energies

Article Performance Enhancement of Direct -Controlled Permanent with a Flexible Switching Table

Ahmed Nasr 1 , Chunyang Gu 1,* , Serhiy Bozhko 1,2 and Chris Gerada 1,2 1 Key Laboratory of More Electric Aircraft Technology of Zhejiang Province, University of Nottingham Ningbo China, Ningbo 315100, China; [email protected] (A.N.); [email protected] or [email protected] (S.B.); [email protected] or [email protected] (C.G.) 2 PEMC Group, University of Nottingham, Nottingham NG7 2RD, UK * Correspondence: [email protected]; Tel.: +86-574-8818-0000 (ext. 8628)

 Received: 7 March 2020; Accepted: 8 April 2020; Published: 14 April 2020 

Abstract: In this paper, a flexible switching table (FST) for direct torque control (DTC) of permanent magnet synchronous motors (PMSMs) was proposed to enhance the steady-state and dynamic performances of the drive system. First, the influence of each converter output vectors on the torque and flux deviation rates was analyzed to assess the voltage selection strategies of the conventional STs and their impact on the DTC system’s performance. Then, a new flexible ST was proposed which uses a simple algorithm to adaptively select the appropriate voltage vector for two of its states according to the system operating condition. The effectiveness and feasibility of the proposed FST were verified through a comparative evaluation with the conventional STs using experimental results obtained from a 0.75 kW PMSM drive system.

Keywords: direct torque control (DTC); permanent magnet synchronous motor (PMSM); voltage vector selection; switching table (ST)

1. Introduction In recent years, permanent magnet synchronous motor (PMSM)-based drive systems are extensively adopted in a variety of applications, such as electric propulsion systems and robotics, because of its high power density, high efficiency, and maintenance-free operation [1]. To allow high-performance operation for PMSM, several control methods are presented in literature such as current (CVC), direct torque control (DTC), and model predictive control (MPC) [2–4]. Direct torque control becomes attractive for applications that desire fast torque response and strong robustness with the motor parameter variation [5,6]. These are because the DTC technique eliminates the pulse width modulation (PWM) and the parameters dependence as compared with the widely used CVC techniques. Moreover, elimination of the current control loops and their associated coordinates transformation makes sensorless control of PMSM using DTC achievable if the initial rotor position is approximately estimated to calculate the initial stator flux linkage [7]. However, efforts are dedicated to solve performance issues of DTC, such as high torque and stator flux ripples, and the variable switching frequency of the inverter [8–11]. Figure1 shows the block diagram of the switching table (ST)-based DTC scheme. The basic idea of this control method depends on selecting appropriate voltage vector from an ST to force the torque re f re f and stator flux to follow predefined reference values (Te , ψs ). The selection of the voltage vector relies on detecting the required deviation direction in the torque and the stator flux (KT, Kψ) by two hysteresis regulators, and the angular position of the stator flux vector (θs) using flux estimator [6].

Energies 2020, 13, 1907; doi:10.3390/en13081907 www.mdpi.com/journal/energies Energies 2020, 13, x FOREnergies PEER2020 REVIEW, 13, 1907 2 of 15 2 of 14

𝑇 𝛫 Voltage 𝑆 + vector ST − 𝑆 𝑇 2L-VSI PMSM + 𝛫 𝑆 𝜓 − 𝜓 x Hysteresis 𝐼 Encoder regulators Sector selector 𝑉 𝜃 abc to αβ Torque and 𝐼 flux estimation 𝜃

Figure 1. Block diagram of the switching table (ST)-based direct torque control (DTC) technique for Figure 1. Block diagrampermanent of magnet the switching synchronous motor table (PMSM). (ST)-based direct torque control (DTC) technique for permanent magnetCompared synchronous with other motor DTC (PMSM) schemes, such. as deadbeat DTC [12], model predictive DTC (MPDTC) [13,14], fuzzy logic-based DTC [15], and duty ratio modulation based DTC (DDTC) [16], the main advantages of the ST-based DTC are fewer computation requirements, ease of implementation, Compared withlower other switching DTC frequency schemes, even if a higher such sampling as frequency deadbeat is used, andDTC more robustness[12], model against predictive DTC the parameter variation of the machine [2]. However, these advantages are provided at the cost of (MPDTC) [13,14], fuzzyhigher torque logic-based and stator flux DTC ripples and[15], the needand for duty a high sampling ratio ratemodulation for digital implementation based DTC (DDTC) [16], the main advantagesto provide of adequate the steady-stateST-based performance. DTC These ar aree becausefewer the selectedcomputation voltage vector fromrequirements, the ease of ST is applied for the whole sampling period [6]. implementation, lowerDi ffswitchingerent STs are proposed frequency in References even [17– 21if] whicha higher vary according sampling to the number freque of levelsncy of is used, and more robustness againstthe the torque parameter hysteresis controller, variation the inclusion of of theth zeroe voltagemachine vectors (ZVVs),[2]. However, and sector boundaries. these advantages are In 1997, the application of DTC in PMSM was firstly reported in Reference [18] using a two-level provided at the cost(2L) of hysteresis higher torque torque controller and and stator an ST that flux employs ripples only the and six active the voltageneed vectors for a (AVVs) high sampling rate for of the two-level voltage source inverter (2L-VSI). In Reference [19], the role of ZVVs in DTC systems digital implementationof PMSM to was provide investigated, adequate and a DTC strategysteady-s wastate proposed performance. using a three-level These hysteresis are torque because the selected voltage vector fromcomparator the ST andis anapplied ST similar for to the the basic whole one which sampling was proposed in period Reference [[6].17] for the induction motors (IMs). It was revealed in Reference [19] that the torque ripple of the DTC system can be reduced Different STs areusing proposed ZVVs, because theyin References cause torque reduction [17–21] with a lowerwhich rate than vary that ofaccording the AVVs. A modified to the number of levels of the torque hysteresisversion of thecontroller, basic ST is presented the ininclusio Reference [20n ] byof redefining the zero the boundaries voltage of the vectors sectors where (ZVVs), and sector the stator flux vector is located. The main control objective of this modification was the torque ripple boundaries. In 1997,reduction; the application however, it caused of a higherDTC stator in fluxPMSM ripple. Thewas effect firstly of using ZVVsreported at only one in state Reference of [18] using a the ST was studied in Reference [21], and the simulation results show that it can be beneficial for the two-level (2L) hysteresissteady-state torque performance controller and the average and switching an ST frequency.that employs However, theonly dynamic the response six active of voltage vectors (AVVs) of the two-levelthe torque voltage was not considered. source In inverter addition, according (2L-VSI). to the analysis In Reference of the ZVVs’ e[19],ffect on the the DTC role of ZVVs in DTC of the PMSM presented in Reference [19], it is supposed to deteriorate when a torque reduction is systems of PMSM wascommanded. investigated Moreover, from, and a practical a DTC point strategy of view, the controlwas algorithmproposed has to using be insensitive a three-level to hysteresis torque comparator theand direction an ofST rotation, similar but the to proposed the basic ST in Reference one which [21] will not was allow proposed the motor speed in reversal, Reference [17] for the as it employs ZVVs to reduce the torque and the stator flux. induction motors (IMs).In this It paper,was the revealed torque and stator in fluxRefere deviationsnce with [19] the dithatfferent the output torque voltage vectorsripple were of the DTC system analyzed to reveal the pros and cons of employing the aforementioned STs in PMSM DTC. Then, a new can be reduced usingflexible ZVVs, ST and abecause simple voltage they selection cause algorithm torque were proposedreduction for optimal with utilization a lower of both rate than that of the AVVs. A modified ZVVsversion and AVVs of the to improve basic the ST overall is presented performance. Furthermore,in Reference these STs [20] were by comparatively redefining the boundaries evaluated in terms of different performance indices through experimental results obtained from a of the sectors where0.75 the kW PMSMstator drive flux system. vector Finally, is some locate conclusionsd. The were drawnmain to control summarize theobjective results. of this modification was the torque ripple reduction; however, it caused a higher stator flux ripple. The effect of using ZVVs at only one state of the ST was studied in Reference [21], and the simulation results show that it can be beneficial for the steady-state performance and the average switching frequency. However, the dynamic response of the torque was not considered. In addition, according to the analysis of the ZVVs’ effect on the DTC of the PMSM presented in Reference [19], it is supposed to deteriorate when a torque reduction is commanded. Moreover, from a practical point of view, the control algorithm has to be insensitive to the direction of rotation, but the proposed ST in Reference [21] will not allow the motor speed reversal, as it employs ZVVs to reduce the torque and the stator flux. In this paper, the torque and stator flux deviations with the different output voltage vectors were analyzed to reveal the pros and cons of employing the aforementioned STs in PMSM DTC. Then, a new flexible ST and a simple voltage selection algorithm were proposed for optimal utilization of both ZVVs and AVVs to improve the overall performance. Furthermore, these STs were comparatively evaluated in terms of different performance indices through experimental results obtained from a 0.75 kW PMSM drive system. Finally, some conclusions were drawn to summarize the results.

