Direct Torque Control using Matrix Converters

Transcription

1 Chapter 5 Direct Torque Control uing Matrix Converter The Direct Torque Control (DTC) i a high-dynamic and high performance control technique for induction motor drive which ha been developed in the lat two decade [1]-[8] a poible alternative olution to DC ervo drive. In direct-torque-controlled adjutable peed drive the motor flux and the electromagnetic torque are the reference quantitie which are directly controlled by the applied inverter voltage vector. At any cycle period, accordingly to the poition of the motor flux pace vector and the output ignal of a flux and a torque hyterei comparator the mot opportune inverter witching tate i elected. The main advantage of the baic DTC cheme are: the implicity, a no coordinate traformation i required; the high dynamic; the robutne; the enorle operation; DTC ha alo ome diadvantage, a the difficulty to control the torque and the flux at very low peed, the higher current and torque ripple which imply higher machine loe and noie, the inherent variable witching frequency, the lack of direct current control. A general block diagram of DTC cheme i repreented in Fig. 1. Switching Configuration Selection * + T ϕ* + T ϕ i v Torque & flux calculation Fig.5.1 Baic DTC block diagram. 105

2 It i evident by the diode rectifier that the AC drive hown in Fig.5.1 doe not have bidirectional energy flow capability. Thi limit might be overcome by a traditional inverter backto-back arrangement but it might be alo olved in a more elegant and effective way by uing a matrix converter. The matrix converter would allow, in addition to a traight- forward bidirectional energy flow, inuoidal input current and the control capability of the input power factor, a conequence of it higher number of witching tate configuration compared to traditional voltage ource inverter (VSI). In thi chapter, after a hort introduction to the direct torque control cheme of induction machine, it i preented a control method for matrix converter which allow, under the contraint of unity input power factor, the generation of the voltage vector required to implement DTC [9]. The performance of the propoed control method are analyzed and dicued on the bai of realitic numerical imulation a well a experimental tet of the whole drive ytem [10]. The control method ha been implemented on a matrix converter adjutable peed drive prototype with the Intitute of Energy Technology at the Univerity of Aalborg, Denmark Direct Torque Control of induction machine The DTC technique wa firtly propoed by Takahahi [1] a a new quick-torque-repone and high efficiency control trategy for induction motor. Thi technique allow to independently control the motor flux, which can be the tator, the rotor or the magnetizing flux, and the electromagnetic torque, at the ame time. If the tator flux i aumed a reference, the etimated value of flux and torque can be calculated jut taking into account the tator current and voltage. Furthermore, the tator reitance i the only motor parameter needed [11]. Thi i a feature which ignificantly contribute to the DTC cheme robutne. The torque control i achieved by quickly changing the poition of the tator flux pace vector ϕ with repect to the rotor flux pace vector ϕ r. In fact, for a ymmetrical three-phae induction machine, the electromagnetic torque T em i proportional to the calar product of the tator flux vector ϕ and the rotor flux vector ϕ r, referred to a tationary tator reference frame. The following relation hold: T em [ ϕ j ϕ ] 3 = p A 2 r with M A = (5.1) 2 L L M where L S i the tator elf-inductance coefficient, L R i the rotor elf-inductance coefficient in a tator reference frame, M i the mutual inductance coefficient and p the number of pole pair. S R 106

3 Now, it can be demontrated that the tator and rotor flux vector the following expreion ϕ and ϕ r are related by M ϕ & r B + ϕr ( 1 j B ωm ) = ϕ L with S 2 M 1 B = LR L (5.2) S RR where ϕ & r i the time derivative of the rotor flux pace vector, R R i the rotor reitance in the tator frame and ω m i the mechanical angular velocity of the rotor. Equation (5.2) how that there i a low-pa filter relation between ϕ and ϕ r.thi mean that the rotor flux vector follow the tator flux vector variation with a finite time delay. The DTC capability to have rapid intantaneou torque variation i baed right on thi time delay. The control quantitie through which the DTC track the reference flux and torque are the radial ϕr and the tangential ϕt component of the tator flux variation ϕ impreed by the inverter voltage vector applied to the motor. The expreion of the tator flux vector variation ϕ in term of it radial and tangential component i given by ϕ = ϕ + ϕ = ϕ rˆ + ϕ tˆ (5.3) r t r t A it can be ened by Fig.5.2, the radial component control the tator flux vector amplitude while the tangential component control the tator flux vector angular poition and hence the torque. q-axi tˆ ϕ rˆ j ϕ r γ ϕ ϕ t ϕ r ϕ r d-axi Fig.5.2 Repreentation of the torque generation operating principle. The tator flux vector variation ϕ i reolved in it radial ϕ r and tangential ϕt vector component. In Fig.5.3 the chematic circuit of a voltage ource inverter i repreented along with the voltage vector corriponding to the eight different witching configuration that it can aume. Two of them determine zero voltage vector, v0 and v 7, while the remaining generate ix equally 107

