, 8, x FOR the PEER proposed REVIEW interleaving carriers at 100 rpm under a 5 Nm torque load. In7 of the 16 conventional algorithm, when applying a triangular carrier, it is apparent that the periodic ﬂux-sector 4. Simulation Results droop happens owing to the long duration of the zero-voltage vectors and also the weakened radial voltageTo componentsconfirm the invalidity the sector of CFTR transitions.-DTC with Consequently, a single carrier this results and CFTR-DTC in the distortions with interleaving of current waveforms.carriers, they Inwere contrast, simulated when using the the interleaving PSIM simula carrierstion tool. are applied,The parameters the stator of the ﬂux induction becomes motor well regulatedare provided and in stable Table owing 3. to the reduction of the ohmic voltage drop, because the zero-voltage vectors haveFigure a shorter 4 shows duration. the Consequently, steady-state performance this leads to excellentof CFTR-DTC improvement with a conventional of the current carrier waveform. and CFTR-DTCFigure5 withshows the the proposed dynamic interleaving responses for carriers the conventional at 100 rpm and under proposed a 5 Nm CFTR-DTC torque load. algorithms In the underconventional a speed algorithm, load of 100 when rpm. applying Figure5a a showstriangular the stepcarrier, change it is apparent of torque that from the 1 periodic to 10 Nm, flux-sector where a singledroop carrierhappens is applied.owing to However,the long duration in Figure of5b, the the ze proposedro-voltage interleaving vectors and carriers also the are weakened implemented radial withvoltage a higher components duty cycle; in the thus, sector the transitions. torque increases Consequently, with the this reduced results intervalin the distortions of the zero-voltage of current vector.waveforms. It can In be seencontrast, that thewhen current the interleaving waveform for ca therriers conventional are applied, CFTR-DTC the stator has flux higher becomes distortions well atregulated light toque and when stable compared owing to tothe the reduction higher torque of the after ohmic the voltage application drop, of because a lager torquethe zero-voltage reference. Nevertheless,vectors have thea shorter proposed duration. CFTR-DTC Consequently, has excellent this current leads waveformto excellent before improvement and after theof applicationthe current ofwaveform. the larger torque reference.

(a) Figure 4. Cont.

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(b)

Figure 4. Simulation results of low-speed performance for CFTR-DTC with (a) single carrier and (b) interleaving carriers.

From the enlarged image in Figure 6, it can be observed that when the reference torque steps up, the arrival time of torque of the proposed CFTR-D(b) TC changes from 1.131 to 0.935 ms as shown in FigureFigure 6b. This 4. Simulation indicates results that the of low-speedCFTR-DTC performance method with for CFTR-DTCproposed interleaving with (a) single carriers carrier andprovides (b) a fasterFigure torque 4. response.Simulation results of low-speed performance for CFTR-DTC with (a) single carrier and (b) interleaving carriers.

Figure 5 shows the dynamic responses for the conventional and proposed CFTR-DTC algorithms under a speed load of 100 rpm. Figure 5a shows the step change of torque from 1 to 10 Nm, where a single carrier is applied. However, in Figure 5b, the proposed interleaving carriers are implemented with a higher duty cycle; thus, the torque increases with the reduced interval of the zero-voltage vector. It can be seen that the current waveform for the conventional CFTR-DTC has higher distortions at light toque when compared to the higher torque after the application of a lager torque reference. Nevertheless, the proposed CFTR-DTC has excellent current waveform before and after the application of the larger torque reference. From the enlarged image in Figure 6, it can be observed that when the reference torque steps up, the arrival time of torque of the proposed CFTR-DTC changes from 1.131 to 0.935 ms as shown in Figure 6b. This indicates that the CFTR-DTC method with proposed interleaving carriers provides a faster torque response. Figure 5. SimulationSimulation results results of of dynamic dynamic torque torque performance performance for for CFTR-DTC CFTR-DTC with ( a)) single single carrier carrier and and (b) interleaving carriers.

From the enlarged image in Figure6, it can be observed that when the reference torque steps up, the arrival time of torque of the proposed CFTR-DTC changes from 1.131 to 0.935 ms as shown in Figure6b. This indicates that the CFTR-DTC method with proposed interleaving carriers provides a faster torque response. The proposed CFTR-DTC with interleaving carriers has been investigated for external load disturbance as shown in Figure7. The load torque is suddenly changed from 10 to 15 Nm. It can be observed that the speed waveform shows very good robustness against the load disturbance. The torque and current ripples are almost identical before and after the larger load disturbance.