2. Analysis of DTC for PMSM

2.1. Machine Model and DTC Concept In DTC, the electrical dynamic behavior of a surface-mounted PMSM is preferable to be represented in the stationary reference frame (αβ) to avoid complex rotor frame transformation, as follows [22]:

Energies 2020, 13, x FOR PEER REVIEW 3 of 14 Energies 2020, 13, 1907 3 of 15

𝑑𝜓 𝑉 =𝑅𝐼 + , (1) 2. Analysis of DTC for PMSM 𝑑𝑡

2.1. Machine Model and DTC Concept 𝜓 =𝐿𝐼 +𝜓, (2) In DTC, the electrical dynamic behavior of a surface-mounted PMSM is preferable to be represented in the stationary reference frame (αβ) to3𝑝 avoid complex rotor frame transformation, as follows [22]: 𝑇 = Im𝜓∗ 𝐼 , (3) 2 dψsαβ Vsαβ = RsIsαβ + , (1) where 𝜓 =𝜓𝑒 and 𝜓 =𝜓𝑒 . Substituting (2) intodt (3), the torque equation can be rewritten as follows: ψsαβ = LsIsαβ + ψrαβ, (2) 3𝑝𝜓𝜓 3p   𝑇 = Te = 𝑠𝑖𝑛(𝜃Im ψ−𝜃∗ Is),αβ , (3) (4) 2𝐿 2 sαβ

jθs jθr while the statorwhere fluxψsαβ can= ψs bee reformulatedand ψrαβ = ψ f e as. shown Substituting in (5) (2) after into (3), integrating the torque equationEquation can (1) be for rewritten a sampling as follows: period of Ts. 3pψ f ψs Te = sin(θs θr), (4) 2Ls − while the stator flux can𝜓 be reformulated=𝑉𝑇 −𝑅 as shown𝐼 in (5) 𝑑𝑡 after+𝜓 integrating, Equation (1) for a sampling (5) period of Ts. Z t0+Ts Equation (4) implies that the torque can be controlled by changing0 the angle between the stator ψs = Vs Ts Rs Is dt + ψ , (5) αβ αβ − αβ sαβ flux vector and the rotor (𝛿=𝜃 −𝜃). Because the electricalt0 time constant of the machine is normally much smaller thanEquation the (4) mechanical implies that thetime torque constant, can be controlledthis angle by can changing be changed the angle betweenby manipulating the stator the flux vector and the rotor (δ = θs θr). Because the electrical time constant of the machine is normally stator flux vector. According to (5), the− stator flux vector moves in the direction of the stator voltage much smaller than the mechanical time constant, this angle can be changed by manipulating the stator vector (𝑉) as illustrated in Figure 2. Thus, both the torque and the stator flux amplitude can be flux vector. According to (5), the stator flux vector moves in the direction of the stator voltage vector controlled by selecting the proper voltage vector from the eight voltage vectors (V0–V7) that are (Vsαβ) as illustrated in Figure2. Thus, both the torque and the stator flux amplitude can be controlled provided byby a selecting 2L-VSI. the To proper achieve voltage that, vector the fromtorque the an eightd the voltage stator vectors flux (V are0–V first7) that estimated are provided using by a either the voltage2L-VSI. or the To achievecurrent that, models the torque given and by the (1) stator an fluxd (2), are firstrespectively estimated using[23]. either Then, the two voltage hysteresis or regulators theare currentused to models decide given whether by (1) andan (2),increase respectively or decrease [23]. Then, in the two controlled hysteresis regulators variables are is used required dependingto on decide the whetherhysteresis an increaseband limits or decrease (±h) inand the the controlled error variablesbetween is requiredthe estimated depending and on reference the hysteresis band limits ( h) and the error between the estimated and reference values. Based on the ± values. Basedhysteresis on the controllers’ hysteresis outputs controllers’ and the sector output wheres theand stator the fluxsector vector where is located, the thatstator can flux be one vector of is 1 6 located, thatsix can sectors be (Sone1–S of6), thesix voltagesectors vector (S –S is), selected the voltage from an vector ST. is selected from an ST.

β-axis

V3 (010) V2 (110) V𝑇 𝜓 S2 S3 𝜓 𝛿 𝜓 𝜃 𝜃 α-axis

V4 (011) S4 V0 (000) V1 (100) V7 (111) S1 S6 S5 V (001) 5 V6 (101) FigureFigure 2. Basic 2. Basic concept concept of of DTC DTC..