4 paced voltage vector having the ame magnitudo. Equation (5.4) give the general expreion for a VSI voltage vector, where U DC i the DC link voltage. In Fig.5.3 it i alo hown how the d-q tator reference frame i divided in ector. v 2 π j(k 1) k DC e 3 k = = U 3 1, 2,.., 6 (5.4) Now, for the induction motor tator winding the following equation in term of pace vector can be written with reference to a tator frame: v dϕ = R i + (5.5) dt where v and i are the tator voltage and current pace vector repectively. If it i aumed, for implicity, to neglect the voltage drop on the tator reitance R and to conider a hort finite time t, repreenting the control cycle period, equation (5.5) reduce to the following equation ϕ = t (5.6) v Some remark can be made with regard to equation (5.6). + INVERTER SA SB SC UDC Induction Motor SA SB SC - (011) = V 4 (010) = V 3 2 V 0 = V V 2 = (110) ϕ (011) = V 5 V 6 = (101) V 1 = (100) ϕ S k = 1 IGBT ON S k = 0 IGBT OFF with k = A, B, C V 7 = (111) V 0 = (000) Fig.5.3 Schematic circuit of a voltage ource inverter and relevant witching configuration voltage vector 108

5 Firt, it how that the applied inverter voltage vector, v = v, directly impree the tator flux pace vector. Thi mean that the required tator flux vector locu will be obtained by uing the opportune inverter output voltage vector and hence inverter configuration. Second, equation (5.6) how that the tator flux pace vector move by the dicrete amount ϕ in the direction of the voltage vector applied by the inverter. The amplitude of the variation depend on the DC link voltage, by way of equation (5.4). For a given DC link voltage level, etting the control cycle period defined. k t the minimum tator flux vector variation Subtituting equation (5.6) in equation (5.3) the following i obtained ϕ rˆ + ϕ tˆ = v t = ( v rˆ + v tˆ ) t (5.7) r t r t ϕ i Equation (5.7) explicitly tate that the decoupled control of the tator flux and the electromagnetic torque can be carried out by way of the election of the opportune inverter voltage vector, and hence witching configuration. It i worth noting that due to the fixed direction of the inverter voltage vector and to the rotating motion of the tator flux vector ϕ in the d-q tator frame, for each inverter voltage vector the amplitude of it radial and tangential component will be variable within a ector. At each cycle period, hereinafter indicated by t C, the election of the proper inverter voltage vector i made in order to maintain the etimated torque and tator flux within the limit of two hyterei band. More preciely, the vector choice i made on the bai of the poition of the tator flux vector and the intantaneou error in torque and tator flux magnitude. A an example, conidering the tator flux vector laying in ector 1, a hown in Fig.5.3, the voltage vector V 2 and V 6 can be elected in order to increae the flux while V 3 and V 5 can be applied to decreae the flux. Among thee, V 2 and V 3 determine a torque increae, while V 5 and V 6 a torque decreae. The zero voltage vector are elected when the output of the torque comparator i zero, irrepective to the tator flux condition. Uing the baic witching table given in Table I it i poible to implement DTC cheme having good performance. Table I Baic DTC inverter configuration election table. Sector of C ϕ = -1 C ϕ = 1 ϕ C T =-1 C T = 0 C T = 1 C T =-1 C T = 0 C T = 1 1 V 2 V 7 V 6 V 3 V 0 V 5 2 V 3 V 0 V 1 V 4 V 7 V 6 V 4 V 7 V 2 V 5 V 0 V 1 4 V 5 V 0 V 3 V 6 V 7 V 2 V 6 V 7 V 4 V 1 V 0 V 3 6 V 1 V 0 V 5 V 2 V 7 V 4 109