Figure 5. Simulation results of dynamic torque performance for CFTR-DTC with (a) single carrier and (b) interleaving carriers.

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Figure 6. Enlargement of simulation results shown in Figure 5 for CFTR-DTC with (a) single carrier and (b) interleaving carriers.

The proposed CFTR-DTC with interleaving carriers has been investigated for external load disturbance as shown in Figure 7. The load torque is suddenly changed from 10 to 15 Nm. It can be observed that the speed waveform shows very good robustness against the load disturbance. The Figure 6. Enlargement of simulation results shown in Figure 5 for CFTR-DTC with (a) single carrier torqueFigure and 6.currentEnlargement ripples of are simulation almost identical results shown before in and Figure after5 for the CFTR-DTC larger load with disturbance. ( a) single carrier and (band) interleaving (b) interleaving carriers. carriers.

Figure 7. Simulation results of external load disturbance for the proposed CFTR-DTC with interleaving Figure 7. Simulation results of external load disturbance for the proposed CFTR-DTC with carriers at 30 rpm. interleaving carriers at 30 rpm. 5. Implementation and Experimental Results 5. Implementation and Experimental Results To investigate the interleaving carriers for the performance of CFTR-DTC of IM, the experimental

setupTo provided investigate in Figure the 8interleaving was used. Itcarriers contains fo ar DSPthe modelperformance TMS320F28335 of CFTR-DTC control boardof IM, and the a experimentalthree-phaseFigure 7. Simulation intelligent setup provided results power of in module external Figure equipped 8load was dist used. withurbance It insulatedcontains for the a gate DSPproposed bipolar model CFTR-DTC transistors TMS320F28335 with (IGBTs) control from boardSEMIKRON.interleaving and a carri three-phase Iners addition, at 30 rpm. intelligent two LAH 50-Ppower current module transducers equipped fromwith LEMinsulated are used gate to bipolar sense thetransistors current. (IGBTs)A 2000 PPRfrom encoder SEMIKRON. was used In addition, to obtain two the LAH measured 50-P current speed. transducers To load the from machine, LEM a are 5.5 used kW IMto 5. Implementation and Experimental Results sensecontrolled the current. by a commercial A 2000 PPR YASUKAWA encoder was inverter used wasto ob used.tain the The measured sampling speed. time of To DTC load and the CFTR-DTC machine, includingTo investigate the proposed the interleaving methods was carriers 40 µs. Thefor parametersthe performance of the inductionof CFTR-DTC machine of are IM, tabulated the in experimentalTable3. It setup is worth provided mentioning in Figure that 8 the was data used. acquisition It contains system a DSP has model a limited TMS320F28335 bandwidth. control Hence, the boardquantization and a three-phase error increases intelligent particularly power module in the equipped zoomed images. with insulated gate bipolar transistors (IGBTs) from SEMIKRON. In addition, two LAH 50-P current transducers from LEM are used to sense the current. A 2000 PPR encoder was used to obtain the measured speed. To load the machine,

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a 5.5 kW IM controlled by a commercial YASUKAWA inverter was used. The sampling time of DTC and CFTR-DTC including the proposed methods was 40 μs. The parameters of the induction machine Electronicsare tabulated2019, 8 , 820in Table 3. It is worth mentioning that the data acquisition system has a limited10 of 15 bandwidth. Hence, the quantization error increases particularly in the zoomed images.

Figure 8. Experimental setup. DSP—digital signal processor.