2.2. Conventional STs There are four main STs utilized in DTC of PMSM, as shown in Table 1, which are designated as BST, MBST, AST, and ZST, respectively, in this work for simplicity. They vary in terms of the number of levels of the torque hysteresis controller, the inclusion of the ZVVs, and sector boundaries. The basic switching table (BST) was originally proposed in Reference [17] for the IM and applied for PMSM in References [19] and [2]. This ST needs a three-level hysteresis controller for the torque and includes both AVVs (V1–V6) and ZVVs (V0, V7). In this case, if both of 𝑇 and 𝜓 are required to rise th (𝛫 = 1, 𝛫 = 1), the AVVs that keep 𝜓 rotating in the same direction are employed based on the x sector where the stator flux vector is located. Therefore, the angle δ increases and the actual torque increases as well. Once the estimated value of 𝑇 reaches the reference value (𝛫 = 0), the ZVVs are

Energies 2020, 13, 1907 4 of 15

2.2. Conventional STs There are four main STs utilized in DTC of PMSM, as shown in Table1, which are designated as BST, MBST, AST, and ZST, respectively, in this work for simplicity. They vary in terms of the number of levels of the torque hysteresis controller, the inclusion of the ZVVs, and sector boundaries. The basic switching table (BST) was originally proposed in Reference [17] for the IM and applied for PMSM in References [2,19]. This ST needs a three-level hysteresis controller for the torque and includes both AVVs (V1–V6) and ZVVs (V0,V7). In this case, if both of Te and ψs are required to rise (Kψ = 1, KT = 1), th the AVVs that keep ψs rotating in the same direction are employed based on the x sector where the stator flux vector is located. Therefore, the angle δ increases and the actual torque increases as well. Once the estimated value of Te reaches the reference value (KT = 0), the ZVVs are selected. If the actual Te becomes greater than the reference value (KT = 1), the AVVs that make ψs moving in the reverse − direction are selected to reduce δ.

Table 1. Voltage selection of the conventional STs.

Voltage Selection Kψ KT BST MBST AST ZST

1 Vx + 1 Vx + 1 Vx + 1 Vx + 1 1 0 ZVV ZVV - - 1 Vx 1 Vx Vx 1 Vx 1 − − − − 1 Vx + 2 Vx + 3 Vx + 2 Vx + 2 1 0 ZVV ZVV - - − 1 Vx 2 Vx 2 Vx 2 ZVV − − − −

For the aim of torque ripple reduction, the modified basic switching table (MBST) was developed in Reference [20] which follows the same conditions of BST, but the AVVs are selected based on modified sector boundaries which become on the six AVVs themselves instead of those of the traditional sector shown in Figure1. Other studies, such as Reference [ 18], show that DTC of PMSM can work well only when the ZVVs are eliminated as in AST, where a 2L hysteresis torque regulator is required. The reason for this is the reduction of ψs due to the stator resistance drop when a ZVV is applied, according to (5). As a result, the stator flux will behave in a way that contradicts what is practically needed at the state “Kψ = 1, KT = 0” of either BST or MBST. In contrast to the previous viewpoint, the rule of ZVVs in PMSM DTC was comprehensively investigated in Reference [19], and it was concluded that the inclusion of ZVVs in ST can improve the system performance. Consequently, ZST was proposed in Reference [21] where the torque needs a 2L hysteresis controller, and ZVVs are employed in case both of the torque and stator flux amplitude are required to decrease (K = 1, KT = 1). Additionally, it was compared with BST and showed better ψ − − steady-state performance with reduced average switching frequency and torque ripple. Owing to the inconsistent viewpoints for the voltage vector selection employed in the conventional STs, a comparative evaluation for their performance can be useful for identifying the main features and drawbacks of each.

2.3. Analyzing the Voltage Selection in the Conventional ST Because the selected voltage vector is applied for the whole control period in ST-DTC, the lower the torque and stator flux deviations produced by the selected voltage vector, the better the steady-state and the slower the dynamic response the system can achieve and vice versa [2]. Hence, analyzing the effect of each voltage vector on the torque and stator flux deviations during one sampling period was used in this work to assess the voltage selection strategy of each ST. From (2) and (3), the torque and stator flux deviation rates can be written as [22]:   dTe 3p   Rs     = Im Vsαβψrαβ Im ψsαβψrαβ ωrRe ψsαβψrαβ , (6) dt 2Ls − Ls − Energies 2020, 13, x FOR PEER REVIEW 5 of 14

It can be observed in Figure 3a that V2 and V3 are the only available options to increase the torque in sector S1 under all operating conditions. Therefore, employing Vx+1 for the state “훫휓 = 1, 훫푇 = 1” and

Vx+2 for the state “훫휓 = −1, 훫푇 = 1” is the optimal solution for BST, AST, and ZST. Moreover, both V1 and V6 can provide negative torque deviation and positive stator flux variation, but V6 is a better choice in this case because of the conflicting torque behavior caused by V1, especially at low-speed and high loading conditions. Thus, selecting Vx−1 for the state “훫휓 = 1, 훫푇 = −1” of BST, AST, and ZST is the best option. Because ZVVs produce very low deviations in the stator flux (around −0.03%), they are acceptable to be used at the states where 훫푇 = 0 in BST and MBST. However, they are more efficiently employed for the state “훫휓 = −1, 훫푇 = −1” in ZST because of their negative produced torque deviations. Moreover, utilizing ZVVs at this state, instead of Vx−2 in AST, can reduce the steady-state ripples, because ZVVs cause lower torque and stator flux deviations than those of V5 as shown in Figure 3a. For the same reason, this will impair the dynamic response of ZST when a torque decrease is demanded. In addition, during speed reversal, the torque deviation rate of ZVVs becomes positive as implied by the second and third terms of Equation (6); thus, selecting a ZVV when 훫푇 = −1 to achieve this task in ZST will cause system instability. Instead, ZVV and V5 are superior choices to be employed during reverse rotation of the motor for the states “훫휓 = 1, 훫푇 = 1” and “훫휓 = −1, 훫푇 = −1”, respectively, in ZST. With the modified sector boundaries, it can be noted from Figure 3b that all AVVs employed in Energies 2020, 13, 1907 5 of 15 MBST when x = 1, i.e., V2, V1, V4, and V5, provide lower torque deviations and higher stator flux deviations compared with V2, V6, V3, and V5, respectively, which are used with the traditional sector dψs 1    = Re ψs∗αβ Vsαβ RsIsαβ , (7) boundaries (see Figure 3a). As a result,dt MBSTψs can provide− lower torque ripple at low speed, and higher stator fluxwhere rippleωr = d θthanr/dt is that the electrical of the angular BST. Additional speed of the rotor.ly, both V4 and V2 fail to increase the torque, especially at high operatingThe abovementioned speed, equations which reveal weakens that the the effect effectiveness of the applied voltage of voltage vector on vector the torque selection based and stator flux deviations varies according to the operating conditions. Thus, the average deviations of on the modifiedthe sector torque and boundaries. the stator flux within each sector, produced by each voltage vector, were calculated for Accordingthe to PMSM the underaforementioned test, with the parameters analysis, given the in AppendixvoltageA vectors, at di fferent are operating more conditions.efficiently selected in Figure3 shows the resulting calculations when the stator flux vector was located at S 1, as an example, ZST for steadywith-state the traditionaloperation, and modifiedwhile sectoremploying boundaries. those The machine of AST operated will atbe steady-state more suitable with a short during system transients. However,sampling period the main (Ts = 25 drawbackµs) to allow the of assumption ZST is that that the it deviation does notrates of allow the torque reversing and the the rotation direction. stator flux during this period were constants [16].