6 It hould be noted that Table I i not the only poible DTC witching table. In general, modified witching table have been propoed in literature with the intention to improve the performance of the DTC cheme at very low and very high rotor peed [3], [7] Matrix Converter pace vector repreentation The propoed control method relie on a pace vector repreentation of the matrix converter witching configuration. A for the SVM modulation trategie preented in chapter 4, thi control method make ue of the active and zero configuration only, which are quoted in Table II. It ha to be highlighted that with repect to Table I of chapter 4, in Table II the output line-to-neutral voltage pace vector e o i conidered. Table II Switching configuration of the matrix converter ued in the propoed DTC control cheme. Switching Configuration A B C v AB v BC v CA i a i b i c e o a o i i b i +1 a b b v ab 0 -v ab i A -i A 0 2/3 v ab 0 2/ 3 i A -π/6-1 b a a -v ab 0 v ab -i A i A 0-2/3 v ab 0-2/ 3 i A -π/6 +2 b c c v bc 0 -v bc 0 i A -i A 2/3 v bc 0 2/ 3 i A π/2-2 c b b -v bc 0 v bc 0 -i A i A -2/3 v bc 0-2/ 3 i A π/2 +3 c a a v ca 0 -v ca -i A 0 i A 2/3 v ca 0 2/ 3 i A 7π/6-3 a c c -v ca 0 v ca i A 0 -i A -2/3 v ca 0-2/ 3 i A 7π/6 +4 b a b -v ab v ab 0 i B -i B 0 2/3 v ab 2π/3 2/ 3 i B -π/6-4 a b a v ab -v ab 0 -i B i B 0-2/3 v ab 2π/3-2/ 3 i B -π/6 +5 c b c -v bc v bc 0 0 i B -i B 2/3 v bc 2π/3 2/ 3 i B π/2-5 b c b v bc -v bc 0 0 -i B i B -2/3 v bc 2π/3-2/ 3 i B π/2 +6 a c a -v ca v ca 0 -i B 0 i B 2/3 v ca 2π/3 2/ 3 i B 7π/6-6 c a c v ca -v ca 0 i B 0 -i B -2/3 v ca 2π/3-2/ 3 i B 7π/6 +7 b b a 0 -v ab v ab i C -i C 0 2/3 v ab 4π/3 2/ 3 i C -π/6-7 a a b 0 v ab -v ab -i C i C 0-2/3 v ab 4π/3-2/ 3 i C -π/6 +8 c c b 0 -v bc v bc 0 i C -i C 2/3 v bc 4π/3 2/ 3 i C π/2-8 b b c 0 v bc -v bc 0 -i C i C -2/3 v bc 4π/3-2/ 3 i C π/2 +9 a a c 0 -v ca v ca -i C 0 i C 2/3 v ca 4π/3 2/ 3 i C 7π/6-9 c c a 0 v ca -v ca i C 0 -i C -2/3 v ca 4π/3-2/ 3 i C 7π/6 0 a a a a b b b b c c c c

7 For the output line-to-neutral voltage vector vector i i the following expreion hold. e o and the matrix converter input current e i i o = = j2π / 3 j4π / 3 j α ( t ) ( e + e e + e e ) = e ( t ) e o oa ob j2π / 3 j4π / 3 j β ( t ) ( i + i e + i e ) = i ( t ) e i ia ib ic oc i o (5.8) (5.9) In Fig.5.4 and 5.5 the output line-to-neutral voltage and the input current vector for the active configuration are repectively hown. ± 4, ± 5, ± 6 2 ± 2, ± 5, ± 8 e o ❷ i i 4 ± 7, ± 8, ± 9 6 α o ± 1, ± 2, ± 3 Sector 1 ❹ ❺ ❻ ± 3, ± 6, ± 9 ± 1, ± 4, ± 7 β i Sector ❶ Fig.5.4 Output voltage vector for active configuration and reference output voltage vector. Fig.5.5 Input current vector for active configuration and reference input current vector. 5.3 The ue of matrix converter in DTC In the ame way a for matrix converter pace vector modulated control method, the reference control quantitie are the output voltage vector and the input current vector phae diplacement with repect to the input line-to-neutral voltage vector. But the choice of the witching configuration to apply i made on a totally different bai. The control of the output voltage i baed on the claical DTC cheme decribed in ection 5.1. A a conequence, at each cycle period the optimum vector, among the eight generated by a VSI, i elected in witching Table I accordingly to the poition of the tator flux vector and the output ignal C ϕ and C T of the tator flux and torque hyterei comparator. In Fig.5.6 and 5.7 the two-level tator flux and the three-level electromagnetic torque hyterei comparator are repectively hown. Once the claical DTC control cheme ha elected the optimum vector to be applied to the machine, it i a matter of determining the correpondent matrix converter witching configuration. If it i aume, for example, that the VSI output vector V 1 ha been choen, 111

8 C ϕ C T B ϕ 0 B ϕ ϕ B T 0 B T T ϕ = ˆϕ * ϕ T = T ~ T * Fig.5.6 Two-level tator flux hyterei comparator. Fig.5.7 Three-level torque hyterei comparator. looking at Table II and Fig.5.3 and 5.4, it can be een that matrix converter can generate the ame vector by mean of the witching configuration ±1, ±2, ±3. But not all of them can be uefully employed to provide vector V 1. In fact, at any intant, the magnitude and the direction of their correponding output voltage vector depend on the poition of the input line-to-neutral voltage vector e i. Among the 6 vector, thoe having the ame direction of V 1 and the maximum magnitude are conidered. If it i aume, for example, that vector e i i in ector 1, the witching configuration to be ued are +1 and 3. In fact, looking at Fig.5.8 and Table II it can be een that within ector 1 thee two witching configuration are thoe which complie with the above mentioned election criteria. v cb v ab v ac v bc Time Fig.5.8 Repreentation of the input line-to-line voltage in the time domain for ector 1 of the input line-to-neutral voltage vector It ha been verified that, whatever i the ector which the vector e i i in, the matrix converter make alway available two witching configuration for each VSI output vector choen by the claical DTC cheme. 112