In the practical implementation,Table the 3. Induction application motor of parameters. the interleaving carriers in CFTR-DTC can improve the flux-sector droop, but at the expense of higher-torque ripples when compared with the Rated power 3.7 kW Stator resistance 0.934 Ohm single-carrier method [25]. Unlike in a previous study [24], where the interleaving carriers were utilized partially for theRated low-speed current region, here, 8.28 theA interleaving Rotor carriers resistance are fully utilized.1.225 Ohm However, in this method, the switchingRated speed frequency 1750of the r/min carrier can Stator also beinductance increased by designing 146.2 mH the step change Rated torque 20.36 Nm Rotor inductance 146.2 mH of carriers ∆Cpeak for both carriers at the same sampling period for investigating the performance of CFTR-DTC withRated interleaving flux carriers. 0.6 Wb In this regard,Mutual threeinductance interleaving 139.5 carriers mH are suggested, as follows. Inertia 0.018 Kg·m2 Pole pairs 2 In the practical implementation, the application of the interleaving carriers in CFTR-DTC can 1. Interleaving CFTR-3 (Figure9a) — Peak of the wave carrier ( Cpeak) is set to 90. ∆Cpeak increments improve the flux-sector droop, but at the expense of higher-torque ripples when compared with the 30 units per step size. Hence, the frequency for each carrier is 4166.66 Hz. single-carrier method [25]. Unlike in a previous study [24], where the interleaving carriers were 2. Interleaving CFTR-4 (Figure9b) — C is set to 100. ∆C increments 25 units per step size. utilized partially for the low-speed region, peakhere, the interleavingpeak carriers are fully utilized. However, Hence, the frequency for each carrier is 3125.00 Hz. in this method, the switching frequency of the carrier can also be increased by designing the step 3. Interleaving CFTR-5 (Figure9c) — Cpeak is set to 100. ∆Cpeak increments 20 units per step size. change of carriers ΔCpeak for both carriers at the same sampling period for investigating the Hence, the frequency for each carrier is 2500.00 Hz. performance of CFTR-DTC with interleaving carriers. In this regard, three interleaving carriers are suggested,Figure as 10 follows. shows the steady-state waveforms of speed, flux, torque, and current at 20 rpm for the conventional1. Interleaving CFTR-DTC CFTR-3 and the (Figure proposed 9a) — CFTR-DTC Peak of the with wave the interleaving carrier (Cpeak carriers,) is set to respectively. 90. ΔCpeak It is clearly shownincrements that the30 units stator per flux step in size. the CFTR-DTCHence, the frequency with conventional for each carrier single is carriers 4166.66 su Hz.ffers from periodic2. Interleaving sector-flux droopCFTR-4 during (Figure low-speed 9b) — Cpeak operation, is set to as100. shown ΔCpeak in increments Figure 10a. 25 As units a result, per step the waveforms ofsize. speed Hence, and current the frequency become for badly each distorted, carrier is and 3125.00 the electrical Hz. torque is not stable. When interleaving3. carriersInterleaving are applied, CFTR-5 significant (Figure 9c) improvement — Cpeak is set is to achieved 100. ΔC inpeak the increments stator-flux 20 regulation units per and,step hence, in the rotorsize. Hence, speed andthe currentfrequency waveforms, for each carrier as shown is 2500.00 in Figure Hz. 10 b. Nevertheless, it is apparent from the figure that the torque and current ripple increase. Next, the performances of CFTR-DTC with the three interleaving methods are evaluated and compared in terms of the motor torque and stator flux ripples. Figure 11 shows the steady-state operation of interleaving CFTR-3, interleaving CFTR-4, and interleaving CFTR-5. To have a fair comparison among the three methods, the investigation was performed under the same speed and load torque conditions so that the rotor speed operated at 500 rpm with a load torque of 5.0 Nm. The calculations of torque ripple (Tripple) and flux ripple (ψripple) for all control methods were done online at steady-state operation using the following expressions [26].

tv Xn 1 T = (Te(i) Te.ave) (11) ripple n − i=1 Electronics 2019, 8, 820 11 of 15

v t n 1 X ψ = (ψs(i) ψs.ave) (12) ripple n − i=1 where n is the number of sampling times, and Te.ave and ψs.ave are the average values of the torque and flux, respectively. The torque ripples were 1.268 Nm for interleaving CFTR-3, 1.319 Nm for interleaving CFTR-4, and 1.423 Nm for interleaving CFTR-5, respectively. The flux ripples of interleaving CFTR-3, interleaving CFTR-4, and interleaving CFTR-5 were found to be 0.0100, 0.0106, and 0.0110 Wb, respectively. It is clearly seen that interleaving CFTR-5 had the largest torque and flux ripples. However, interleaving CFTR-3Electronics had 2019 the, 8, x smallest FOR PEER torque REVIEW ripples and flux ripples owing to the increase of the carrier11 frequency. of 16

FigureFigure 9. 9. DiscreteDiscrete implementationimplementation of of the the upper upper triangular triangular carriers: carriers: (a) ( aInterleaving) Interleaving CFTR-3, CFTR-3, (b) (b) interleavingElectronicsinterleaving 2019 CFTR-4,,CFTR-4, 8, x FOR PEER and ( (REVIEWc)) interleaving interleaving CFTR-5. CFTR-5. 12 of 16

Figure 10 shows the steady-state waveforms𝜔𝑟 of speed, flux, torque, and current at 20 rpm for the conventional CFTR-DTC and the proposed CFTR-DTC with the interleaving carriers, respectively. It is clearly shown that the stator flux in the CFTR-DTC with conventional single carriers suffers from 𝜓𝑠 periodic sector-flux droop during low-speed operation, as shown in Figure 10a. As a result, the waveforms of speed and current become badly distorted, and the electrical torque is not stable. When

interleaving carriers are applied, significant improvement 𝑇is𝑒 achieved in the stator-flux regulation and, hence, in the rotor speed and current waveforms, as shown in Figure 10b. Nevertheless, it is

apparent from the figure that the torque𝑖𝑎 and current ripple increase.