(a)

(b)

Figure 3. AverageFigure torque 3. Average and torque stator and statorflux fluxdeviations deviations inin percentage percentage of their of rated their values, rated produced values by, produced by each voltage vector at different operating conditions, sampling period of 25 µs, and x = 1 with (a) the each voltage vectortraditional at different sector boundaries operating (θs [ 30 conditions,, 30 ]) and (b) sampling the modified boundariesperiod of (θ 25s [0μs,, 60 and]). x = 1 with (a) the ∈ − ◦ ◦ ∈ ◦ ◦ traditional sector boundaries (휃푠 ∈ [−30°, 30°]) and (b) the modified boundaries (휃푠 ∈ [0°, 60°]). It can be observed in Figure3a that V 2 and V3 are the only available options to increase the torque in sector S1 under all operating conditions. Therefore, employing Vx+1 for the state “Kψ = 1, KT = 1” and Vx for the state “K = 1, KT = 1” is the optimal solution for BST, AST, and ZST. Moreover, +2 ψ − both V1 and V6 can provide negative torque deviation and positive stator flux variation, but V6 is a better choice in this case because of the conflicting torque behavior caused by V1, especially at Energies 2020, 13, 1907 6 of 15

low-speed and high loading conditions. Thus, selecting Vx 1 for the state “Kψ = 1, KT = 1” of BST, − − AST, and ZST is the best option. Because ZVVs produce very low deviations in the stator flux (around 0.03%), they are acceptable − to be used at the states where KT = 0 in BST and MBST. However, they are more efficiently employed for the state “K = 1, KT = 1” in ZST because of their negative produced torque deviations. Moreover, ψ − − utilizing ZVVs at this state, instead of Vx 2 in AST, can reduce the steady-state ripples, because ZVVs − cause lower torque and stator flux deviations than those of V5 as shown in Figure3a. For the same reason, this will impair the dynamic response of ZST when a torque decrease is demanded. In addition, during speed reversal, the torque deviation rate of ZVVs becomes positive as implied by the second and third terms of Equation (6); thus, selecting a ZVV when KT = 1 to achieve this task in ZST will − cause system instability. Instead, ZVV and V5 are superior choices to be employed during reverse rotation of the motor for the states “K = 1, KT = 1” and “K = 1, KT = 1”, respectively, in ZST. ψ ψ − − With the modified sector boundaries, it can be noted from Figure3b that all AVVs employed in MBST when x = 1, i.e., V2,V1,V4, and V5, provide lower torque deviations and higher stator flux deviations compared with V2,V6,V3, and V5, respectively, which are used with the traditional sector boundaries (see Figure3a). As a result, MBST can provide lower torque ripple at low speed, and higher stator flux ripple than that of the BST. Additionally, both V4 and V2 fail to increase the torque, especially at high operating speed, which weakens the effectiveness of voltage vector selection based on the modified sector boundaries. According to the aforementioned analysis, the voltage vectors are more efficiently selected in ZST for steady-state operation, while employing those of AST will be more suitable during system transients. However, the main drawback of ZST is that it does not allow reversing the rotation direction.

3. Proposed Flexible ST and Voltage Selection Strategy

From the aforementioned analysis, selecting ZVV at the state “K = 1, KT = 1” can be beneficial ψ − − for the steady-state performance, but this will cause slow torque response when a reduction is commanded. Furthermore, the ZVV at this state cannot achieve speed reversal, as in case of ZST. To overcome these two issues, AVV (Vx 2) is the optimal choice to be applied. To keep the steady-state − performance of ZST while rotation in the reverse direction, ZVV needs to be employed at the state “Kψ = 1, KT = 1” instead of Vx+1 because the torque deviation of the former becomes less positive. Therefore, for overall performance enhancement of ST-DTC technique, the voltage vector selection criteria need to be more flexible by considering additional factors besides the traditional factors, i.e., the system operating state and the direction of rotation. Table2 shows the proposed flexible switching table (FST). The voltage vectors at two states of this ST, (K = 1, KT = 1) and (K = 1, KT = 1), are flexibly selected depending on the system operating ψ ψ − − state and the direction of rotation. This is achievable using a simple voltage selection strategy whose flowchart is illustrated in Figure4. As can be seen in the flowchart, the system operating state can be re f re f re f detected by the reference torque transition (∆Te (k) = Te (k) Te (k 1)) to avoid the usage of − − torque sensor that will increase the system cost and complexity. If any change in the demanded torque re f is detected (∆Te (k) , 0), AVVs will be activated for all states of the ST to achieve fast torque response. This activation has to be kept until the torque error (T err(k)) reaches a value within the hysteresis e err band of the torque controller ( Te (k) hT), and the direction of rotation becomes the same as that re f ≤ of the reference torque (Te (k) ωr 0) to allow speed reversal if required. Thus, maintaining the × ≥ AVVs activated is guaranteed using a “flag” that will reset only when either of the aforementioned re f conditions is not satisfied. On the other hand, as long as no torque transition is detected (∆Te (k) = 0), which means that the system operates in steady-state mode, ZVVs will be activated at only one state based on the direction of rotation which can be detected by the position sensor. Following this strategy allows overcoming the drawbacks associated with ZST. Energies 2020, 13, x FOR PEER REVIEW 6 of 14

3. Proposed Flexible ST and Voltage Selection Strategy

From the aforementioned analysis, selecting ZVV at the state “𝛫 = −1, 𝛫 = −1” can be beneficial for the steady-state performance, but this will cause slow torque response when a reduction is commanded. Furthermore, the ZVV at this state cannot achieve speed reversal, as in case of ZST. To overcome these two issues, AVV (Vx−2) is the optimal choice to be applied. To keep the steady-state performance of ZST while rotation in the reverse direction, ZVV needs to be employed at the state

“𝛫 = 1, 𝛫 = 1” instead of Vx+1 because the torque deviation of the former becomes less positive. Therefore, for overall performance enhancement of ST-DTC technique, the voltage vector selection criteria need to be more flexible by considering additional factors besides the traditional factors, i.e., the system operating state and the direction of rotation. Table 2 shows the proposed flexible switching table (FST). The voltage vectors at two states of this ST, (𝛫 = 1, 𝛫 = 1) and (𝛫 = −1, 𝛫 = −1), are flexibly selected depending on the system operating state and the direction of rotation. This is achievable using a simple voltage selection strategy whose flowchart is illustrated in Figure 4. As can be seen in the flowchart, the system operating state can be detected by the reference torque transition (Δ𝑇 (𝑘) =𝑇 (𝑘) − 𝑇 (𝑘 − 1)) to avoid the usage of torque sensor that will increase the system cost and complexity. If any change in the demanded torque is detected (Δ𝑇 (𝑘) ≠ 0), AVVs will be activated for all states of the ST to achieve fast torque response. This activation has to be kept until the torque error (𝑇 (𝑘)) reaches a value within the hysteresis band of the torque controller (|𝑇 (𝑘)| ≤ hT), and the direction of rotation becomes the same as that of the reference torque (𝑇 (𝑘) ×𝜔 ≥ 0) to allow speed reversal if required. Thus, maintaining the AVVs activated is guaranteed using a “flag” that will reset only when either of the aforementioned conditions is not satisfied. On the other hand, as long as no torque transition is detected (Δ𝑇 (𝑘)= 0), which means that the system operates in steady-state mode, ZVVs will be activated at only one state based on the direction of rotation which can be detected by the position sensor. Following this strategy allows overcoming the drawbacks associated with ZST.