9 Such redundancy give the opportunity to control a further variable in addition to the tator flux and the electromagnetic torque. In the propoed control method the average value of the ine of the diplacement angle ψ i between the input current vector and the correponding input line-to-neutral voltage vector ha been choen a third variable. Thi variable will be indicated by in ψ. i If the contraint to comply with i an unity input power factor, uch aim can be achieved keeping the value of in ψ i to zero. The variable in ψ i i directly controlled by the hyterei comparator hown in Fig.5.9. The average value of in ψ i i obtained applying a lowpa filter to it intantaneou etimated value. C ϕ B ψ 0 B ψ i in ψ ψ = in ψ in ψ i Fig.5.9 Hyterei comparator of the in ψ value. i i * i The control of the input power factor i poible becaue the input current vector for witching configuration +1 and 3 have different direction, a it can be een from Table II and hown in Fig ❹ i i e i ❶ ❺ ❻ +1 Fig.5.10 Repreentation of an unity control of the input power factor. Keep going with the previou example, it i aumed by Fig.5.10 that the reference input diplacement angle i et to zero. A a conequence the reference value of in ψ i alo et to zero, in ψ = 0. i * i Now, if the etimated value of in ψ i poitive, C Ψ = +1, which mean that the input i current vector i i i lagging the voltage vector e i, then the configuration 3 ha to be applied. 113

10 On the contrary, if the etimated value of in ψ i negative, C Ψ = -1, which mean that i the input current vector i i i leading the voltage vector applied. The witching table baed on thee principle i hown in Table III. Table III Matrix Converter Switching Table for DTC control. e i, the configuration +1 ha to be in ψ i Hyterei comparator Voltage Vector elected by the baic DTC ❶ ❷ ❹ ❺ ❻ C ψ V V V V V V Input Current Vector ector number The firt column on the left hand ide contain the voltage vector elected by the baic DTC cheme in order to keep the tator flux and torque within the limit of the correponding hyterei band. The other ix bold column, are related to the ector of the matrix converter input current vector i i. Depending on the output value of the C ψ hyterei comparator, the left or the right column ha to be ued in electing the witching configuration of the matrix converter. When a zero voltage vector i required from Table I, the zero configuration of the matrix converter which minimize the number of commutation i elected. The output of the hyterei regulator C ψ, together with the ector number of the input current vector and the voltage vector required by the DTC, are the input to the matrix converter witching configuration election algorithm repreented by Table III. It i worth noting that in [19] the ector were related the input line-to-neutral voltage vector e i. The matrix converter witching configuration elected on the bai of the e i or i i vector ector are identical only in the cae of unity input power factor. In the cae of an input power factor different from unity, for a proper control of the matrix converter input current, the witching configuration election ha to be referred to the ector of the i i vector. But likewie to the pace vector modulated matrix converter, if the input power factor i controlled to be le than unity, a reduction in the voltage tranfer ratio i the reult, which in the DTC application turn into a reduction of the dynamic performance of the drive. In Fig.5.11 it i hown the block diagram of the propoed DTC control cheme for the matrix converter. 114

11 * T ϕ * < ψ > i in( ) T + + ϕ c T c ψ c ϕ Switching Config. Selection Switching ϕ 3 2 State i o { e i e i { Matrix Converter T ϕ < in ψ > i Torque & Flux e o Etimator Switching State < in ψ i > Etimator i i i o i o i o e i Induction Motor Fig.5.11 Block diagram of the propoed DTC cheme for matrix converter. With reference to Fig.5.11, in the lower part of the diagram the etimator of the electromagnetic torque, the tator flux and the average value of in ψ i are repreented. It i evident that thee etimator require the knowledge of input and output voltage and current. However, only the input voltage and the output current are meaured in each cycle period, becaue the other quantitie can be calculated on the bai of the actual witching configuration of the matrix converter which i known. 5.4 Numerical imulation and experimental tet of a Matrix-DTC drive ytem In order to verify the feaibility of thi drive ytem and it performance, a numerical analyi ha been firtly carried out uing the mathematical model of a implified matrix converter drive ytem, whoe chematic circuit i hown in Fig The reult obtained by the analyi [9], demontrated the feaibility of the DTC control cheme a well a it good performance. In Fig ome reult are hown. The imulation were carried out auming a cycle period of 40 µ and ideal witching device. Phenomena like the influence of dicretization and the delay caued by the ampling of ignal were alo taken into account. The tet machine wa a tandard 4 kw, 4-pole, 220 V, 50 Hz cage induction motor having the following parameter: R S = 0,51 Ω R R =0,42 Ω L S =58.2 mh L R =58.2 mh M=56 mh 115