𝜔𝑟 Figure 10. Cont.

𝜓𝑠

𝑇𝑒

𝑖𝑎

Figure 10. Experimental results of low-speed performance for CFTR-DTC with (a) single carrier and (b) interleaving carriers.

Next, the performances of CFTR-DTC with the three interleaving methods are evaluated and compared in terms of the motor torque and stator flux ripples. Figure 11 shows the steady-state operation of interleaving CFTR-3, interleaving CFTR-4, and interleaving CFTR-5. To have a fair comparison among the three methods, the investigation was performed under the same speed and load torque conditions so that the rotor speed operated at 500 rpm with a load torque of 5.0 Nm. The

calculations of torque ripple (𝑇) and flux ripple (𝜓) for all control methods were done online at steady-state operation using the following expressions [26].

1 𝑇 = (𝑇 (𝑖) −𝑇 ) (11) 𝑛 .

1 𝜓 = (𝜓 (𝑖) −𝜓 ) (12) 𝑛 .

where n is the number of sampling times, and 𝑇. and 𝜓. are the average values of the torque and flux, respectively. The torque ripples were 1.268 Nm for interleaving CFTR-3, 1.319 Nm for interleaving CFTR-4, and 1.423 Nm for interleaving CFTR-5, respectively. The flux ripples of interleaving CFTR-3, interleaving CFTR-4, and interleaving CFTR-5 were found to be 0.0100, 0.0106, and 0.0110 Wb, respectively. It is clearly seen that interleaving CFTR-5 had the largest torque and flux ripples.

Electronics 2019, 8, x FOR PEER REVIEW 12 of 16

𝜔𝑟

𝜓𝑠

𝑇𝑒

𝑖𝑎

Electronics 2019, 8, 820 12 of 15

𝜔𝑟

𝜓𝑠

𝑇𝑒

𝑖𝑎

Electronics 2019, 8, x FOR PEER REVIEW 13 of 16

FigureHowever,Figure 10. Experimental interleaving10. Experimental CFTR-3 results results ofhad of low-speed low-speedthe smallest performanceperformance torque ripples for for CFTR-DTC CFTR-DTC and flux withripples with (a) single (owinga) single carrier to the carrier and increase and (bof) interleaving the(b )carrier interleaving frequency. carriers. carriers.

Next, the performances of CFTR-DTC with the three interleaving methods are evaluated and

compared in terms of the motor torque𝜓𝑠 [1and Wb/div] stator flux ripples. Figure 11 shows the steady-state operation of interleaving CFTR-3, interleaving CFTR-4, and interleaving CFTR-5. To have a fair comparison among the three methods, the investigation was performed under the same speed and load torque conditions so that the rotor speed operated at 500 rpm with a load torque of 5.0 Nm. The calculations of torque ripple (𝑇 )𝑇 𝑒and[5 Nm/div] flux ripple (𝜓 ) for all control methods were done online 𝑇𝑟𝑖𝑝𝑝𝑙𝑒 = 1.268 𝑁𝑚 at steady-state operation using the following expressions𝜓 𝑟𝑖𝑝𝑝𝑙𝑒[26]. = 0.0100 𝑊𝑏 𝑖𝑎 [10 A /div] 1 𝑇 = (𝑇 (𝑖) −𝑇 ) (11) 𝑛 . 0 0.2 0.4 0.6 0.8 1 Time (s) (a) 1 𝜓 = (𝜓 (𝑖) −𝜓 ) (12) 𝑛 . 𝜓𝑠 [1 Wb/div]

where n is the number of sampling times, and 𝑇. and 𝜓. are the average values of the torque and flux, respectively. The torque ripples were 1.268𝑇 𝑒Nm[5 Nm/div] for interleaving CFTR-3, 1.319 Nm for interleaving CFTR-4, 𝑇𝑟𝑖𝑝𝑝𝑙𝑒 = 1.319 𝑁𝑚 and 1.423 Nm for interleaving CFTR-5, respectively. The flux ripples of interleaving CFTR-3, 𝜓𝑟𝑖𝑝𝑝𝑙𝑒 = 0.0106 𝑊𝑏 interleaving CFTR-4, and interleaving𝑖𝑎 [10 A /div] CFTR-5 were found to be 0.0100, 0.0106, and 0.0110 Wb, respectively. It is clearly seen that interleaving CFTR-5 had the largest torque and flux ripples.