Table 2. Proposed flexible switching table (FST). Energies 2020, 13, 1907 7 of 15

𝛫 𝛫 Voltage Selection Table 2. Proposed flexibleVx switching+ 1 table (FST). 1 1 Kψ KT Voltage SelectionZVV −1 1 Vx +V1 x − 1 1 ZVV

1 1Vx V +x 2 1 − − 1 Vx −1 1 Vx − 2 + 2 − −1 1 Vx 2 − − ZVVZVV

Start

k = 1, flag = 0, Vi (k − 1) =V0

Calculate: ∆𝑇 (k) = 𝑇 (k)−𝑇 (k − 1) 𝑇 (k) = 𝑇 (k)−𝑇(k) Wait for the next Yes No sampling instant flag = 1 ∆𝑇 (k)≠ 0

Use AVVs at all ST states flag = 0 No Update Vi (k − 1) Yes V(k − 1) ∈ {V , No Ye s |𝑇 (k)| ≤ ℎ i 0 AND V1, V3, V5} (𝑇 (k) × 𝜔 )≥0 Yes flag = 0 ZVV = V ZVV = V No 0 7 No 𝜔 ≥ 0 Yes

Use ZVV at state (𝛫 = 1, 𝛫 = 1) Use ZVV at state (𝛫 = −1, 𝛫 = −1)

Figure 4. Figure 4. FlowchartFlowchart of voltage of voltage vector vector selection selection strategy strategy for the for proposed the proposed FST. FST. For further steady-state performance improvement, the switching frequency can be reduced by th carrying out a trade-off between employing V0 or V7 at the k sample when the ZVVs are activated in the proposed FST. This was fulfilled by checking the selected voltage vector at the previous sampling instant (V (k 1)); if it is V ,V ,V or V , the ZVV “V ” will be employed, while V will follow the i − 0 1 3 5 0 7 other voltage vectors to minimize the number of switching instances. In this way, the proposed ST is flexible because, unlike conventional STs, it does not have a fixed structure, but it takes changing forms according to the working condition of the DTC system and, hence, exploiting the benefits of employing both AVVs and ZVVs in the ST more efficiently. The effectiveness of the proposed FST and the voltage selection strategy will be confirmed by the experimental results in the next section.

4. Experimental Results Experimental verifications were carried out on a 0.75 kW PMSM (ACSM80G02430LZ) to validate the effectiveness of the proposed FST. Figure5 illustrates the schematic diagram and the corresponding experimental setup for the PMSM drive system used in this work. The PMSM was fed by a 2L-VSI using the SiC MOSFET power module (CCS050M12CM2, CREE, North Carolina, USA) and its gate driver board (CGD15FB45P1). The DC-side of the inverter consisted of a 220 V DC power supply and 20*10 µF voltage stabilizing capacitors (MKP1848S1010JY, VISHAY, Pennsylvania, USA). The stator currents and the DC-side voltage were measured via HAIS 50-P and LV 25-P Hall sensors, respectively, produced by Energies 2020, 13, x FOR PEER REVIEW 7 of 14

For further steady-state performance improvement, the switching frequency can be reduced by carrying out a trade-off between employing V0 or V7 at the kth sample when the ZVVs are activated in the proposed FST. This was fulfilled by checking the selected voltage vector at the previous

sampling instant ( 푖(푘 1)); if it is V0, V1, V3 or V5, the ZVV “V0” will be employed, while V7 will follow the other voltage vectors to minimize the number of switching instances. In this way, the proposed ST is flexible because, unlike conventional STs, it does not have a fixed structure, but it takes changing forms according to the working condition of the DTC system and, hence, exploiting the benefits of employing both AVVs and ZVVs in the ST more efficiently. The effectiveness of the proposed FST and the voltage selection strategy will be confirmed by the experimental results in the next section.

4. Experimental Results Experimental verifications were carried out on a 0.75 kW PMSM (ACSM80G02430LZ) to validate the effectiveness of the proposed FST. Figure 5 illustrates the schematic diagram and the corresponding experimental setup for the PMSM drive system used in this work. The PMSM was fed by a 2L-VSI using the SiC MOSFET power module (CCS050M12CM2, CREE, North Carolina, USA) and its gate driver board (CGD15FB45P1). The DC-side of the inverter consisted of a 220 V DC power supply and 20*10 μF voltage stabilizing capacitors (MKP1848S1010JY, VISHAY, Pennsylvania, USA). The stator currents and the DC-side voltage were measured via HAIS 50-P and LV 25-P Hall sensors, respectively, produced by LEM (Geneva, Switzerland). The DTC scheme, shown in Figure 1, was simulated in MATLAB/Simulink (The MathWorks, Massachusetts, USA) and realized using the MicroLabBox (DS1202, dSPACE GmbH, Paderborn, Germany) rapid control-prototyping system which also can accomplish the sampling tasks of the measured voltage and currents; the rotor angular position and speed were obtained from an incremental encoder that had a resolution of 2500 pulses Energies 2020, 13, 1907 8 of 15 per revolution; the motor shaft was coupled to an electromagnetic brake fed from a 24 V variable DC- supply to control the load torque. 푟푒푓 푟푒푓 LEMIt (Geneva, should beSwitzerland). noted that The휓푠 DTC was scheme, obtained shown from in Figurethe demanded1, was simulated torque in (𝑇푒 MATLAB) based/Simulink on the maximum(The MathWorks, torque Massachusetts,per ampere principle USA) and using realized Equation using (8) the to MicroLabBox increase the (DS1202, system dSPACEefficiency GmbH, [22], whereasPaderborn, the Germany)torque and rapid stator control-prototyping flux estimations were system fulfilled which using also (2) can and accomplish (3) for simplicity the sampling. tasks

of the measured voltage and currents; the rotor angular position and speed were obtained from an 2퐿 𝑇푟푒푓 incremental encoder that had a resolution휓푟푒푓 = √ of휓 2500 ( pulsess 푒 ) per revolution; the motor shaft was coupled 푠 푓 3푝휓 (8) to an electromagneticC brake fed from a 24 V variable DC-supply푓 to control the load torque.