12 Induction Motor Fig.5.12 Schematic circuit of the implified matrix converter DTC drive. Fig.5.13 Stator current at 1000 rpm, 25 Nm. (reprinted from [9], Fig.9, pp.747) Fig.5.14 Stator flux magnitude at 1000 rpm, 25 Nm. (reprinted from [9], Fig.10, pp.747) Fig.5.15 Input line-to-neutral voltage and filtered input current at 1000 rpm, 25 Nm. (reprinted from [9], Fig.12, pp.747) Fig.5.16 Electromagnetic torque at 1000 rpm, 25 Nm. (reprinted from [9], Fig.11, pp.747) Afterward the control cheme ha been implemented on the 7 kva matrix converter prototype. The experimental reult howed that the input filter and the AC main upply impedance could not be neglected in order to get realitic reult for the input line current. For thi reaon, the mathematical model of Fig.5.12 ha been modified in order to match the more realitic chematic circuit hown in Fig The numerical reult hown hereinafter have been obtained uing thi new implemented mathematical model. 116

13 Furthermore, with a comparion of the numerical and experimental reult in view, the imulation parameter have been et equal to the experimental one. Then, a cycle period of 83 R F E S L m R m L F I.M. C F Fig.5.17 Schematic circuit of the matrix converter DTC drive. µ, correponding to a witching frequency of 12 khz, ha been et. The tet machine data are quoted in Table IV. Table IV. Induction motor nameplate data and rated parameter value. Power = 1.1 kw Voltage = 380 V Current = 2.7 A Pole-pair = 2 coϕ = 0.79 R S =10.21 Ω R R =5.98 Ω L S =0.623 H L R =0.623 H M=0.603 H For the tator flux magnitude a reference value ϕ Sref of 0.97 Wb and an hyterei band equal to ±0.5% of the reference value ha been conidered. For the electromagnetic torque a reference value T ref of 7.5 Nm with a hyterei band of ±10% ha been ettled. The rotation peed of the motor wa 500 rpm. A far a the other ytem parameter i concerned their value are quoted in Table V with reference to the label hown in Fig Table V. AC main and input filter parameter value. E Smax L m R m R F L F C F 310 V 200 µh 0.5 Ω 37 Ω - 7 W 1.2 mh 14.8 µf In Fig ome numerical reult are hown. In Fig.5.18 the tator current i hown. A it can be een the current waveform i inuoidal with a high frequency ripple. The performance in term of tator flux and electromagnetic torque are good even though not a good a in Fig.5.14 and Thi i due to the doubled control cycle period, which alo double the delay caued by the ampling of the ignal. 117

14 Looking at Fig.5.22 it can be verified that the control operate in order to keep the matrix converter input current in phae with the correpondent line-to-neutral voltage. Thi demontrate the validity of the propoed control method in achieving unity input power factor. In Fig.5.23 the etimated value of the average value of in ψ i i hown. A Wb Time [] Fig.5.18 Stator current Fig.5.19 Stator flux magnitude. V 320 A 10 Nm Time [] Time [] Fig.5.20 Input line-to-neutral voltage and relevant line current. Fig.5.21 Electromagnetic torque V A Time [] Time [] Fig.5.22 Input line-to-neutral voltage and Fig.5.23 Etimated in ψ i. relevant input current. Lat but not leat, in Fig.5.20 the input line current and the relevant input line-to-neutral voltage are hown. It can be clearly een that the input line current ha a ignificant harmonic ditortion and i leading the voltage. The leading phae diplacement i due to the input filter capacitance which i overized with repect to the induction motor rated power for getting an unity power factor on the AC main. Some comment about the capacitance overizing and the line current harmonic ditortion will be given in ection

15 5.5 Implementation of the DTC cheme and laboratory etup of the drive ytem The propoed control trategy ha been implemented on a 7 kva matrix converter prototype feeding a tandard three phae 1.1 kw, 4-pole, 380 V tar connected, 50 Hz cage induction motor. A block diagram of the ytem i hown in Fig AC Power Source Univeral Power Analyzer Input Filter Input voltage Matrix Converter Commutation control Gate Drive Circuit Microcontroller board Dual Port RAM RS-232 Output current Control Sytem Induction Motor PC DSP Ez-Lab Fig.5.24 Block diagram of the laboratory Matrix-DTC drive ytem. The ytem etup i baically the one that ha been ued for the SVM modulation trategie tet and that ha been already decribed in ection For thi reaon, in thi ection only detail on different ytem etting with repect to that decription will be given. The AC Power Source have been ued to generate a balanced and inuoidal three phae upply voltage ytem with a 310 V peak value for the line-to-neutral voltage. The line impedance wa et to 0.5 Ω phae reitance and 200 µh phae inductance. The capacitance of the LC filter have been increaed depite of the lower rated load power and et to 14,8 µf. Thi wa done to reduce the input filter cut-off frequency. In addition, in order to damp ocillation, a 37Ω-7W reitor wa applied in parallel to the filter inductance. With regard to the control ytem, it i worth noting that everal modification have been brought to the micro-controller program. With repect to the SVM control, the timing of the cycle period wa modified. Moreover, the program wa modified in order to apply to the motor jut one matrix witching configuration per cycle period. The value of the reference control quantitie were thoe quoted in the previou ection for the numerical imulation: reference tator flux amplitude and electromagnetic torque equal to 0.97 Wb and 7.5 Nm repectively. The hyterei band wa ± 0.5% for the tator flux and ± 10% for the torque. Zero wa the value for the reference i * in ψ a well a for it hyterei band. The ampling frequency wa 12 khz ( 83 µ cycle period). The motor wa operated at 500 rpm approximately. 119