0 0.2 0.4 0.6 0.8 1 Time (s) (b)

𝜓𝑠 [1 Wb/div]

𝑇𝑒[5 Nm/div] 𝑇𝑟𝑖𝑝𝑝𝑙𝑒 = 1.423 𝑁𝑚 𝜓𝑟𝑖𝑝𝑝𝑙𝑒 = 0.0110 𝑊𝑏

𝑖𝑎 [10 A /div]

0 0.2 0.4 0.6 0.8 1 Time (s) (c) FigureFigure 11. Experimental 11. Experimental results results of steady-state of steady-state performance performance for (a) interleavingfor (a) interleaving CFTR-3, CFTR-3, (b) interleaving (b) CFTR-4,interleaving and (c) interleaving CFTR-4, and CFTR-5.(c) interleaving CFTR-5.

Figure 12 shows the dynamic torque performance for the conventional CFTR-DTC and interleaving CFTR-3, interleaving CFTR-4, and interleaving CFTR-5. A step change of torque from 1 to 9 Nm was applied during operation at 300 rpm. Although the conventional CFTR-DTC had the smallest torque ripples, it had the slowest torque dynamic response of 3.73 ms when compared with the proposed interleaving methods. All the CFTR-DTC methods with interleaving carriers had excellent torque performance. However, interleaving CFTR-3 had the fastest torque response of 0.67 ms.

Electronics 2019, 8, 820 13 of 15

Figure 12 shows the dynamic torque performance for the conventional CFTR-DTC and interleaving CFTR-3, interleaving CFTR-4, and interleaving CFTR-5. A step change of torque from 1 to 9 Nm was applied during operation at 300 rpm. Although the conventional CFTR-DTC had the smallest torque ripples, it had the slowest torque dynamic response of 3.73 ms when compared with the proposed interleaving methods. All the CFTR-DTC methods with interleaving carriers had excellent torque Electronicsperformance. 2019, 8, x FOR However, PEER REVIEW interleaving CFTR-3 had the fastest torque response of 0.67 ms. 14 of 16

Electronics 2019, 8, x FOR PEER REVIEW 14 of 16 0.8 ms 3.73 ms

𝑇𝑟𝑒𝑓 [2.5 Nm/div] 𝑇𝑟𝑒𝑓 [2.5 Nm/div] 0.8 ms 3.73 ms 𝑇𝑒 [2.5 Nm/div] 𝑇𝑟𝑒𝑓 [2.5 Nm/div] 𝑇 [2.5 Nm/div] 𝑇𝑟𝑒𝑓 [2.5 Nm/div] 𝑒 𝑇𝑒 [2.5 Nm/div] 2 ms/div 𝑇𝑒 [2.5 Nm/div] 2 ms/div 2 ms/div (a) (c) 2 ms/div

0.67 ms (a) 0.72 ms(c)

0.67 ms 0.72 ms 𝑇𝑟𝑒𝑓 [2.5 Nm/div] 𝑇𝑟𝑒𝑓 [2.5 Nm/div] 𝑇𝑒 [2.5 Nm/div] 𝑇𝑒 [2.5 Nm/div] 𝑇𝑟𝑒𝑓 [2.5 Nm/div] 𝑇𝑟𝑒𝑓 [2.5 Nm/div] 𝑇𝑒 [2.5 Nm/div] 𝑇𝑒 [2.5 Nm/div]