13 PC 1 220 V DC 9 Power Supply Voltage _ + sensing Host-PC AI circuit 2 dSPACE DS1202 DC-link Capacitors (LV 25-P) DTC algorithm MKP1848S1010JY DI/O 10 8 Current 3 SiC MOSFET sensing circuit C C 11 (HAIS 50-P) Interface Module, CREE, CCS050M12CM2 Board 1 and Gate Driver, 7 CGD15FB45P1 24 V DC Gate Supply signals _ 12 + Interface 6 4 PMSM Controllable Board 2 electromagnetic ACSM8G02430LZ 5 brake (3A) Incremental encoder (a) (b)

FigureFigure 5. 5. PMSMPMSM-based-based drive drive system: system: (a ()a )Schematic Schematic diagram; diagram; (b (b) )Experimental Experimental setup. setup.

re f re f TheIt should effectiveness be noted of that theψ proposeds was obtained FST was from verified the demanded through comparative torque (Te ) basedassessment on the with maximum BST, MBST,torque AST, per ampere and ZST principle in terms using of the Equation steady (8)-state to increase and the the dynamic system performances efficiency [22 ], provided whereas by the applyingtorque and each stator ST in flux the estimations DTC system, were and fulfilled collecting using the (2) experimental and (3) for simplicity.results under the same control parameters, given in Appendix A, as used in the analysis presented in Section 2. The experimental uv t  re f 2 2L T  re f 2  s e  ψs = ψ f +   (8)  3pψ f 

The effectiveness of the proposed FST was verified through comparative assessment with BST, MBST, AST, and ZST in terms of the steady-state and the dynamic performances provided by applying each ST in the DTC system, and collecting the experimental results under the same control parameters, given in AppendixA, as used in the analysis presented in Section2. The experimental results were captured by ControlDesk software installed on a PC connected to the MicroLabBox, and then drawn using MATLAB. First, the DTC steady-state performances provided by the conventional STs and proposed FST were compared under the same operating conditions. The reference torque was set to 1 Nm, and the load torque was adjusted using the electromagnetic brake until the speed reached the required value. Figures6 and7 show the experimental waveforms of the electromagnetic torque and the stator flux locus, respectively, at 1000 rpm. Additionally, to consider the effect of speed variation on the steady-state performances, Table3 gives quantitative comparison for all STs in terms of the torque ripple, the stator flux ripple, and the average switching frequency under three different speeds. The steady-state torque and flux ripples were calculated using (9), while the average switching frequency (fav) was obtained by averaging the total number of switching instances of the three legs of the inverter during a fixed period [2]. v t m 1 X 2 y = (y(k) yav) , (9) ripple m − k=1

where y can be the torque or the stator flux amplitude, y(k) is the instantaneous value, yav is the average value, and m is the number of samples. Energies 2020, 13, x FOR PEER REVIEW 8 of 14 results were captured by ControlDesk software installed on a PC connected to the MicroLabBox, and then drawn using MATLAB. First, the DTC steady-state performances provided by the conventional STs and proposed FST were compared under the same operating conditions. The reference torque was set to 1 Nm, and the load torque was adjusted using the electromagnetic brake until the speed reached the required value. Figures 6 and 7 show the experimental waveforms of the electromagnetic torque and the stator flux locus, respectively, at 1000 rpm. Additionally, to consider the effect of speed variation on the steady- state performances, Table 3 gives quantitative comparison for all STs in terms of the torque ripple, the stator flux ripple, and the average switching frequency under three different speeds. The steady- state torque and flux ripples were calculated using (9), while the average switching frequency (fav) was obtained by averaging the total number of switching instances of the three legs of the inverter during a fixed period [2].

푚 1 푦 = √ ∑ (푦(푘) 푦 ) , (9) 푟푖푝푝푙푒 푚 푣 푘 = 1 where 푦 can be the torque or the stator flux amplitude, 푦(푘) is the instantaneous value, 푦 푣 is the average value, and 푚 is the number of samples.

Table 3. Quantitative comparison of the STs under different operating speeds.

Speed Switching tables Index (rpm) BST MBST AST ZST FST 500 0.272 0.255 0.307 0.209 0.208

𝑇푟푖푝푝푙푒 (Nm) 1000 0.279 0.264 0.305 0.244 0.246 2000 0.274 0.431 0.299 0.263 0.263 500 3.672 4.848 3.714 3.251 3.252

휓푟푖푝푝푙푒 (mWb) 1000 3.715 4.704 3.828 3.311 3.311 2000 3.794 4.562 3.975 3.682 3.682 500 10.27 9.08 9.85 4.58 4.31

fav (kHz) 1000 9.49 8.44 9.20 5.96 5.73 2000 8.61 8.15 8.43 6.42 6.13 Energies 2020, 13, 1907 9 of 15

BST: Basic switching table (Nm) 푒 𝑇

(a)

MBST: Switching table with modified boundaries (Nm) 푒 𝑇

(b)

AST: Switching table with only active voltage vectors (Nm) 푒 𝑇

Energies 2020, 13, x FOR PEER REVIEW 9 of 14 (c)

ZST: Switching table with zero voltageFigure vector 6. Cont. at one state

(Nm) 푒 𝑇

(d)

FST: Flexible switching table (Nm) 푒 𝑇

(e)

Figure 6. FigureExperimental 6. Experimental waveforms waveforms of the of the steady steady-state-state torque torque response response at 1000 at rpm1000 and rpm 1 Nm and load: 1 Nm load: (a) BST; (b(a)) MBST; BST; (b) MBST;(c) AST; (c) AST;(d) ZST; (d) ZST; (e ()e F) FST.ST. (Reference(Reference torque: torque red,: Estimatedred, Estimated torque: blue).torque: blue). From Figures6 and7, it can be observed that the application of BST and AST gave almost an identical steady-state performance, and MBST generated lower torque ripple than them while its flux rippleBST was the highest. BothMBST ZST and FST exhibitedAST the lowest torque and statorZST flux ripples. FST According to Table3, when the machine ran at 500 or 1000 rpm, the application of MBST reduced the torque ripple compared with BST by 6% on average; however, the stator flux ripple increased by 29%. When the speed increased to 2000 rpm, the torque ripple associated with MBST became significantly higher than that of BST by 57%. By removing ZVVs from BST, as in case of AST, the torque (Wb)

and stator flux ripples increased by an average of 10% and 3%, respectively, under all operating speeds. 휓 On the other hand, utilizing ZVVs at one state in both ZST and FST achieved the highest torque and flux ripples reduction which were 32% and 12%, respectively, when compared to those of AST at 500 rpm. These torque and flux ripple reductions decreased to 12% and 7%, respectively, when the speed increased to 2000 rpm. 휓 (Wb) (a) (b) (c) (d) (e)

Figure 7. Experimental results of the steady-state response of stator flux at 1000 rpm and 1 Nm load: (a) BST; (b) MBST; (c) AST; (d) ZST; (e) FST.

From Figures 6 and 7, it can be observed that the application of BST and AST gave almost an identical steady-state performance, and MBST generated lower torque ripple than them while its flux ripple was the highest. Both ZST and FST exhibited the lowest torque and stator flux ripples. According to Table 3, when the machine ran at 500 or 1000 rpm, the application of MBST reduced the torque ripple compared with BST by 6% on average; however, the stator flux ripple increased by 29%. When the speed increased to 2000 rpm, the torque ripple associated with MBST became significantly higher than that of BST by 57%. By removing ZVVs from BST, as in case of AST, the torque and stator flux ripples increased by an average of 10% and 3%, respectively, under all operating speeds. On the other hand, utilizing ZVVs at one state in both ZST and FST achieved the highest torque and flux ripples reduction which were 32% and 12%, respectively, when compared to those of AST at 500 rpm. These torque and flux ripple reductions decreased to 12% and 7%, respectively, when the speed increased to 2000 rpm. In addition to the better performance achieved by utilizing ZVVs at one ST state during steady- state operation, the average switching frequency was significantly reduced by the proposed voltage selection strategy that carries out a trade-off between employing V0 or V7 for every control sample as mentioned in Section 3. Compared with BST, MBST, AST, and ZST, the FST provided lower average switching frequency, at all operating speeds by an average of 42%, 37%, 40%, and 5%, respectively. Apart from the steady-state performance experiments, the torque dynamic performances of the DTC system using the different STs were also tested and compared in Figures 8 and 9. In this experiment, the load torque was set to 1.8 Nm and the reference torque was stepped up from 0 to 2 Nm to test the torque response during start-up. Then, it was stepped down from 2 to −2 Nm to confirm the torque response during speed reversal. The corresponding speed responses of the machine for these two scenarios are presented to the right of the torque response in both figures.