16 Fig.5.25 Stator current 2.5 A/div, 20 m/div, Fig.5.26 Input line-to-neutral voltage and line curand relevant harmonic pectrum. rent, 160V/div, 5A/div, 4m/div, with harmonic 20 db/div, 625 Hz/div. T ref =7.5 Nm. pectrum 20 db/div, 625 Hz/div. T ref =7.5 Nm. Fig.5.27 Input line-to-neutral voltage and input current, 160V/div, 5A/div, 4m/div, with harmonic pectrum 20dB/div, 625Hz/div. T ref =15Nm. Fig.5.28 Input line-to-neutral voltage and line current, 160V/div, 5A/div, 4m/div, with harmo nic pectrum 20dB/div, 625Hz/div. T ref =15Nm. In Fig.5.25 the meaured tator current i hown. It waveform i inuoidal with a high frequency ripple, in accord with the numerical reult hown in Fig With regard to the input line current performance the imulation reult hold in the practical cae too, a hown by Fig In Fig.5.27 and 5.28 the matrix converter input current and the line current for a doubled reference torque value are repectively hown. Fig.5.27 how that the input current i in phae with the correponding line-to-neutral voltage, confirming that the propoed control can accomplih unity input power factor for the matrix converter. The meaurement of the matrix converter input current for Fig.5.27 wa carried out following the procedure afore-decribed in ection The phae diplacement of the line current in Fig.5.28 i reduced by the doubled power delivered to the load, but it i evident that the harmonic ditortion i increaed. In Fig.5.29 and 5.30 the tator flux magnitude and electromagnetic torque etimated by the DSP, run-time, are hown. In Table VI and VII meaurement data collected for T ref =7.5Nm 120

17 by the power analyzer are quoted. 1.2 [Wb] 1 10 [Nm] Time [m] Time [m] Fig.5.29 Stator flux magnitude etimated run-time by the DSP. Table VI Meaured data for no-load condition. Phae a Phae b Phae c V rm I rm Watt Var coϕ I ithd Fig.5.30 Electromagnetic torque etimated run-time by the DSP. Table VII Meaured data for T ref = 7.5 Nm. Phae a Phae b Phae c V rm I rm Watt Var coϕ I ithd Comparing the experimental reult to the numerical one it can be tated that there i a good accordance. Thi prove the validity of the implemented numerical model, which can be ued for further analyi. 5.6 Input line current analyi A it ha been hown by the previou figure and by the Table VII the input line current i ignificantly ditorted. The wide ocillation of the input line current are due to a reonance phenomenon which occur between the AC main line impedance and the impedance of the input current filter. In Fig the complex harmonic pectrum of the input line current vector i relevant to the cae of Fig.5.20 and 5.26 i hown. For diplaying purpoe, the cale of the y axi ha been truncated to 1A. It can be een that the current harmonic component with higher amplitude are centered around the reonance frequency of the inductive-capacitive impedance of the AC maininput filter ytem, which i approximately 1.1 khz. 121

18 The reaon of thi reonance phenomenon are related to the control cycle period, to the DTC technique and to the matrix converter witching configuration election table, Table III, ued by the porpoed control cheme. The matrix converter cycle period ued in the imulation and in the experimental tet wa 83 µec. Thi value i higher than the cycle period value commonly ued in DTC drive. Fig.5.32 clearly how the benefit, in term of input current ditortion, of a reduced control cycle period. [A] [A] [Hz] Fig.5.31 Harmonic pectrum of the input line current vector. T ref =7.5Nm. t C = 83 µ. [Hz] Fig.5.32 Harmonic pectrum of the input line current vector. T ref =7.5Nm. t C = 40 µ. With regard to the DTC technique, a problem arie from it inherent variable witching frequency, due to the tator flux and the torque hyterei regulator [6]-[8], [12], [13]. A a conequence, input current and output voltage have frequency pectra which how harmonic component even at frequencie below the ampling frequency. Thi make more difficult the deign and the optimization of the input current filter. A far a the matrix configuration election algorithm i concerned it i needed to refer to Table III and Table I. Hereinafter it i rewritten the mot left hand ide column of Table III and the input/output feature of the relevant configuration. ❶ C ψ +1 V 1-3 V 2 9 V 3-6 V 4 3 V 5-9 V 6 6 Table VIII. S.C. A B C v AB v BC v CA i a i b i c e o a o i i b i c a a a c c a c a c a c a a c c c a v ca 0 -v ca -v ca 0 v ca -v ca v ca 0 v ca -v ca 0 0 -v ca v ca 0 v ca -v ca -i A 0 i A i A 0 -i A -i B 0 i B i B 0 -i B -i C 0 i C i C 0 -i C 2/3 v ca 0-2/3 v ca 0 2/3 v ca 2π/3-2/3 v ca 2π/3 2/3 v ca 4π/3-2/3 v ca 4π/3 2/ 3 i A 7π/6-2/ 3 i A 7π/6 2/ 3 i B 7π/6-2/ 3 i B 7π/6 2/ 3 i C 7π/6-2/ 3 i C 7π/6 122