2 ms/div 2 ms/div 2 ms/div (b)2 ms/div (d) Figure 12. Experimental results (b)of steady-state performance for (a) conventional CFTR-DTC, (d) (b) Figure 12. Experimental results of steady-state performance for (a) conventional CFTR-DTC, (b) interleavingFigure CFTR-3, 12. Experimental (c) interleaving results CFTR-4, of stea anddy-state (d) interleaving performance CFTR-5. for ( a) conventional CFTR-DTC, (b) interleaving CFTR-3, (c) interleaving CFTR-4, and (d) interleaving CFTR-5. interleaving CFTR-3, (c) interleaving CFTR-4, and (d) interleaving CFTR-5. Finally,Finally, the proposed the proposed CFTR-DTC CFTR-DTC with withinterleavi interleavingng carriers carriers has been has beenalso alsotested tested in the in real the real Finally, the proposed CFTR-DTC with interleaving carriers has been also tested in the real experimentexperiment for external for external load loaddisturbance disturbance as shown as shown in Figure in Figure 13. As 13 in. As the in simulation, the simulation, the load the loadtorque torque experiment for external load disturbance as shown in Figure 13. As in the simulation, the load torque is suddenlyis suddenly changed changed from from 10 to 10 16 to Nm 16 when Nm when the IM the is IM running is running at very at verylow speed low speed (i.e., (i.e.,30 rpm). 30 rpm). It can It can is suddenly changed from 10 to 16 Nm when the IM is running at very low speed (i.e., 30 rpm). It can be observedbe observed that the that speed the speed waveform waveform shows shows very verygood good robustness robustness against against the load the loaddisturbance disturbance since since be observed that the speed waveform shows very good robustness against the load disturbance since it has fast recovery after the load disturbance. The torque and current ripples are almost identical it hasit has fast fast recovery recovery after after the the load load disturbance. disturbance. TheThe torquetorque and current ripples ripples are are almost almost identical identical before and after the larger load disturbance. The torque error is also constant before and after the beforebefore and and after after the the larger larger load load disturbance. disturbance. TheThe torquetorque error is also constant constant before before and and after after the the disturbance. It is worth mentioning that all discrete interleaving carriers can show the same response disturbance.disturbance. It isIt worthis worth mentioning mentioning that that all all discrete discrete interleavinginterleaving carriers can can show show the the same same response response against load disturbance. againstagainst load load disturbance. disturbance.

𝜔 𝑟 𝜔𝑟 𝑇 𝑒 𝑇𝑒

𝑇𝑒𝑟𝑟 𝑇𝑒𝑟𝑟

𝑖𝑎 𝑖𝑎

FigureFigure 13. Experimental13. Experimental results results of external of external load disturbance load disturbance for the proposed for the proposed CFTR-DTC CFTR-DTC with interleaving with Figure 13. Experimental results of external load disturbance for the proposed CFTR-DTC with carriersinterleaving at 30 rpm. carriers at 30 rpm. interleaving carriers at 30 rpm. 6. Conclusions 6. Conclusions Interleaving carriers for the CFTR-DTC drive of induction machines were presented, and the Interleavingsimulation carriers and experimental for the CFTR-DTC results were drive evaluate of inductiond. The interleavingmachines were carrier-based presented, CFTR-DTC and the is simulationcapable and ofexperimental reducing the results impact wereof Ohmic evaluate voltaged. The drop interleaving when long null-voltagecarrier-based vectors CFTR-DTC are selected is capable forof reducingthe low-speed the impact region. of In Ohmic addition, voltage the simulationdrop when and long experiment null-voltage showed vectors that are the selected proposed for the carrierslow-speed can region.achieve fastIn addition, dynamic torquethe simulation performance. and Various experiment frequencies showed of thethat interleaving the proposed carrier carriers werecan achieve designed fast in dynamic the experimental torque performance. implementation Various considering frequencies the ofdiscrete the interleaving nature of DSPs. carrier The were designed in the experimental implementation considering the discrete nature of DSPs. The

Electronics 2019, 8, 820 14 of 15

6. Conclusions Interleaving carriers for the CFTR-DTC drive of induction machines were presented, and the simulation and experimental results were evaluated. The interleaving carrier-based CFTR-DTC is capable of reducing the impact of Ohmic voltage drop when long null-voltage vectors are selected for the low-speed region. In addition, the simulation and experiment showed that the proposed carriers can achieve fast dynamic torque performance. Various frequencies of the interleaving carrier were designed in the experimental implementation considering the discrete nature of DSPs. The interleaving carriers with large frequencies produced the best torque dynamic performance and fewer torque and ﬂux ripples. In addition, the CFTR-DTC with interleaving carriers has been investigated under large load disturbance and showed excellent robustness in the simulation and experimental results. The main advantages of the proposed methods are their simplicity and simultaneously retaining the CFTR features of torque ripple reduction and constant switching frequency. The eﬀectiveness of the proposed methods was demonstrated with simulation and experimental results.

Author Contributions: Supervision, K.-B.L.; writing—original draft, I.M.A. Funding: This research was supported by Korea Electric Power Corporation. (Grant number: R19XO01-20). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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