Energies 2020, 13, x FOR PEER REVIEW 9 of 14

ZST: Switching table with zero voltage vector at one state (Nm) 푒 𝑇

(d)

FST: Flexible switching table (Nm) 푒 𝑇

(e)

Figure 6. Experimental waveforms of the steady-state torque response at 1000 rpm and 1 Nm load:

Energies(a2020) BST;, 13 (,b 1907) MBST; (c) AST; (d) ZST; (e) FST. (Reference torque: red, Estimated torque: blue). 10 of 15

BST MBST AST ZST FST (Wb)

휓

휓 (Wb) (a) (b) (c) (d) (e)

FigureFigure 7.7. Experimental results of the steady-statesteady-state response of stator fluxflux at 1000 rpm and 1 Nm load:load: ((aa)) BST;BST; ((bb)) MBST;MBST; ( (cc)) AST; AST; ( d(d)) ZST; ZST; ( e(e)) FST. FST.

Table 3. Quantitative comparison of the STs under different operating speeds. From Figures 6 and 7, it can be observed that the application of BST and AST gave almost an identical steady-state performance, and MBST generated lowerSwitching torque Tables ripple than them while its flux Index Speed (rpm) ripple was the highest. Both ZST and FST exhibitedBST the MBST lowest torque AST and stator ZST flux ripples. FST According to Table 3, when500 the machine 0.272 ran at 500 0.255 or 1000 rpm, 0.307 the application 0.209 of MBST 0.208 reduced the torqueT rippleripple(Nm) compared with1000 BST by 6% 0.279 on average; 0.264 however, 0.305 the stator 0.244 flux ripple 0.246 increased by 29%. When the speed increased2000 to 2000 0.274 rpm, the 0.431 torque ripple 0.299 associated 0.263 with MBST 0.263 became significantly higher than that500 of BST by 57%. 3.672 By removing 4.848 ZVVs 3.714 from BST, 3.251 as in case 3.252 of AST, the torque andψripple stator(mWb) flux ripples1000 increased 3.715 by an average 4.704 of 10% 3.828 and 3%, 3.311 respectively, 3.311 under all operating speeds. On the other2000 hand, utilizing 3.794 ZVVs 4.562at one state 3.975 in both ZST 3.682 and FST 3.682 achieved the highest torque and flux ripples500 reduction which 10.27 were 9.0832% and 12%, 9.85 respectively, 4.58 when 4.31compared to those of ASTfav (kHz) at 500 rpm. These1000 torque 9.49 and flux ripple 8.44 reductions 9.20 decreased 5.96 to 12% 5.73 and 7%, 2000 8.61 8.15 8.43 6.42 6.13 respectively, when the speed increased to 2000 rpm. In addition to the better performance achieved by utilizing ZVVs at one ST state during steady- stateIn operation, addition tothe the average better performanceswitching frequency achieved was by utilizing significantly ZVVs reduced at one ST by state the during proposed steady-state voltage operation,selection strategy the average that switchingcarries out frequency a trade-off was between significantly employing reduced V0 byor V the7 for proposed every control voltage sample selection as strategymentioned that in carries Section out 3. aCompared trade-off between with BST, employing MBST, AST, V0 or and V7 forZST, every the FST control provided sample lower as mentioned average inswitching Section3 frequency,. Compared at withall operating BST, MBST, speeds AST, by and an average ZST, the of FST 42%, provided 37%, 40%, lower and average 5%, respectively. switching frequency,Apart atfrom all operatingthe steady speeds-state performance by an average experiments, of 42%, 37%, the 40%, torque and dynamic 5%, respectively. performances of the DTCApart system from using the the steady-state different STsperformance were also experiments, tested and compared the torque in dynamic Figures performances 8 and 9. In this of theexperiment, DTC system the load using torque the di wasfferent set STsto 1.8 were Nm also and testedthe reference and compared torque was in Figures stepped8 andup 9from. In 0 this to 2 experiment,Nm to test the load torque torque response was set during to 1.8 Nm start and-up. the Then, reference it was torque stepped was down stepped from up from 2 to −20 to Nm 2 Nm to toconfirm test the the torque torque response response during during start-up. speed Then, reversal. it was stepped The corresponding down from 2 speed to 2 Nm responses to confirm of the − torquemachine response for these during two scenarios speed reversal. are present Theed corresponding to the right of speed the torque responses response of the in machine both figures. for these two scenarios are presented to the right of the torque response in both figures. In Figure8, it can be seen that there was insignificant di fferences between the torque rising times provided by BST, AST, ZST, and proposed FST, which was about 0.1 ms. However, it was higher in case of MBST (almost 0.2 ms), because the employed AVV at the state “Kψ = 1, KT = 1” produced lower torque deviation with the modified sector boundaries than that with the traditional sector boundaries (see Figure3). Energies 2020, 13, x FOR PEER REVIEW 10 of 14

In Figure 8, it can be seen that there was insignificant differences between the torque rising times provided by BST, AST, ZST, and proposed FST, which was about 0.1 ms. However, it was higher in case of MBST (almost 0.2 ms), because the employed AVV at the state “훫휓 = 1, 훫푇 = 1” produced lower torque deviation with the modified sector boundaries than that with the traditional sector boundaries (see Figure 3). When the reference torque decreased from 2 to −2 Nm, as shown in Figure 9, all the STs achieved almost the same torque falling time (0.2 ms) except ZST, which had a torque that took nearly 1 ms to reach the reference value. This was because the ZVV employed at the state “훫휓 = −1, 훫푇 = −1” in ZST produced lower torque deviation than the AVV used in the other STs. Additionally, the DTC system that used ZST becomes unstable when the speed dropped to zero during speed reversal, as shown in the zone (10 ms/div.) of Figure 9d, because the torque deviation provided by ZVVs also reversed as mentioned in Section 2. Conversely, FST allows faster torque drop and smooth speed reversal as can be seen in Figure 9e, because its voltage selection strategy replaces ZVV with AVV during the dynamic state of the system. After speed reversal, ZVV is activated only at the state “훫휓 = 1, 훫푇 = 1” to achieve a steady-state performance similar to that before reversing the direction of rotation. This is confirmed in the zoomed zone (2 ms/div.) of Figure 9e. Energies 2020, 13, 1907 11 of 15

BST (Nm) 푒 𝑇

(a)

MBST (Nm) 푒 𝑇

(b)