19 Table IX. ❶ C ψ -1 V 1 1 V 2-7 V 3 4 V 4-1 V 5 7 V 6-4 S.C. A B C v AB v BC v CA i a i b i c e o a o i i b i a b b b a a b a b a b a b b a a a b v ab 0 -v ab -v ab 0 v ab -v ab v ab 0 v ab -v ab 0 0 -v ab v ab 0 v ab -v ab i A -i A 0 -i A i A 0 i B -i B 0 -i B i B 0 i C -i C 0 -i C i C 0 2/3 v ca 0-2/3 v ca 0 2/3 v ca 2π/3-2/3 v ca 2π/3 2/3 v ca 4π/3-2/3 v ca 4π/3 2/ 3 i A 7π/6-2/ 3 i A 7π/6 2/ 3 i B 7π/6-2/ 3 i B 7π/6 2/ 3 i C 7π/6-2/ 3 i C 7π/6 Before to proceed it i important to remind that only a witching configuration per cycle period i applied to the matrix converter and uch configuration change only when the output ignal of one of the three hyterei comparator change or the input current vector change it ector. Bearing in mind thee remark Table VIII i conidered. Table VIII how that when vector i i i in ector ❶ and the hyterei comparator C ψ i equal to +1, all the witching configuration quoted in the relevant column keep to zero the ame matrix converter input current, which in the cae i i b. In the ame way, all the witching configuration quoted in the column of C ψ equal to 1, Table IX, keep to zero the input current i c. The ame happen for the other ector of i i. What doe thi imply? Thi mean that for a given ector of i i, whoe value doe not vary for 1/6 of the fundamental period, and a given value of the hyterei regulator C ψ, whoe rate of change depend on the time contant of the in ψ i low pa filter, whatever vector i required by the DTC control, the correpondent matrix converter configuration keep to zero the ame converter input current. The effect i a further reduction of the input current witching frequency which lead to the appearance of ignificant current harmonic component even around the reonance frequency of the input filter-ac main impedance ytem. How thi harmonic ditortion might be reduced? Looking at Table VIII and IX, it can be noted that the matrix witching configuration which, for ector ❶ of i i, are lited in different column of C ψ, keep to zero different converter input phae current. It can be verified by Table I and III that thi rule hold for any ector of the i i vector. It i then of interet to give a glance to the in ψ i control variable by whom the ignal C ψ depend on. In the numerical imulation a well a in the prototype DSP implemented control program, a firt order digital filter truncated at the econd order wa ued in order to obtained in ψ. Thi digital filter i equivalent to a low pa filter whoe cut off frequency depend on i the filter time contant. Higher the time contant lower the cut off frequency. In other word, 123

20 etting a high value for the digital filter time contant the reponivene of the filter to the intantaneou variation of in ψ i i reduced and conequently the ignal C ψ ha a minor rate of change. On the bai of thee conideration ome improvement might be expected decreaing the time contant of the digital filter in order to increae the rate of change of C ψ. In thi way, a more frequent witching between the two column of the current ector of i i will occur, yielding an increae of the converter input current witching frequency. The reult obtained by the experimental tet have met uch expectation. Decreaing the digital filter time contant a reduction of the input line current total harmonic ditortion (THD) wa obtained. Yet, the time contant can not be decreaed indefinitely, becaue below a certain value the filter doe no longer carry out the needed filtering action. 5.7 Modified control method for improving the input line current On the bai of the previou input line current analyi, a modified control method ha been implemented and verified by mean of numerical imulation. Thi control method allow to reduce the harmonic content of the input line current without any negative effect on the drive performance and it control implicity. The baic principle i to ue, within a cycle period, both the witching configuration that the matrix converter provide to the claical DTC cheme. Intead of chooing one of thee two configuration, accordingly to the hyterei comparator output ignal C ψ, both the configuration are applied but for different time interval, in uch a way that, in a cycle period, the average effect on the converter input current vector i that required by C ψ. The improvement obtained with thi olution i due to the fact that the two configuration keep to zero different converter input current along with an increae of the matrix converter witching frequency. The following example i given to explain the modified control method. The cycle period i till 83 µec. It i aumed that the DTC cheme repreented by Table II require the application of vector V 1, the vector i i i in ector ❶ and the input power factor hyterei comparator et C ψ = +1. The original control, accordingly to Table III, would apply the witching configuration -3 for the whole cycle period t C. The modified control will apply both the witching configuration 3 and +1, for a time period t -3 and t +1 repectively, where t t 3 = α I t C (5.10) = α with +1 II t C I II α > α (5.11) 124

21 and α I and α II are contant whoe optimum value have been determined by a trial and error method. In thi way, within a cycle period, the average effect on the converter input current vector diplacement angle i that required by C ψ. In Fig.5.33 the harmonic pectrum of the input line current vector for the modified control trategy i hown. The operating condition are the ame of Fig It can be een that the modified control trategy allow a reduction of the higher amplitude harmonic component. With regard to the tator flux and the electromagnetic torque, the modified control method preerve the good performance of the original one, a it can be een from Fig.5.34 and From an implementation point of view, the modified control method need only few additional calculation. [A] [Hz] Fig.5.33 Harmonic pectrum of the input line current Modified control trategy. Time [] Fig.5.34 Stator current. Modified control trategy. [Wb] [Nm] Fig.5.35 Stator flux magnitude. Modified control trategy. Time [] Time [] Fig.5.36 Electromagnetic torque. Modified control trategy. 5.8 Concluion In thi chapter a control method baed on claical direct torque control technique ha been preented for a matrix converter induction motor drive. 125

22 The control method i baed on witching table which allow the direct control of the matrix converter accordingly to the motor and input power factor requirement. By mean of thi new control method the advantage of matrix converter over traditional VSI-PWM converter, uch a unity power factor control, inherent bi-directional power flow and inuoidal input current capability, have been combined with the control implicity and robutne of the DTC technique. At any cycle period, the opportune matrix converter witching configuration to apply i elected entering the witching table by the output of three hyterei controller applied to the error of tator flux, electromagnetic torque and input power factor, repectively. The performance of the control cheme have been analyzed both by numerical imulation and experimental tet. The analyi ha hown that the propoed control cheme can provide good performance for the induction motor and unity input power factor but the input line current can be ignificantly ditorted if the ampling frequency i not ufficiently high. In fact, due to the inherent variable witching frequency of the DTC cheme and to the feature of control witching table, the input current can have harmonic component at frequency much below the ampling frequency which can excite reonance phenomena of the AC main impedance and input current LC filter. On the bai of the analyi carried out a modified control cheme which improve the input line current quality without negatively affecting the drive performance ha been preented and verified by numerical imulation. Reference [1] I.Takahahi, T. Noguchi, A new quick-repone and high-efficiency control of an induction motor, IEEE Tranaction on Indutry Application, Vol. IA-22,N. 5, Sept./Oct. 1986, pp [2] M. Depenbrok, Direct Self-Control (DSC) of Inverter-Fed Induction Machine, IEEE Tranaction on Power Electronic, Vol. PE-3,N. 4, Oct. 1988, pp [3] I.Takahahi, T. Noguchi, Ultra-Wide peed control with a quick torque repone AC ervo by a DSP, Proceeding EPE 91, Firenze, Italy, Vol. 3, pp [4] I. Boldea and S.A. Naar, Torque Vector Control (TVC) - A Cla of Fat and Robut Torque Speed and Poition Digital Controller for Electric Drive, Proceeding of EMPS, vol. 15, 1988, pp [5] J.N. Nah, Direct Torque Control, Induction Motor Vector Control Without an Encoder, IEEE Tranaction on Indutry Application, Vol. 33, N. 2, March/April 1997, pp

23 [6] D. Caadei, G. Grandi, G. Serra, A. Tani Effect of flux and torque hyterei band amplitude in direct torque control of induction machine, Proceeding of IECON 94, 5-9 September 1994, Bologna, Italy, pp [7] D. Caadei, G. Grandi, G. Serra, A. Tani Switching trategie in direct torque control of induction machine, Proceeding of ICEM 94, Pari, France, 5-8 September 1994,pp [8] Ch. Lochot, X. Roboam, P. Mauion, A new direct torque control trategy for an induction motor with contant witching frequency operation, Proceeding of EPE 95, Sevilla, Spain, pp [9] D. Caadei, G. Grandi, G. Serra, A. Tani The ue of matrix converter in direct torque control of induction machine, Proceeding of IECON 98, Aachen, Germany, Augut 31- September 4, 1998, pp [10] F. Blaabjerg, D. Caadei, M. Matteini, G. Serra, A. Tani, Direct Torque Control uing Matrix Converter: Improvement of the Input Line Current Quality, Proceeding of EPE 2001, Graz, Autria, Augut, 2001, CD-ROM, pp. 1-10, [11] H. Bauch, R. Blumel, W. Zeng, Flux- Etimation of a PWM-Inverter-Fed Torque- Controlled Induction Machine baed on Terminal Quantitie, Proceeding of ICEM 92, Mancheter (UK), September ,pp [12] D. Caadei, G. Serra, A. Tani, Performance Analyi of a DTC control cheme for Induction Motor in the low peed range, Proceeding of EPE 97, Trondheim, Norway, 8-10 September 1997, Vol. 3, pp , [13] I. Ludtke, M. G. Jayne, A comparative tudy of high performance peed control trategie for voltage-ourced PWM inverter-fed induction motor drive, Proceeding of EMD 95, Durham, UK, September, 1995, pp ,