AST (Nm) 푒 𝑇

(c)

ZST (Nm) 푒 𝑇

(d)

FST (Nm) 푒 𝑇

(e)

Figure 8. FigureThe torque 8. The torquedynamic dynamic response response and and the the corresponding speed speed response response for step for change step in change the in the a b c d e reference referencetorque from torque 0 from to 2 0 Nm to 2 Nmfor forthe the different different STs:STs: ( ()a BST;) BST; ( ) ( MBST;b) MBST; ( ) AST; (c) ( AST;) ZST; ( andd) ZST; ( ) FST. and (e) FST. When the reference torque decreased from 2 to 2 Nm, as shown in Figure9, all the STs achieved − almost the same torque falling time (0.2 ms) except ZST, which had a torque that took nearly 1 ms to reach the reference value. This was because the ZVV employed at the state “K = 1, KT = 1” in ZST ψ − − produced lower torque deviation than the AVV used in the other STs. Additionally, the DTC system that used ZST becomes unstable when the speed dropped to zero during speed reversal, as shown in the zone (10 ms/div.) of Figure9d, because the torque deviation provided by ZVVs also reversed as mentioned in Section2. Conversely, FST allows faster torque drop and smooth speed reversal as can be seen in Figure9e, because its voltage selection strategy replaces ZVV with AVV during the dynamic Energies 2020, 13, 1907 12 of 15

state of the system. After speed reversal, ZVV is activated only at the state “Kψ = 1, KT = 1” to achieve a steady-state performance similar to that before reversing the direction of rotation. This is confirmed Energies 20in20 the, 1 zoomed3, x FOR zone PEER (2 REVIEW ms/div.) of Figure9e. 11 of 14

BST (Nm) 푒 𝑇

(a)

MBST (Nm) 푒 𝑇

(b)

AST (Nm) 푒 𝑇

(c)

ZST (Nm) 푒 𝑇

(d)

FST (Nm) 푒 𝑇

(e)

FigureFigure 9. The 9. torqueThe torque dynamic dynamic response response and and the the corresponding corresponding speed response speed response for step change for step in the change in the reference torque from 2 to 2 Nm for the different STs: (a) BST; (b) MBST; (c) AST; (d) ZST; and (e) FST. reference torque from 2 to −2 Nm for the different STs: (a) BST; (b) MBST; (c) AST; (d) ZST; and (e) FST.

The abovementioned results confirm the theoretical analysis presented in Section 2 and reveal that the proposed FST provides the lowest steady-state ripples in torque and stator flux as those achieved by ZST while reducing the average switching frequency and enhancing the torque decreasing response and system stability during speed reversal.

5. Conclusions This article proposed a flexible ST with a structure, unlike the conventional STs, changes according to the system operating state to improve the overall performance of the DTC system of 2L- VSI PMSM while maintaining its ease of implementation. A simple yet effective strategy used to decide the voltage vectors arrangement in the FST which only requires information about the reference torque and the rotation direction. Compared to BST, MBST, and AST, the main features achieved by FST are summarized as follows: 1) reduction of torque and stator flux ripples by an average of 22% and 10%, respectively; 2) the average switching frequency was remarkably reduced

Energies 2020, 13, 1907 13 of 15

The abovementioned results confirm the theoretical analysis presented in Section2 and reveal that the proposed FST provides the lowest steady-state ripples in torque and stator flux as those achieved by ZST while reducing the average switching frequency and enhancing the torque decreasing response and system stability during speed reversal.

5. Conclusions This article proposed a flexible ST with a structure, unlike the conventional STs, changes according to the system operating state to improve the overall performance of the DTC system of 2L-VSI PMSM while maintaining its ease of implementation. A simple yet effective strategy used to decide the voltage vectors arrangement in the FST which only requires information about the reference torque and the rotation direction. Compared to BST, MBST, and AST, the main features achieved by FST are summarized as follows: 1) reduction of torque and stator flux ripples by an average of 22% and 10%, respectively; 2) the average switching frequency was remarkably reduced by 31% on average. Although ZST provides steady-state performance similar to FST, the latter is more suitable for practical applications, as it allows speed reversal and gives better torque dynamic response. It should be noted that, although the analysis and experiments in this paper were based on the traditional ST-DTC, the proposed FST can also be extended and used in other switching-table-based DTC approaches, such as the duty ratio modulation methods, for further performance improvement.

Author Contributions: All the authors gave their contribution to all the aspects of this work. A.N. formulated the voltage selection strategy of the proposed FST and developed the analytical results; A.N. and C.G. (Chunyang Gu) arranged the experimental setup and performed the tests; A.N. wrote the paper; S.B. and C.G. (Chunyang Gu) reviewed and edited the paper and together with C.G. (Chris Gerada) supervised all the work. All authors have read and agreed to the published version of the manuscript. Acknowledgments: This research was supported by Zhejiang Natural Science Foundation under Grant LQ19E070002, Ningbo Science and Technology Bureau under Grant 2018A610146. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

Vsαβ,Isαβ Stator voltage (V) and current (A) vectors in stationary reference frame ψsαβ, ψrαβ Stator and rotor flux vectors in stationary reference frame (Wb) ψs, ψf Stator and rotor (permanent magnet) flux amplitude (Wb) θs, θr Electrical angular position of the stator and rotor flux vectors (degree) Te Electromagnetic torque (Nm) Rs,Ls Stator winding resistance (Ω) and inductance (H) Ts Sampling period (s) KT,Kψ Digital indicators of the torque and flux deviation directions δ Electrical load angle (degree) k Sampling index x (subscript) Sector index ref, 0 (superscript) Reference value and initial value err (superscript) Error value (superscript) Conjugate of a complex space vector ∗ Sa,Sb,Sc Switching states of the inverter legs div. Division ST Switching table DTC Direct torque control PMSM Permanent magnet synchronous motor CVC Current vector control MPC Model predictive control AVV Active voltage vector ZVV Zero voltage vector Energies 2020, 13, 1907 14 of 15

2L-VSI Two-level voltage source inverter BST Basic switching table in Reference [19] MBST Basic switching table with modified sector boundaries in Reference [20] AST Switching table with only active voltage vectors in Reference [18] ZST Switching table with zero voltage vector at one state in Reference [21] FST Flexible switching table (proposed) SiC Silicon carbide MOSFET Metal-oxide-semiconductor field-effect transistor DC RMS Root mean square

Appendix A

Table A1. PMSM and control parameters.

Machine Parameters Value Control Parameters Value

Stator resistance (Rs) 0.901 Ω DC bus voltage (Vdc) 220 V Inductance (Ls) 6.552 mH Sampling frequency (fs) 40 kHz Number of pole pairs (p) 4 Torque hysteresis band ( h ) 2% of T ± T ± rated PM flux linkage (ψ ) 0.09427 Wb Flux hysteresis band ( h ) 2% of ψ f ± ψ ± f Rated current (Is) 4.2 A (RMS) Rated shaft output power 0.75 kW Rated speed 3000 rpm Rated torque (Trated) 2.4 Nm Inertia coefficient (J) 1.2 kg m2 10 4 · · −

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